zoology - If I put a cup over a spider, and leave it there for a day, will the spider survive?

To answer the first part of your question: it is extremely unlikely that the spider will die or be weakened after just one day.

Wolf spiders (Lycosids) are all predators. Due to variations in prey populations, and low efficiency of consumption at higher trophic levels, they are subject to inconsistent and unpredictable food supply (Greenstone and Bennett, 1980). They are very well adapted to this lifestyle and consequently, long periods of starvation often yield no behavioural changes (Persons, 1999). It is highly unlikely that the spider will die after just one day: Anderson, (1974) observed no changes in activity after starving Lycosa lenta (a species of wolf spider) for 30 days; and Tanaka and Ito, (1982) observed Pardosa astrigera (another species of wolf spider) living for up to 54 days of starvation. Age and sex of the spider are more likely to affect its behaviour and performance than food or oxygen availability (Persons, 1999).

As for oxygen consumption, Greenstone and Bennett, (1980) measure an oxygen consumption of 100µL/hr for wolf spiders. Assuming that your cup is of the size of the unit of volume of the same name, the cup (~0.237L), a small calculation (see figure) shows that there will be enough oxygen for the spider to survive for over 98 days. The oxygen concentration within the cup may decrease as it is used by the spider, however this is likely to have a minimal effect as a cup placed on a surface is unlikely to be hermetically sealed.

In short, oxygen availability is unlikely to have an effect on the spider before other limitations (such as food) are reached. However neither of these effects are likely to cause behavioural changes during the first month.

References

• Anderson, J.F., 1974. Responses to Starvation in the Spiders Lycosa Lenta Hentz and Filistata Hibernalis (Hentz). Ecology, 55(3), pp.576-585.


• Greenstone, M.H. & Bennett, A.F., 1980. Foraging Strategy and Metabolic Rate in Spiders. Ecology, 61(5), pp.1255-1259.


• Persons, M.H., 1999. Hunger effects on foraging responses to perceptual cues in immature and adult wolf spiders (Lycosidae). Animal Behaviour, 57(1), pp.81-88.


• Tanaka, K. & Itô, Y., 1982. Decrease in respiratory rate in a wolf spider,Pardosa astrigera (L. Koch), under starvation. Researches on Population Ecology, 24(2), pp.360-374.

What is Curved DNA? - Biology

I'm hardly an authority on this topic, but I distinctly recall an amazing report the mid-1990s of the co-crystal structure the yeast TATA binding protein in complex with DNA. The structure shows that TBP bends the DNA axis by approximately 80 degrees, presumably in order to expose bases and improve recognition. The structure is available at RCSB: http://www.rcsb.org/pdb/explore.do?structureId=1ytb . (Make sure you check out the Jmol view.)

Thermodynamically speaking, bending DNA would require energy. Therefore, DNA that was pre-bent (e.g., due to auxiliary binding proteins or composition bias) would improve binding.

So, I suspect that in the context DNA binding proteins, "curved" refers to the static curvature of unbound DNA or to the bending of DNA upon binding in order to facilitate recognition.

Tidal lock of earth and moon

The Earth and the Moon do interact, but because they have different sizes and masses the effect on each is different.

The Moon rotates once in its orbit around the Earth, causing it to constantly show the same face. This was the Earth's effect on the Moon due to tidal dragging by gravity.

It's pretty stable, the Moon will continue to show the same face to the Earth even as the tidal forces cause it to orbit farther and farther away.

We actually see slightly more than 50% of the Moon. The Moon's orbit causes its aspect to nod because its orbit is slightly elliptical and shimmy because it's not orbiting directly over the equator. Over time we actually see almost 60 percent of the surface of the Moon (an effect called libration).

The Moon's effect on the Earth has been to slow its daily rotation to 24 hours. In the past, the Moon was much closer to the Earth, and the day was much shorter. As time passes and the Moon moves into a wider orbit, the length of the Earth's day will increase (see e.g. this Scientific american post).

I've read that the Moon would recede to a certain point, then begin approaching the Earth again, but unfortunately the Sun will swell into a red giant before then and swallow the Earth and the Moon.

distances - Where can I look up the 3D positions of the closest stars?

You can determine the 3D position for a star, $p$, by using the distance from Earth, $R$, as well as the right ascension, $Omega$, and declination, $delta$, within the following formula.

$p = R begin{bmatrix} cos Omega cos delta \ sin Omega cos delta \ sin delta \ end{bmatrix}$

Note this will yield positions within the Earth-centered inertial reference frame.

molecular biology - In C. elegans, why does knock-down of cco-1 in some tissues increase lifespan, and knock-down of cco-1 in other tissues decrease lifespan?

Let us first answer the question: what is the effect of cco-1 knock-down in C. elegans. Durieux J., Wolff S. and Dillin A. in their paper "The cell-non-autonomous nature of electron transport chain-mediated longevity". Cell 144:79-91 (2011) provide the following explanation:

The life span of C. elegans can be increased via reduced function of
the mitochondria; however, the extent to which mitochondrial
alteration in a single, distinct tissue may influence aging in the
whole organism remains unknown.

So, by slowing-down the mitochondria function you manage to slow-down the normal wear-and-tear of the mitochondrial enzymes, which are normally responsible for the so-called respiratory chain -- one of the fundamental biological process for storing energy in cells (despite the common belief, ATP is rarely to store energy, but mostly to transfer it to the target!).

If we group the tissues where the knock-down leads to similar effects we will get muscle cells opposed by neurons and intenstine cells.

This is just my suggestion, but if we approach those groups with the idea of energy storage and re-use in mind, we'll see that muscle cells have much higher turnover of energy (for contraction and even more for dilation), whereas nerve and intestine cells are not that dependent upon energy and have much lower baseline of energy consumption and turnover.

Now we can suggest that cco-1 knock-down decreases the functions of mitochondria in muscle cells below the acceptable level and the decreased life span is due to depletion of mitochondrial energy storage under light stress conditions which would have been easily coped with under normal conditions. And vice versa, nervous/intenstine cells requiring a constant energy source at a much lower level just help the animal to cope with stress more effectively even during old age, leading to increased life span.

observation - Is stacking welder's glasses a safe way to watch at the eclipse?

You can find in many place on the Internet that welder's glass #14 is good for looking at an eclipse. Tomorrow (March, 20th 2015 at 10:45 CET) there's a solar eclipse and yesterday I could only find glasses #11 and #9. I tried briefly this morning, and combining a #11 and a #9 was giving me a good view of the sun. Using 2 #11 gave a too dark image. Now, I read different opinions on the internet.

Against (Perkins Observatory):
http://perkins.owu.edu/solar_viewing_safety.htm

Be careful that you use the right kind of glass! Welder's glass is
numbered from 1 to 14 with 14 being the darkest. It is only number 14
glass that is dark enough for solar viewing! And NO STACKING! A pair
of number 7's or a 10 and a 4 together DO NOT have the same protection
as a single piece of number 14 (see unsafe methods for more details).

Favorable (Royal Astronomical Society of Canada):
https://www.rasc.ca/tov/safety

If SN14 filter is not available, it is possible to combine lower shade
numbers to get roughly the same level of eye protection from solar
radiation, e.g. combining SN 6 and SN 8 filters. However the image
quality may be considerably poorer than that seen through the single
SN14 filter

I could not find a table or something explaining which kind of protection gives each number; according to the Canadian website, the only concern is about how much infrared light goes through, ultraviolet does not seem to be a problem in almost any case (I was surprised to read that).

Note: It's not my intention to open here the discussion on what could be other safe methods to watch the eclipse, this is well explained everywhere around. I read too late about the eclipse to order specific glasses.

Edit:
One of the answers here report the following formula: (more insight at this link)

13 or darker is safe enough. Also, you CAN add up welding glass, using
the formula S(sum) = S1 + S2 -1. S(sum) should be greater than or
equal to 13

fundamental astronomy - Finding Mass of Star with only Luminosity

Sounds like homework (correct me if that assumption is wrong, as you may want a somewhat different answer then.), so here is a hint:

Clean up the equation first, to something that looks more like an equation for mass:

$$frac{L}{L_{sun}} = left(frac{M}{M_{sun}}right)^{3.5}$$

$$left(frac{L}{L_{sun}}right)^{frac{1}{3.5}} = frac{M}{M_{sun}}$$

botany - How will rising carbon dioxide levels in the troposphere affect photosynthetic producers?

There are several key ways in which rising atmospheric CO₂ concentrations will affect photosynthesis, and these are related to the different types of photosynthesis. In order to properly answer your question, I'll provide some background about photosynthesis itself.

Photosynthesis evolved in a high-CO₂ atmosphere, before the oxygen-enrichment of the atmosphere (which actually happened as a result of photosynthesis). Most plant species operate C3 photosynthesis. In these plants, carbon dioxide diffuses into the cell where it is fixed by Ribulose-1,5-bisphosphate carboxylase oxygenase (RuBisCO) into a 3-carbon molecule (hence C3), which is then polymerised to make sugars. A crucial fact about RuBisCO is that it has both carboxylase (carbon-fixing) activity and oxygenase (oxygen-fixing) activity. This means that oxygen and carbon dioxide compete for the active site on the enzyme complex, leading to RuBisCO being quite inefficient and slow at fixing carbon in higher oxygen concentrations. That didn't matter in the high-CO₂ atmosphere of the early Earth, but in todays atmosphere O₂ concentrations are high enough that they severely limit the productivity of C3 plants.

However, plants haven't just been growing slowly all that time - several mechanisms for increasing photosynthetic efficiency have evolved. The most influential systems involve concentrating carbon dioxide in a particular area, excluding oxygen, and concentrating RuBisCO in that same area. This avoids the oxygen competition for the active site and allows RuBisCO to operate more efficiently. The key adaptation here is C4 photosynthesis - the system which is present in most grasses and many of the most productive plants on Earth (e.g. maize, sugarcane, Miscanthus). It has evolved at least 62 times independently. It works by having RuBisCO concentrated within 'bundle sheath' cells which are surrounded by a layer of suberin wax. This layer prevents CO₂ escaping and O₂ from getting in. CO₂ from the atmosphere is then fixed in different cells - 'mesophyll cells' - by another enzyme - Phosphoenolpyruvate carboxylase (PEPC), resulting in a four-carbon molecule (hence C4). This 4-carbon acid, (malate or oxaloacetate depending on the system) is then shuttled into the bundle sheath cells. There, the CO₂ is released again by a variety of enzymes depending on the system, creating a high CO₂ concentration in the cell where RuBisCO can then work efficiently.

In general, C4 plants are much (about 50%) more efficient than their C3 counterparts, and they are particularly well adapted to high temperatures and moist environments. So, to answer your first question: as atmospheric CO2 levels continue to rise, C3 plants will gradually be able to photosynthesise more efficiently. Interestingly though, C4 plants are predicted to also benefit from increased atmospheric CO₂. If global temperatures rise as predicted, both C3 and C4 plants will be able to operate more efficiently than they currently do, up to a maximum temperature beyond which enzymes will begin to denature faster and efficiency will drop. One consideration is that the difference in efficiency between C3 and C4 systems will decrease, which may significantly alter the makeup of plant communities around the world.

This is a vast oversimplification, but it is accurate for the predicted overall effects. Localised effects (i.e. productivity changes in a particular region or for a particular crop) will depend on habitat, physiology, etc.

Some key papers to launch you into the literature:

• Leakey, A.D.B., Bernacchi, C.J., Dohleman, F.G., Ort, D.R. & Long, S.P. (2004) Will photosynthesis of maize (Zea mays) in the US Corn Belt increase in future [CO2] rich atmospheres? An analysis of diurnal courses of CO2 uptake under free‐air concentration enrichment (FACE). Global Change Biology. [Online] 10 (6), 951–962. Available from: doi:10.1111/j.1529-8817.2003.00767.x [Accessed: 31 January 2012].


• Morgan, J.A., LeCain, D.R., Pendall, E., Blumenthal, D.M., Kimball, B.A., Carrillo, Y., Williams, D.G., Heisler-White, J., Dijkstra, F.A. & West, M. (2011) C4 grasses prosper as carbon dioxide eliminates desiccation in warmed semi-arid grassland. Nature. [Online] 476 (7359), 202–205. Available from: doi:10.1038/nature10274 [Accessed: 31 January 2012].

Are cells really the basic unit of all life?

According to Gerry Joyce: "Life is a self-sustained chemical system capable of undergoing Darwinian evolution."

From a meta-analysis of 123 definitions of life: "Life is metabolizing material informational system with ability of self-reproduction with changes (evolution), which requires energy and suitable environment."

According to Alexander Oparin: “Any system capable of replication and mutation is alive”.

At hand are some key elements in order to match these criteria. Maintaining a Darwinian cycle requires replication, mutation, and selection. Thus, we can break down the above into 5 criteria (personal communication with Gerry Joyce).

• Life stores information


• Life reproduces its information


• Life alters that information


• Life does something with that information (uses energy)


• Life does all of this in a self-sustained manner

I would point out that the above criteria is quite different from what is currently on wikipedia described by metabolism and homeostasis. There are certainly additional criteria that certainly raise the threshold for what may be considered life. The common discussion revolves around viruses which do many of these things but not in a self-sustained way.

The question at hand then asks if cells are the minimum unit of life? What makes a cell a cell is that there is compartmentalization. The underlying reason behind this compartment is due to the necessity of tying the phenotype to the genotype. Paraphrasing using our definition of life, it links the information with the function that the information carries out. In the modern biological scheme, it keeps the proteins (phenotype) with the DNA (genotype).

The necessity of compartmentalization is negated when the phenotype is already linked with the genotype. The most frequent example is RNA where the material that carries the information is also the material that carries out its function. It tend, is reasonable to hypothesize that life can be made entirely with RNA without the need for compartmentalization (although compartmentalization certainly helps see Paegal and Joyce and Chen and Szostak).

Recent experiments by Gerry Joyce and others have been able to satisfy several of the requirements of life. The have self-replicating RNAs, that store information, that reproduce their information, that introduce alterations to their information, and do it in a self-sustained manner. What Gerry and his colleagues agree on is that their current self-replication Ribozyme system doesn't do anything particularly novel. However, by introducing a larger variety of functional elements to their ribozymes perhaps they will.

stellar evolution - If a star were to suddenly lose nearly all of its stored heat, would it be able to return to its normal state?

If you suddenly sucked all the heat out of a normal star like the Sun, nuclear reactions would cease, the gas pressure would fall to zero. The star would collapse, initially on a freefall timescale (about 1 hour for the Sun).

The released gravitational potential energy would half be radiated away and half would go into re-heating the interior. The temperature would rapidly rise, the collapse would be halted, nuclear reactions would restart, the star would slowly expand again and a thermal and hydrostatic equilibrium should be restored on a Kelvin-Helmholtz timescale (about 10 million years for the Sun).

One way to see this, is to compare the current thermal content of a star with its capacity for generating new heat by nuclear reactions. e.g. approximate the Sun as a uniform ball of ideal gas at an average temperature of a few million degrees. The thermal content is roughly $10^{41}$ J. The Sun generates this much energy in nuclear reactions in only 8 million years - coinciding with the timescale to reestablish an equilibrium. Or you could compare it with the gravitational potential energy of around $2times 10^{41}$ J. i.e. There is enough gravitational potential energy to reheat the Sun.

However, not everything would be a continuation. The collapse and reheating would be similar to the star repeating its pre main sequence phase. During this phase the star becomes fully convective and so the core material would get completely mixed with the rest of the star again. This would have the effect of rejuvenating the star as a new zero age main sequence star, but with a slightly higher helium abundance.

gravity - Is there any way a meteor can hit at less than escape velocity?

Edited.
No if you talk about the escape velocity form Earth. This follows simply from the fact that energy $E$ is conserved. An object that is not gravitationally bound to Earth has $E>0$ and hence $v>v_{mathrm{esc}}$ when hitting ground.

---

Yes, if you meant the escape velocity from the Solar system, because the Earth moves with $v_{rm Earth}=v_{rm escape}/sqrt{2}$ relative to (but not towards) the Sun. Here $v_{rm escape}=sqrt{2GM_{odot}/1{rm AU}}$ is the local escape speed from the Sun, while $v_{rm Earth}=sqrt{GM_{odot}/1{rm AU}}$ is the speed of the local circular orbit. An object at 1AU form the Sun and bound to the Sun cannot have speed greater than $v_{rm escape}$.

Now, the impact speed of an object that moves at $v_{rm escape}$ can be as low $v_{rm escape}-v_{rm Earth}=v_{rm escape}(1-1/sqrt{2})$ if it hits Earth "from behind", i.e. moving in the same direction as Earth at the time of impact.

Note also that meterors typically move not faster than $v_{rm escape}$, for they don't come from outer space, but from the Solar system.

solar system - Were there any images of a transitary event of Jupiter or Saturn as imaged by a deep probe mission

I'm quite certain that there isn't any actual images of a transitory event of Jupiter or Saturn across the solar disk from say e.g.,s the Voyager probe, Pioneer 10/11 or even recent New Horizons mission?

Another related question I have, what would the approximate transit of Jupiter look like as seen from Saturn. The distance between Saturn and Jupiter is approximately 4-5AU, and the diameter of Jupiter is one tenth that of the Sun's. Are we looking at perhaps a transit which covers 10-15% of the solar disk?

N.B. Please note I understand that to observe a transit of Jupiter we have to be superior to it in the Solar System, hence I am asking for images taken by deep Solar System probes only.

immunology - How does the immune system "learn" from a vaccine?

Vaccines work by introducing an attenuated strain of the pathogen (or alternatively the antigens that are normally present on the pathogens surface) into the body, whereupon the body mounts an immune response. As this will (hopefully) be the first time that the body has encountered the antigens on the pseudo-pathogen's surface, the response is called the primary response.

This consists of two main divisions: the cell mediated pathway and the humoral pathway. In vaccination it is the humoral pathway that is important. This is where a division of white blood cells (B-Cells) produce antibodies that are complementary to the antigens on the pathogen surface, causing a negative effect to the pathogen (death, inability to reproduce, de-activation of toxins, etc.). However as each B-Cell produces a different antibody, there needs to be a mechanism to select the correct one:

1. Antigen Presentation (technically part of the cell-mediated-response) - a phagocyte engulfs the pathogen and displays the pathogenic antigens on its own surface.


2. Clonal Selection - B-Cells that are attracted to the invasion site attempt to bind their antibodies onto the pathogen's antigens. It takes time for this to occur successfully as you are essentially waiting for the correct mutation to happen.


3. Clonal Expansion - Once a complementary antibody producing B-Cell has been found it is then activated with the help of a T-Helper cell. This causes it to divide rapidly whereupon these cloned specific B cells can secrete their antibodies which will cause detriment to the pathogen.

---

It's at this point that I can start to answer your specific question. The large clone of B cells will then sub-divide into two types. Plasma Cells remain in the blood and produce antibodies to fight the infection. The other type, much smaller in proportion, are called Memory Cells. These cells have a very long lifetime and move to lymph nodes across the body (including the spleen), where they remain dormant until the same pathogen is found again.

When this is the case, the memory cells are activated by T-helpers so that they can divide into massive numbers of plasma cells to fight the infection the second time. This secondary response is a much faster as the clonal selection stage does not have to wait for the right mutation - they are already waiting in the lymph nodes. The response is also much stronger as each memory cell can produce large numbers of plasma cells - i.e. you can start with multiple activated B-cells (as many as you have memory cells) rather than just the one that has mutated into a complementary shape in the primary immune response.

The aim of the vaccine is for the secondary response to be so quick that potentially life threatening symptoms do not occur; the body has time to find and store the correct antigen in a safe environment as the pathogen has been deactivated.

orbit - Longitude of the Ecliptic

I originally went to math.stackexchange.com and they suggested I try here as well.

I'm trying to figure out how to calculate times of moonrise and moonset for a given position on the earth on a particular date. I'm using Vallado's Fundamentals of Astrodynamics and Applications because there is an example in the book that lays out a simplified process. I'm stuck at the point where I'm trying to calculate Longitude of the ecliptic for the Moon. The formula is below where T = -0.013634497.

λEcliptic = 218.32° + 481,267.8813T + 6.29Sin(134.9 + 477,198.85T) - 1.27Sin(259.2 - 413,335.38T) + 0.66Sin(235.7 + 890,534.23T) + 0.21Sin(269.9 + 954,397.70T) - 0.19Sin(357.5 + 35,999.05T) - 0.11Sin(186.6 + 966,404.05T)

The expected answer is -0.8412457°. However, I'm unable to figure out how to get this answer. My calculations are below:

1) 218.32° + 481,267.8813T = -6343.525

2) 6.29Sin(134.9 + 477,198.85T) = 5.963779

3) -1.27Sin(259.2 - 413,335.38T) = -0.900843

4) 0.66Sin(235.7 + 890,534.23T) = -0.292285

5) 0.21Sin(269.9 + 954,397.70T) = -0.126871

6) -0.19Sin(357.5 + 35,999.05T) = 0.138211

7) -0.11Sin(186.6 + 966,404.05T) = 0.054722

Simply adding or subtracting gets me -6338.688731. How can I get the value -0.8412457° from this. My trigonometry is rusty and I'm not sure how to get the right answer. Any help would be greatly appreciated. Thanks.

zoology - intravenous (IV) in the tail vein of an anaesthetized mouse

Cleaning the tail with ethanol is of some help and also, as you said, warming the tail. We sometimes put one of those flexible lamps (such as this) to heat up only the tail.

When anesthesized (ketamine/xylazine or isoflurane) we keep our mice on a heated pad anyways.

Cannulation in the tail does not sound like a good idea to me, especially if you are going to have the animal wake up afterwards. If you're going to cannulate then go for the jugular, but be aware that doing it on a mouse requires quite a bit of experience and it's definitely way longer than a tail injection.

It really depends on your experiment

Is there any difference between rotation axis 90 degrees and 270 degrees?

No, I don't believe there's any meaningful distinction.

A planet's axial tilt can be thought of as a 2-dimensional quantity: its angle relative to the ecliptic (or to whatever baseline you're using), and the direction in which it's tilted. When we talk about a planet's axial tilt as a number of degrees, we're only talking about the first component.

A planet whose rotation axis is perpendicular to the ecliptic would have a tilt of 0°. If its rotation axis is parallel to the ecliptic (rotating "on its side"), its tilt is 90°. If its axis is "vertical" but it's spinning backwards, its tilt is 180°. The range from 0° to 180° is enough to express all possible tilts, both prograde and retrograde.

Consider taking a planet with a 0° tilt and tilting its axis by 270°. The result is exactly the same as tilting it 90° in the opposite direction. Since the axial tilt is usually expressed as just the magnitude of the tilt, and not its direction, the distinction between 90° and 270° can be ignored.

And if we want to express the direction as well, we'll just say that it's tilted 90° in some specified direction.

We could have had a convention where the tilt ranges from 0° to just under 360°, with the direction specified more narrowly, but that would be less useful; the particular direction of a planet's axial tilt is less interesting than its magnitude. Also, the direction varies over time due to precession.

We could also have had a convention where the tilt ranges from 0° to 90°, and we also specify whether it's retrograde or not; then Venus would have a tilt of 3° rather than 177°.

Which are the best American universities/colleges for observational astronomy?

Out of curiosity: where does this limit of 70 lightyears come from? Exoplanets can be detected to way beyond that. This strikes me as a strangely restrictive limit.

Be that as it may. There are several great astronomy departments in the US, and it really depends on what you want to do exactly. For exoplanets, Harvard would be a great choice. Professor David Charbonneau is a heavy weight in the field.

Similarly, many of the other renowned Universities have good astronomy departments. Yale, for instance, or Berkeley (although since the Geoff Marcy incident I imagine the exoplanet department has taken a hit).

So at this point it is not really a matter of choosing 'the best' University. I suggest you have a look at some papers by the professors at different Universities, to get a sense of what you'd like to work on.

And don't forget: for your research to be fruitful the environment is also very relevant. Just have a look and see what city you'd like to live in.

atmosphere - Why do most meteors vanish just before hitting the ground?

Only very few meteors actually make it anywhere near the surface of Earth; most burn up 75–100 km above the surface. From your point of view, however, the curvature of Earth's surface may make it look as if they get much closer, and even fall below the horison. But depending on where you live, the horison often has quite a lot more background light (e.g. from cities far away). That means that when they get near the horison, which you may interpret as "several feet above the ground", the seemingly disappear.

general relativity - Can we measure/detect GR light bending during solar eclipse using ordinary equipment?

The deflection you are looking for is $sim 1.7$ arc seconds, which should be within the seeing limits at a good site. It should also be within the resolution limits of a telescope with $ge200$mm diameter primary.

Having said that you will not be able to see it with the naked eye, you will need to be able to photography the star field during the eclipse and again when it is visible at night and then do some arduous plate measuring and data reduction to detect the shifts of stars in the field.

So amateur equipment is up to detecting the bending of light around the Sun in a total eclipse, but if by witness you mean see the stars move with the naked eye the answer is almost certainly no.

biochemistry - What limits the maximum spacing of Nodes of Ranvier and which organisms tend to have the widest gaps?

This is best answered via something called cable theory. Basically, as the action potential (AP) propagates along the membrane of the axon, it's tripping voltage gated channels that "renew" the flux of ions into the stream at the nodes. There are no ion channels under the sheathing (or they are there anatomically and inactive, but I don't remember), so the current is able to zip through that area. There's no renewal of AP, but there's no loss due to leak of ions either. Since there's no influx of ions from outside of the membrane until the next node, the capacitance and resistance of the membrane is exponentially decaying the voltage. So, if the distance between the nodes was too long, the voltage would just die off and the AP wouldn't propagate.

I don't have any anatomical data about individual species, but know that only the smaller diameter axons require sheathing to compensate for the slower ion flow due to higher resistance (e.g., the squid giant axon(not to be confused with the "giant squid" axon) has no myelination due to its large diameter).

Are there collected data about the direction of rotation of black holes and the direction of the magnetic field?

Is there a relation between the direction of rotation of black holes or neutron stars and the magnetic dipole moment of BH or neutron stars? BTW, are there different directions of this two parameters for suns?

Edit

I want to be sure there are or there are not the direction of rotation (which one can expressed by an arrow on the rotation axis) and the direction of the magnetic field (expressed by an arrow from the south to the north pole (both arrows are simple conventions)) parallel only. I'm not sure that the direction of the magnetic field is observable at all. And the comment from Zibadawa Timmy about pulsars perhaps a good extension to my question about BH, neutron stars and Suns.

mars - What is the next planned mission that can discover life on another planet?

The Exomars rover of ESA and Roscosmos would be the obvious answer. To be launched in 2018. It will drill 2 meters deep and as far I know is the only mission since the Vikings in the 1970's, to explicitly be equipped to find biosignatures, signs of life. But the Russians, who will land the rover, have had a very poor Mars mission success rate, ESA cooperates with them since NASA abandoned the project a few years ago, and ESA's only own landing attempt on Mars failed too, Beagle 2. And some biologists think it is more challenging to detect sparse exotic microbial life than what that rover is capable of. It weights about 1/3 of MSL Curiosity, and underground life can maybe be very local.

I want to recommend the blogger Robert Walker who writes at great length and well informed, still interestingly speculative, about possibilities for life on Mars, what one maybe should be looking for.

I should add that since 1960 SETI uses telescopes to pick up evidence of interstellar life which is powerful enough to somehow change its environment to make itself astronomically detectable. That's the other main potential except for probes in the Solar system. But not even SETI people sit up waiting for it any more.

astrophysics - When is it a good aproximation to consider a star to be an ideal gas?

I am currently taking a first course on stellar astrophysics, and I noticed that in some cases we use the ideal gas equation of state for stars, so we also use $gamma =5/3$. Of course it can only be applied where there is no nuclear reaction, so there is a limit in the temperature.

Also, if the radiation pressure if relevant, you have to consider the parameter $beta$ to calculate the total pressure and the adiabatic coefficient $gamma$. It is also incorrect (I think) if there are degeneration or relativistic considerations.

I don't know if I have to consider other factors before I can use this equation of state and value for $gamma$, maybe it is important if it is a convective or radiative area, or other factors I didn't consider.

My question is: can anybody tell me the limits of the ideal gas approximation? (quantitative better than qualitative but any help will be well received)

the sun - What would the effects be on Earth if Jupiter was turned into a star?

Before I start, I'll admit that I've criticized the question based on its improbability; however, I've been persuaded otherwise. I'm going to try to do the calculations based on completely different formulas than I think have been used; I hope you'll stay with me as I work it out.

Let's imagine that Lucifer becomes a main-sequence star - in fact, let's call it a low-mass red dwarf. Main-sequence stars follow the mass-luminosity relation:

$$frac{L}{L(s)} = left(frac{M}{M(s)}right)^a$$

Where $L$ and $M$ are the star's luminosity and mass, and $L(s)$ and $M(s)$ and the luminosity and mass of the Sun. For stars with $M < 0.43M(s)$, $a$ takes the value of 2.3. Now we can plug in Jupiter's mass ($1.8986 times 10 ^{27}$ kg) into the formula, as well as the Sun's mass ($1.98855 times 10 ^ {30}$ kg) and luminosity ($3.846 times 10 ^ {26}$ watts), and we get

$$frac{L}{3.846 times 10 ^ {26}} = left(frac{1.8986 times 10 ^ {27}}{1.98855 times 10 ^ {30}}right)^{2.3}$$

This becomes $$L = left(frac{1.8986 times 10 ^ {27}}{1.98855 times 10 ^ {30}}right)^{2.3} times 3.846 times 10 ^ {26}$$

which then becomes

$$L = 4.35 times 10 ^ {19}$$ watts.

Now we can work out the apparent brightness of Lucifer, as seen from Earth. For that, we need the formula

$$m = m(s) - 2.5 log left(frac {L}{L(s)}left(frac {d(s)}{d}right) ^ 2right)$$

where $m$ is the apparent magnitude of the star, $m(s)$ is the apparent magnitude of the Sun, $d(s)$ is the distance to the Sun, and $d$ is the distance to the star. Now, $m = -26.73$ and $d(s)$ is 1 (in astronomical units). $d$ varies. Jupiter is about 5.2 AU from the Sun, so at its closest distance to Earth, it would be ~4.2 AU away. We plug these numbers into the formula, and find

$$m = -6.25$$

which is a lot less brighter than the Sun. Now, when Jupiter is farthest away from the Sun, it is ~6.2 AU away. We plug that into the formula, and find

$$m = -5.40$$

which is dimmer still - although, of course, Jupiter would be completely blocked by the Sun. Still, for finding the apparent magnitude of Jupiter at some distance from Earth, we can change the above formula to

$$m = -26.73 - 2.5 log left(frac {4.35 times 10 ^ {19}}{3.846 times 10 6 {26}}left(frac {1}{d}right) ^ 2right)$$

By comparison, the Moon can have an average apparent magnitude of -12.74 at full moon - much brighter than Lucifer. The apparent magnitude of both bodies can, of course, change - Jupiter by transits of its moon, for example - but these are the optimal values.

While the above calculations really don't answer most parts of your question, I hope it helps a bit. And please, correct me if I made a mistake somewhere. LaTeX is by no means my native language, and I could have gotten something wrong.

I hope this helps.

Edit

The combined brightness of Lucifer and the Sun would depend on the angle of the Sun's rays and Lucifer's rays. Remember how we have different seasons because of the tilt of the Earth's axis? Well, the added heat would have to do with the tilt of Earth's and Lucifer's axes relative to one another. I can't give you a numerical result, but I can add that I hope it wouldn't be too much hotter than it is now, as I'm writing this!

Second Edit

Like I said in a comment somewhere on this page, the mass-luminosity relation really only works for main-sequence stars. If Lucifer was not on the main sequence. . . Well, then none of my calculations would be right.

genetics - Which patterns do I have to avoid when modifying the 3'-UTR?

If your goal is to avoid regulatory elements, I would not believe any prediction program, since new regulatory elements are found every day. The best way would be empirical and just clone and infect with a mutated 3'UTR and see if your gene's regulation is perturbed. You could at least swap the entire 3'UTR with that from another gene to see if there are even any gene regulatory elements in the 3'UTR.

general relativity - Gravitational field released during supernovae

What you are missing is that the shell theorem, which says that for a spherically symmetric mass distribution (we can count the pre- and post-supernova states as this for the sake of argument), that the gravitational field at some distance $d$ from the mass is the same as if all the mass were concentrated at the centre of the distribution.

Therefore the gravitational field due to the pre-supernova star is unchanged after the supernova at a distance $d$ until some of the mass (or equivalently in General Relativity, energy) as travelled beyond a distance $d$.

After a core-collapse supernova, if the pre-supernova star was say $15 M_{odot}$, then what might happen is that $1.4 M_{odot}$ is left as a neutron star remnant, whilst $10^{46}$ J of energy is released - mostly in the form of neutrinos travelling at almost the speed of light and the envelope of the star expanding outwards at tens of thousands of km/s and a kinetic energy of about $10^{44}$ J.

The neutrinos carry an equivalent rest mass of a mere $0.05M_{odot}$, so if you were on a (indestructable) planet in orbit around the supernova, then yes, after the main neutrino pulse has passed there would be a small decrease in the gravitational force felt towards the centre of the planet's orbit (not instantaneously, the neutrino pulse lasts some tens of seconds) that would result in an outward acceleration and the orbit widening slightly.

Sometime later (the orbital radius divided by the supernova ejecta speed) the main mass loss from the supernova would pass by and this would result in a drastic decrease in the gravitational force and a drastic widening of the orbit.

speed - Is Darkness Faster Than Light?

I've been looking around, and can't find a solid answer. Many websites say darkness is the speed of light due to the fact it is the absence of light, but other sources say otherwise, that in some cases darkness is actually faster in some cases. Could someone clarify this for me?

zoology - How do baby animals that primarily subsist on cellulose get their initial gut flora?

In the case of mammals like giraffes and koalas, is that bacteria common on the plants they eat so when a baby starts to try to stick something besides its mother's milk in its mouth, it can't digest the cellulose at all the first time, but along with the cellulose, into its mouth went some cellulose-digesting flora that then begins a lifelong colony in the animal's gut? Is that about how it happens?

the sun - Can our Sun become a black hole

No, the sun won't ever become a black hole.

The choice between the three fates of stars (white dwarf, neutron star, black hole) is entirely determined by the star's mass.

A star on the main sequence (like most stars, including our sun) is constantly in a balance between the inward pressure of gravity and the outward pressure of the energy generated by the hydrogen fusion that makes it "burn".¹ This balance stays relatively stable until the star runs out of whatever its current fuel is - at that point, it stops burning, which means there's no longer outward pressure, which means it starts collapsing. Depending on how much mass there is, it might get hot enough as it collapses to start fusing helium together. (If it's really massive, it might continue on to burn carbon, neon, oxygen, silicon, and finally iron, which can't be usefully fused.)

Regardless of what its final fuel is, eventually the star will reach a point where the collapse from gravity is insufficient to start burning the next fuel in line. This is when the star "dies".

White dwarfs

If the star's remains² mass less than 1.44 solar masses (the Chandrasekhar limit³), eventually gravity will collapse the star to the point where each atom is pushed right up against the next. They can't collapse further, because the electrons can't overlap. While white dwarfs do shed light, they do so because they are extremely hot and slowly cooling off, not because they're generating new energy. Theoretically, a white dwarf will eventually dim until it becomes a black dwarf, although the universe isn't old enough for this to have happened yet.

Neutron stars

If the collapsing star is above the Chandraskhar limit, gravity is so strong that it can overcome the "electrons can't overlap" restriction. At that point, all the electrons in the star will be pushed into combining with protons to form neutrons. Eventually, the entire star will composed primarily of neutrons pushed right up next to each other. The neutrons can't be pushed into occupying the same space, so the star eventually settles into being a single ball of pure neutrons.

Black holes

Black holes are the step beyond neutron stars, although they're worth discussing in a bit more detail. Everything, in theory, has a Schwarzschild radius. That's the radius where a ball of that mass would be so dense that light can't escape. For example, the Schwarzschild radius for Earth is about 9mm. However, for all masses smaller than somewhere between 2-3 times the mass of the sun, it's impossible to squeeze the matter small enough to get it inside that radius. Even a neutron star isn't massive enough.

But a star that becomes a black hole is. We don't actually know what happens to a star once it's become a black hole - the edges of the "hole" itself is simply the Schwarzschild radius - the point light can't escape. From outside, it doesn't matter whether the matter collapsed to the point that the neutrons started overlapping, whether it stopped just inside the radius, or whether it continued collapsing until it broke all known physical laws. The edges are still the same, because they're just a cutoff based on the escape velocity.

---

¹ I'm ignoring the red giant phase here, since it's just a delay in the "run out of fuel" step. Basically, the core is helium "ash", while the hydrogen fusion process takes place further and further out. Once that runs out, you get a nova and the collapse continues.

² Likewise, I'm ignoring the mass that stars shed in their various nova phases. All given masses are based on the remnants left behind.

³Every source I've found for Chandrasekhar mass, except Wikipedia, gives 1.44 or 1.4 solar masses (which are compatible). Wikipedia gives 1.39, and gives at least one source to back that number.

microbiology - What is the advantage of using starter cultures for growing bacteria?

Growth can be quite slow for some species under certain conditions when the concentration of cells is too low. Log-phase growth is powerful, and so one would like to keep cells in this state for the experiment at hand. Different genes are expressed then compared to a stationary phase.

In addition, you'd like your culture to out-compete a contaminant if there is one. That is more easily accomplished with a starter culture, which is then used to inoculate a larger culture for scale-up. Inoculating directing into the large-sized flask may allow your bacteria to enter a stationary phase, thus giving an opportunity for other species to out-compete your bacteria.

How quickly does a supernova heat up/expand?

Suppose there's a star out there that's a lot more massive than the Sun.

Suppose further that orbiting this star is a planet not unlike Earth. Water, oxygen, civilization, and all.

Now the star decides to go supernova. How quick, or slow, is the process?

How long will it take it to heat up to make life on that planet impossible? A month? A year? A hundred years? A thousand years?

And how long will it take for the supernova to engulf the planet? A day? A month? A year? A million years?

star - Why are black holes that massive?

Here comes positive feedback - if something is heavy it tends to attract more things so it is even heavier and heavier. At one point it will clean its surroundings. This is the process for those supermassive black holes to create. In middle of galaxies there is lot of stuff (stars) that can be "eaten" by these huge black holes. Plus they had a lot of time to do so.

EDIT (thanks for questioning the answer I was very sure with it but there are some problems):

As Rob Jeffries said, the mass could not be acquired this way (probably not all of it) because of radiation pressure: when stuff falls towards black hole in accretion disk there is lot of heat created which pushes the rest of gas away. See Eddington limit. https://en.wikipedia.org/wiki/Eddington_luminosity

So after checking some pages those are the theories I found:
http://science.nasa.gov/astrophysics/focus-areas/black-holes/

"One possible mechanism for the formation of supermassive black holes involves a chain reaction of collisions of stars in compact star clusters that results in the buildup of extremely massive stars, which then collapse to form intermediate-mass black holes. The star clusters then sink to the center of the galaxy, where the intermediate-mass black holes merge to form a supermassive black hole."

Another source:
http://astronomy.swin.edu.au/cosmos/S/Supermassive+Black+Hole

"Stellar black holes result from the collapse of massive stars, and some have suggested that supermassive black holes form out of the collapse of massive clouds of gas during the early stages of the formation of the galaxy. Another idea is that a stellar black hole consumes enormous amounts of material over millions of years, growing to supermassive black hole proportions. Yet another, is that a cluster of stellar black holes form and eventually merge into a supermassive black hole."

special relativity - Photon Paradox?

Imagine a photon reaching the Hubble Space Telescope today had originally been emitted from a star in the early universe 13 billion years ago. Einstein’s Special Relativity tells us, traveling at the speed of light, that from the photon’s frame of reference, no time will have passed for the photon between the moment it was emitted from the star and the instant it was recorded by the Hubble telescope. In addition, at the speed of light, the length contraction (or Lorentz contraction) is said to shrink the distance between these two objects (the ancient star and the Hubble telescope) to zero. But herein lies the apparent paradox in two parts: 1) In the early universe 13 billion years ago when the star first emitted the photon, there was no Hubble Telescope for the photon to instantaneously collide with from its frame of reference. In other words, how can the photon instantly collide with something which won't be invented for 13 billion years? 2) Given the complete length contraction of all points in space to zero at the speed of light, how can a single photon ever be absorbed at any one particular point when, if all distance between points in the universe is zero from the photon’s frame of reference, the photon will hit each and every point throughout the universe simultaneously, not just one?

If you could help me understand this apparent paradox in laymen’s terms, it would be greatly appreciated.

galaxy - Is there a difference between the terms 'elliptical' and 'elongated' for galaxies?

tl;dr: "Elliptical" refers to a special kind of galaxies. "Elongated" is a loose term meaning that a galaxy is stretched out in one direction.

Etymologically, "elliptical" means having a shape that can be described by a certain mathematical function — the ellipse. For a three-dimensional object, the proper term is "ellipsoidal", but still it refers to being described by a certain equation. In contrast, "elongated" is a more loose term, meaning something like "significantly deviating from a spherical shape in one direction".

In the context of galaxies, the term "elliptical" refers to a certain type of galaxies that tends to be not actively star-forming, have no or very little structure (as opposed to the beautiful spiral arms of spiral galaxies), be quite massive, as well as other characteristica. Having no ongoing star formation, the massive, short-lived stars, which have blue colors, have died long ago, leaving behind the less massive, red stars. In addition, elliptical are often quite dusty, further reddening the light. Thus, ellipticals appear red in color.

The shape of an elliptical galaxy is described by the relative size of its three axes, $a$, $b$, and $c$. If two axes, say $a$ and $b$, are roughly the same size and are larger than $c$, the galaxy is said to be "oblate", whereas if they are less than $c$, it is said to be "prolate".

As in the etymological meaning, an elongated galaxy is not a specific type, but rather refers to a galaxy departing from spherical shape in one direction. This could for instance be a prolate elliptical, but it could also by any other galaxy that has been distorted by merging with another galaxy.

Usually, though (I think), it will refer to ellipticals. The "elongation" of an elliptical is defined as $10times(1 - b/a)$, where $a$ and $b$ is now the observed axes, i.e. of the two-dimensional projection on the sky. Ellipticals are classified according to this number as E0 (being spherical, such that $a=b$) to E7 (being very elongated). In principle, you could have even higher E-numbers, but that's not observed.

R.A. and DEC. for Constellation area vertices

They are defined on the coordinate grid of 1875; precession has shifted and rotated them since then, and a map for the present epoch must account for that. In addition to the vertices, you may need to interpolate a few points along the edges.
Davenhall and Leggett 1989 provide boundary coordinates for epochs 1875 and 2000.
For determining which constellation contains a given point, Roman 1987 provides regions and lookup code.

What would be the outcome for life in our galaxy if the merger of the Milky Way and Andromeda creates a Quasar?

If predictions are correct, the Milky Way and Andromeda are set to collide in around 4 billion years. If, when this occurs, a Quasar is formed by matter being accreted to the common galactic center (perhaps with the two supermassive black holes forming a binary), what would be the outcome for life in the new galaxy?

It's known that galactic collisions were much more common in the early universe; most Quasars are observed at high redshifts. It isn't clear if there are other conditions necessary to produce a quasar other than just the galactic collision itself, so obviously this is just speculation, but it is clear that Quasars are some of the most energetic systems in the Universe; if one were ignited so close to home, would every trace of life in the galaxy go out in a blaze of glory?

How similar are Circulating Tumor Cells and Cancer Stem Cells?

There are several competing models of metastasis, and this question does go right to the differences between them.

The primary thing to remember about CSCs is that all evidence suggests that they are a tiny, tiny subset of tumor cells.

CTCs, meanwhile, consist of whichever cells manage to acquire the right combination of motility, invasiveness, and resistance to anoikis (apoptosis caused by lack of attachment to neighboring cells or extracellular matrix).

So, one possible explanation is that CTCs are drawn from the whole population of tumor cells, and that CSCs therefore make up a very small, nigh-undetectable subset of CTCs-- but that this is the subset that ends up founding the distant metastases while the rest of the CTCs get cleaned up by the immune system or lie dormant in the target tissue. You could call this the stochastic model: CSCs form some small, randomly determined fraction of the CTCs, but they preferentially survive and found secondary tumors.

Another model posits that the cells undergo substantial changes in phenotype driven by responses to their microenvironment. CSCs, like normal stem cells, presumably require a pretty specific niche to maintain their stemness. CTCs, meanwhile, acquire their invasiveness and anoikis-resistance in response to conditions in the tumor, such as hypoxia. So, another possiblity is that, in response to stimulus from the microenvironment, a cell with the potential to be a CSC undergoes some phenotypic changes and becomes a CTC. It circulates for a while, finds a target tissue, extravasates, invades the target microenvironment, then starts re-setting up the microenvironmental niche to re-establish its stem-like properties. Call this the dynamic hypothesis: it's a single potential CSC the whole time, but it looks like a CTC while it's circulating and like a CSC only in its niche.

star systems - How do the orbits of Nu Scorpii and AR Cassiopeiae work?

I apologize for the way this question is worded but I don't think I know the proper verbiage. Basically, I want to know how the stars orbit one another in the two septuple star systems. For example, are there two massive stars in the middle that have the five remaining stars orbiting similar to the planets of our system; does one of the orbiting stars have one or more smaller star-"moons;" maybe there are stars trapped in one of the Lagrange Points. I hope that clears up the question.

I am aware that the orbits of these systems may not be known/understood. If that is the case, then I would appreciate the orbital relationships between the stars in the highest-multiple star system. If that is confusing, I mean, if we know the orbits for the stars in a sextuple system; if not then a quintuple... etc.

Finally, as an added bonus, I would appreciate being told the correct verbiage. Thank you, much.

Binary Star question - Astronomy

Since every object in the known universe which has mass has an infinite gravitational field every object in the universe affects one another.
Every star in our surrounding affects Our solar system but the relative proximity of the sun masks these effects to us.
However if the sun would be a part of a binary system of stars

1. Our planet should have been affected by it because a star is a much larger mass when compared to the planets.


2. Since the star and our sun interact with each other they would produce a noticeable wobble.


3. Any such star would definitely be very close to the sun so as to be able to influence it and hence easily visible yet no evidence has been found for this.

So for now one can say that we and the sun are not part of any binary star system which has been (if it exists) undiscovered till recently

structural biology - How many human proteins have a solved 3D structure?

PDB is a good resource for answering such questions, since it will let you filter results by many additional parameters. To count and extract 3D structures of human proteins:

1. Open Advanced search tab of the PDB website.


2. Select Biology -> Source organism from the menu.


3. Type Homo sapiens (human).


4. You can reduce redundancy by checking Remove Similar Sequences at n% identity below.


5. Submit query.

To add further filters, click Refine Query with Advanced Search. There you can extract structures by deposition date, quality (eg. resolution or R-factors for structures solved by X-ray diffraction), ligands, enzyme classification, etc. (by checking Add Search Criteria)

Search for human proteins with removal of homologues with 90% identity cutoff fetches 7117 structures. The number of good quality X-ray protein structures (resolution < 2.5A) is currently 3964 (with the same identity cutoff).

You can then download the fetched list or create custom reports (menus below).

A good tool (also used by PDB) for generating non-redundant protein datasets is cd-hit.

astrophysics - Could a pair of binary black holes form within a star?

After the discovery of gravitational waves by LIGO last week the team behind the Fermi gamma-ray telescope released a paper that showed a soft gamma ray burst was detected only 0.4s after the gravitational wave was detected at LIGO, and it was also located in the right area of the sky. This could be evidence of a gravitational wave source with a detected EM counterpart.

Ultimately though the Fermi group resist claiming a full discovery as no electromagnetic signature is expected form a binary black hole merger, but whats interesting is that I saw another paper today that claimed a GRB could be caused by a binary black hole merger inside a massive rapidly rotating star.

Is such a system realistic or even possible?

observation - How Soon Could a Waxing Crescent Moon Be Seen?

Apart from a Solar Eclipse, How much time is needed until a Waxing Crescent Moon be seen following a New Moon?

1. Would the time of year be significant? The Vernal Equinox + 1 Month.


2. Could it be seen the same night that it occurs?


3. Could it be seen in the day when it occurs?


4. Would this be affected if the viewer was in a rural location, without lights? Or would city lights help?

Ancient Lunar calendars depended on observation of the New Moon, (like political / religious obligations).

What was the potential margin of error? Hours? a Day? (Not considering bad-weather.)

From Wikipedia - A New Moon Cannot be Seen:

In astronomy, new moon is the first phase of the Moon, when it orbits as seen from the Earth, the moment when the Moon and the Sun have the same ecliptical longitude. The Moon is not visible at this time except when it is seen in silhouette during a solar eclipse when it is illuminated by earthshine.

Related:

fundamental astronomy - Equation of the Center constant factor

This questions concerns the longitudinal aspect of the Equation of Time, also called the Equation of the Center. In some sources the equation looks like the following:

$nu - M = 2varepsilon sin M$ (1)

where $nu$ is the True Anomaly of the Sun's position from the Earth, $M$ is the Mean Anomaly, and $varepsilon$ is the eccentricity of the Earth's orbit (0.0167). $nu - M$ is the difference between the Sun's actual angle and the and the angle that would exist if the Earth's orbit were circular.

Other sources have a first-order approximation that looks like the following:

Time deviation (minutes) = $-7.655 sin d$ (2)

where d is the day of the year.

My difficulty is reconciling these two equations. None of the sources actually make this connection explicit. I assume that the difference has to do with converting angles and times, and I have tried various approaches to making the numbers work out, without avail. I would appreciate it if someone could tell me how the value of -7.655 minutes is derivable from $2 varepsilon$ and or point me at a resource that demonstrates the connection between them.

(Note I realize that both (1) and (2) are approximations. At this stage, I am trying to understand the situation in its simplest form before adding refinements.

human biology - What is the number of cells in a line of a fingerprint?

I have been reading a little about the size of cells and was curious as to how small they really were.

I have noticed that on my finger, the outlines of the fingerprint are made up of thin lines. In fact, some of them are so thin that I have difficulty imagining anything thinner I can make out with the naked eye.

I have read that the naked eye has a resolution of 0.1 millimeters = 100 micrometers, whereas eukaryotic cells range in diameter of 10 - 100 micrometers.

Putting this information together, would it be reasonable to conclude that the lines on my fingers have a width ranging from 1 - 10 skin cells? Is there any satisfactory method to verify this without fancy equipment? Is it even true?

P.S.

Are there also more scientific names for these "finger lines" so that I can look it up somewhere? Googling "finger lines" brings up a lot of stuff about palm reading.

How does time "add up" for observers outside of and travelers inside of a Krasnikov tube?

A ship travels 99% of c from Earth (leaving at Time A, say 2016) to Destination Star (arriving at Time B, say 2020, accounting for relativistic effects) to stretch the tube, leaves a buoy at Destination Star, then uses the tube's topology to return to Earth, effectively faster-than-light, moments after it left, according to how the Krasnikov tube is supposed to work (Time A plus a few minutes).

It just can't work like this. Think about what a clock actually does. Time is a measure of local motion, that's all. It's "how much local motion has occurred". If you move very fast, the rate of local motion is of necessity reduced because the maximum rate of motion is c, because of the wave nature of matter. Hence you suffer time dilation. See the simple inference of time dilation on Wikipedia. Note that if you have two parallel-mirror light-clocks and one stays at home whilst the other goes on a fast out-and-back trip, the light-path lengths are the same. And they meet back up at the same time. They don't miss each other by a week. Time dilation is not time travel.

Can the ship now return to Time B (2020) from "Time A (2016) plus a few minutes" using the tube just as quickly?

No, it absolutely can not. At .99c the Lorentz factor is 7, so if your journey takes you four years by your clock, your destination star is 28 light years away. When you get there it's circa 2044 according to Earth clocks. There is no way you can get back to Earth in 2016. For that to happen all the motion that occurred has to be undone. And there is no way that that can happen.

If so, would its return to Time B mean "Destination Star in the ship's year 2020, the moment when it arrived / first stretched the tube to this destination?" And if so, would it mean returning to the system "before" the ship dropped the buoy? My understanding of a Krasnikov tube is that it's a theoretical means for FTL travel that doesn't violate causality, because a ship traveling along the return path of a tube "rolls back" time to just moments before the ship originally left.

It's just science fiction I'm afraid, with no basis in physics.

Now, I understand that there is a way to construct a return tube that would violate causality (http://arxiv.org/pdf/gr-qc/9702049.pdf), but let's assume for a moment there's some "chronology protection" in place that doesn't allow that to happen (the tube implodes when you try to do that), and that the question of the exotic matter needed to create such a tube isn't an issue for the ship's makers.

The chronology projection conjecture is yet more speculation I'm afraid. It's superfluous because we don't actually move forward through time. Hence moving backwards through time is a non-starter.

Am I even thinking about this correctly? Where have I messed up?

You didn't watch carefully, and you fell for the smoke-and-mirrors and the sleight of hand.

I don't understand how a system of Krasnikov tubes, as some sources suggest, could be used to create an interstellar network for FTL travel. It seems to me that the traveller in the ship can never actually have an impact on his exit or return points, since he will always be returning to Time A (2016) moments after he left, or Time B (2020), the moment he arrives?

If he can go from 2044 to 2016, it's a time machine. Only he can't, so it isn't.

biochemistry - Human perception of time depending on age

This is not really a biological answer, but a psychological one:

One important fact to consider is that the perception of time is essentially a recollection of past experience, rather than perception of the present.

Researchers who study autobiographical memory have suggested that part of this effect may be explained by the number of recallable memories during a particular time period. During one's adolescence, one typically has a large number of salient memories, due to the distinctness of events. People often make new friends, move frequently, attend different schools, and have several jobs. As each of these memories is unique, recollection of these (many) memories gives the impression that the time span was large.

In contrast, older adults have fewer unique experiences. They tend to work a single job, and live in a single place, and have set routines which they may follow for years. For this reason, memories are less distinct, and are often blurred together or consolidated. Upon recollection, it seems like time went by quickly because we can't remember what actually happened.

In other words, it can be considered a special case of the availability heuristic: people judge a time span to be longer in which there are more salient/unique events.

Incidentally, (and to at least mention biology), episodic memory has been shown to be neurally distinct from semantic memory in the brain. In particular, a double dissociation has been shown for amnesics who suffer from semantic or episodic memory, but not both.

My apologies for the lack of citations, but a good bit about autobiographical memories can be found in:

Eysenck, M.W., & Keane, M.T. (2010). Cognitive Psychology: A
Student's Handbook.

You may also be interested in some responses or references to a related question on the Cognitive Science StackExchange:

Perception of time as a function of age

why hasn't Nasa gone back to our Moon?

We didn't only visit the Moon once! Neil Armstrong, Buzz Aldrin and Michael Collins were the first manned mission to land on the Moon with the famous Apollo 11 landing, but 5 later Apollo missions also landed safely on the Moon and did various exciting things.
This Wikipedia article gives a brief list of all the manned and unmanned missions that have investigated the Moon, and this NASA article gives a nice history of the Apollo program with all the manned missions. (So far the US are the only country to land astronauts on the Moon.)

As for why there haven't been more visits since Apollo, there are a couple of points:

1) We have continued investigating the Moon, through remote observation, close encounters and landings, just not with humans on board. The future of human space flight is quite a debated question, since humans are very fragile, have lots of requirements in terms of food, space, health etc. and are not really very efficient at many tasks. Automated investigation of space is by far cheaper and easier. The main advantages humans have are intuition and adaptability. We can change plans, make snap decisions and respond much quicker than a robot controlled by people far away on Earth.

2) Turn the question around: why would we go back to the Moon? Why spend money and time investigating this rather boring lump of cold rock when we could go to places we have absolutely no data on, or very shaky theories, or places that have environments hugely different to our own? If we want to test scientific theories, we often want extreme environments, not just something a little bit different to home. And if, as your comment says, we are looking for other life or future homes, these things are very rare so we will have to look a lot further away than the Moon to find something that interesting!

space - Why are Hubble images "Cut"

The "stair-step" pattern visible in the first image is characteristic of the the Hubble's Wide Field and Planetary Camera 2 (WFPC2). This pattern is created by the arrangement of the four CCD chips. This image shows how the three larger "wide field" chips and the smaller, single "planetary camera" chip are arranged to create the pattern.

The bottom picture appears to be a slice of the original Hubble Deep Field, which was also captured with WFPC2.

So the answer, for these two images, is that the shape of the image is an artifact of image capture.

However, in general, finished images such as these could take up any arbitrary shape. Many of the modern images contain data from multiple views, multiple cameras, even multiple telescopes all drizzled together using specialized photo processing software.

homework - Are Bovine serum albumin, Avidin, Ficoll-70 and Dextran-70 positively charged or negatively charged?

For charge, you could check this one by sequence level, for example for Bovine Albumin (Uniprot: P02769) you can get the theoretical pI of 5.82, as the mean of pKa aminoacid values, to do this can use protparm, so when the pH > pI, the protein has a net negative charge and when the pH < pI, the protein has a net positive charge.

And there are only two organic polar solvents I known to work proteins, DMSO (pKa = 35) and
Dimethylformamide (DMF, pKa=-0.01 (20ºC))

amateur observing - Does weight influence Earth's spin?

The Earth does spin like an unbalanced top. The Earth's rotation axis is not fixed. It instead moves in a complex manner due to a combination of external torques exerted by the Moon and Sun, a torque-free nutation due to the oblate shape of the Earth, and also due to changes on and in the Earth.

The torque-induced motions are called precession and nutation, distinguished by period. The largest and slowest of these motions is the axial precession. This causes the Earth's rotation axis to trace out a cone over the course of 26000 years.

The torque-induced nutations are also cyclical motions induced by the Moon and the Sun. These are much smaller in magnitude and have a much shorter period. The largest of these has a magnitude of about 20 arc seconds and a period of 18.6 years. All other nutation terms have much smaller magnitude and have shorter period.

The torque-free nutation would have a period of about 305 days if the Earth was solid. The oceans, the atmosphere, and the outer core alter this. The Chandler wobble has a period of about 433 days and a magnitude of less than an arc second. Because the Chandler wobble isn't as predictable as are precession and nutation, it's lumped into a catch-all category called "polar motion." The redistribution of water over the course of a year (e.g., snow on Siberia in the winter but not in the summer) results in a yearly component of the polar motion.

There are lots and lots of other factors, all small. Polar motion is observed after the fact.

botany - How to store vegetables in the refrigerator: In plastic bags or not?

My wife and I are having a debate similar to this one:

I claim that it's better to take the fresh veggies out of the bags and put them in the crisper with humidity control because:

1. That's what the crisper with humidity control is for.


2. If they are in the (plastic) bag, the humidity control is pointless.


3. It's easier to notice vegetables in their early stage of rotting (it doesn't feel right to throw out an entire bag of rotten cucumbers or zucchinis before we got a chance to enjoy them).


4. It's more pleasing to the eye. It's more convenient.

She claims that it's better to leave the fresh veggies in their supermarket bags when putting them in the fridge because she could swear she noticed that they rot more slowly when left in their bags.

As you can see from the few links in this question, I tried to conduct my own search on the subject, but all answers seem to be opinions or "experiences", not an authoritative answer based on scientific research or knowledge.

So I am hoping that with the help of biology professionals (or students) I can finally find an authoritative answer to the question: Do vegetables really last longer if they are kept in their (supermarket) plastic bags when put in the crisper?

Update: I found this formal excerpt from the refrigerator's manual:

Low (open) lets moist air out of the crisper for best storage of fruits and vegetables with skins.

• Fruit: Wash, let dry and store in refrigerator in plastic bag or crisper. Do not wash or hull berries until they are ready to
  use. Sort and keep berries in original container in crisper, or
  store in a loosely closed paper bag on a refrigerator shelf.


• Vegetables with skins: Place in plastic bag or plastic container and store in crisper.

High (closed) keeps moist air in the crisper for best storage of fresh, leafy vegetables.

• Leafy vegetables: Wash in cold water, drain and trim or tear off bruised and discolored areas. Place in plastic bag or plastic container and store in crisper.

While this seems a bit more authoritative (because it comes from the manufacturer of the refrigerator), it still leaves quite a few questions open:

If leafy vegetables should be "placed in plastic bag or plastic container and stored in crisper", why set the humidity on "High"? How does humidity get the lettuce inside the plastic bag or plastic container? (is it sealed?)

Assuming that some humidity does get into the bag, why is the bag needed? Why not let humidity flow freely?

the sun - The relation between the light of full moon and the distance between the sun and the earth

The strength of the light from the Sun scales with the inverse square of distance [note 1]. That means that we would need to have the Earth-Moon system at $frac{1}{sqrt{2}}$ (approx 0.7) AU for the full Moon to be twice as bright [note 2].

Note 1: The fact that the Sun is not a point source of light has only a very minor effect on the scaling.
Note 2: Technically, it will be slightly brighter because more of the absorbed radiation will be radiated away in the visible spectrum. This is however also a negligible effect.

data analysis - Where can I find a catalog of all stars in the Milky Way?

No, such a catalogues does not (yet) exist. There are two reasons.

1 The Milky Way galaxy is about 20kpc (1pc ~= 3 lyr) across and only the very brightest stars are individually identifyable across such large a distance (such bright stars by their nature are very massive and hence young). Astronomers tend to cataloge stars by their apparent brightness, which for stars of identical luminosity declines as $1/d^2$ ($d$=distance). As a consequence, most catalogues contain only stars in the immediate galactic neighbourhood of the Sun. The Hipparcos catalogue (mentioned in another answer), for example, has most stars within a mere 100pc of the Sun.

2 Obtaining distances for individual stars is inherently difficult, in particular the more distant the star in question is. Accurate distances for stare several kpc away can currently only be obtained by indirect methods applicable only to certain types of stars (such as RR Lyrae variables). The classical trigonometric parallax measurement for such distances, however, is subject of ESA's ongoing Gaia mission.

ESA's Gaia satellite launched last year aims at cataloguing about $10^9$ stars across the Milky Way, including their velocity. The first preliminary versions of resulting catalogue, however, will still take some time to appear.

How to calculate full (mechanical) energy on the hyperbolic orbit?

The total energy is the sum of the kinetic energy and the potential energy. It is constant, unless some interaction such as a collision between bodies occurs.

The kinetic energy is easy to understand. For a mass $m$ and velocity $v$ it is given by

$$E_k = ½mv^2$$

The potential energy formula is (technically) given as

$$U = -μm/r$$

where $μ$ is the Standard gravitational parameter. (I say technically because it can be hard to grasp the concept of negative energy. See the linked articles).

In the case of a hyperbolic orbit the velocity and distance from the sun must be measured; one cannot be derived from the other as is the case with a known elliptical orbit.

See also

astrophysics - What happens to the Gas Pressure when working out the Eddington Luminosity?

The Eddington luminosity is defined in this way - but I guess that is not the answer you are looking for!

However, if we ask what isotropic luminosity is required in order to balance the inward gravitational force on a lump of gas then yes we could consider gas pressure as well.

The correct formulation is that the pressure gradient due to gas plus radiation balances the density times local gravity.

The justification for neglecting gas pressure would depend on the application. For example, when using the mass limit to justify an approximate upper mass limit for stars, it is reasonably easy to show that the ratio of radiation pressure to gas pressure $sim 0.1 (M/M_{odot})^{2}$, where $M$ is the stellar mass in solar units. Thus for stars $>3M_{odot}$, radiation pressure dominates, and because $L_{edd} simeq 3times10^{4} (M/M_{odot}) L_{odot}$ and $L simeq (M/M_{odot})^{3.5} L_{odot}$ for a main sequence star, then $L<L_{edd}$ means that
$$ (M/M_{odot})^{3.5} < 3times10^{4} (M/M_{odot})$$
and hence $M < 61 M_{odot}$. At this mass the radiation pressure will be nearly 400 times the gas pressure, justifying the use of a "gas pressure-free" Eddington limit.

I suspect, though I can't give chapter and verse, that for the intense radiation fields normally associated with the Eddington limit this will always be the case.

If we are talking about spherical accretion, then because the luminosity is constant at any radius, then the Eddington limit applies to material at any radius. But at greater radii from the central source, for a constant velocity inflow, the density will fall as $r^{-2}$, and the temperature will be lower at large radii. Thus the ratio of radiation to gas pressure will likely increase with radius and so at some point it will always be appropriate just to consider the radiation pressure.

What this implies is that reaching the Eddington limit could stop the accretion, but that even if it does not (e.g. clumpy accretion), then the increasing gas pressure at smaller radii could limit the accretion if the compressed gas is unable to cool.

Luminosity Schechter function for galaxies

Just a question I am having trouble understanding. I have the Schechter luminosity function for galaxies, given as:

$$Phi(L)dL=Phi_{0}left({frac{L}{L_{star}}}right)^{alpha}e^{-frac{L}{L_{star}}}frac{dL}{L_{star}}$$

I need to consider the case when $alpha=-1$. And then show that the average luminosity of a galaxy is exactly $L_{star}$. Could somebody explain how I could go about doing this and perhaps a hint or some part of a setup would be excellent. I really need to understand this.

Another part, which is related to the above question, is asking me to explain why the total luminosity is a finite number, whereas the total number of galaxies diverges. By this does it mean that the total number is infinite? Any extra comments on this would also be really appreciated.

fundamental astronomy - Which is more rare: Lunar eclipse or Solar eclipse?

The reason that solar and lunar eclipses are about equally common, is that they occur when the moon is "close enough" to the plane of the ecliptic at the point where it is full (lunar eclipse) or new (solar eclipse). Otherwise it completely misses the sun (solar eclipse) or the earth's shadow (lunar eclipse), and you don't get even a partial eclipse.

If the moon orbited precisely in the ecliptic plane, then there would be a total lunar eclipse every full moon, and every new moon a solar eclipse that's either total or annular according to the distance of the moon from the earth at that moment. But the moon doesn't orbit in that plane, it intersects it twice a month, at a time that most months isn't when it's close enough to being lined up with the earth and sun.

"Close enough" in the case of a solar eclipse is when the earth, as viewed from somewhere on the sun, is partly obscured by the moon (therefore: part of the sun is obscured by the moon when viewed from part of the earth). Whereas "close enough" for a lunar eclipse is when the moon is partly obscured by the earth from the somewhere on the sun (and therefore part of the earth's shadow falls on part of the moon). This is just about the same size target area.

What the sun "sees" as the moon orbits the earth is similar to what we see when we look at the moons of Jupiter: the moon moves from one side to the other and back. Sometimes it passes "over" the earth, sometimes "under", sometimes through. What's required for a partial eclipse of either kind is that it moves through, such that those two disks intersect as viewed from the sun. The difference from Jupiter, is that Jupiter is really big, so passing through is more likely for the moons of Jupiter than our moon.

If you really want to know which kind is a few percentage points more or less frequent, then you're beyond my ability to predict. Consult a table of eclipses covering a long period of time, or wait for an answer from someone with better qualifications :-)

Why did Venus not lose its atmosphere without magnetic field?

There is an interesting article on the magnetosphere of Venus on the ESA Science and Technology site. You can find the article here and it will probably answer your question.

The article states, like you did, that there are planets, like Earth, Mercury, Jupiter and saturn, have magnetic fields interland induced by there iron core. These magnetic fields shield the atmosphere from particles coming from solar winds. It also confirms your statement that Venus lacks this intrinsic magnetosphere to shield its atmosphere from the solar winds.

The interesting thing, however, is that spacecraft observations, like the ones made by ESA's Venus Express, have shown that the ionosphere of Venus direct interaction with the solar winds causes an externally induced magnetic field, which deflects the particles from the solar winds and protects the atmosphere from being blown away from the planet.

However, the article also explains that the Venus magnetosphere is not as protective as earth's magnetosphere. Measurements of the Venus magnetic field show several similarities, such as deflection of the solar winds and the reconnections in the tail of the magnetosphere, causing plasma circulations in the magnetosphere. The differences might explain the fact that some gasses and water are lost from the Venus atmosphere. The magnetic field of Venus is about 10 times smaller as the earth's magnetic field. The shape of the magnetic field is also different. Earth has a more sharp magnetotail facing away from the sun and Venus has a more comet shaped magnetotail. During the reconnections most of the plasma is lost in the atmosphere.

The article explains therefore that although Venus does not have an intrinsic magnetic field, but the interaction of the thick atmosphere with the solar winds causes an externally induced magnetic field, that deflect the particles of the solar winds. The article suggests, however, that the different magnetic field may cause that lighter gasses are not that much protected and therefore are lost into space.

I hope this sufficiently answers the question.

Kind regards,
MacUserT

Is there a limit to the size of a black hole?

There's no theoretical limit. If you had enough energy to move stars or galaxies, you could in theory keep feeding a black hole until it became enormously large, larger even than the Milky way for example. But there are practical limits past which black holes are unlikely to grow.

The two reasons for this are that 1), black holes aren't efficient at taking in matter. They can spit out as much as 90% of the energy from the matter that falls into them, and 2) once they reach a certain size, black holes are too large to form accretion disks, so matter tends to orbit around them rather than funnel into them.

Source and Source.

As to your 2nd question

Imagine that all the matter in the universe formed a black hole.
Should that be possible or is there a law which forbids creating it?

I've pondered this one myself and I have no idea the answer. Is there a size past which Dark Energy would overcome gravitation? Dark energy operating inside the black hole might overcome the gravitation past a certain size, but that's just my novice speculation and I think the black hole would need to be billions of light years across for that to happen.

I don't know the answer to that one. I'd be curious if anyone does though.

the sun - Could the sun burn a human floating next to it?

From the conditions you give, yes. Absolutely. The photon flux would simply transfer too much energy for the molecules in your body to stay fixed (the radiation would be immense). Another potential way to re-phrase this question would be: "How close could a human, without protection from any form of radiation, get to the Sun before their skin burns?"

gravity - When black holes such as those detected by LIGO merge, in what ways does the Schwarzschild Radius warp?

I was reading the paper about LIGO's detection of gravitational waves, and I wanted to know what the Schwarzschild Radius did. For example, I feel like the simulation here is oversimplified, and that reality wouldn't actually have that simple bump together of the two radii.

human biology - How are the gene sequences of individual sperm and egg cells "randomized"?

I think we can attribute this to sheer probability. The human genome contains around 3 billion base pairs. When you consider recombination from chromosomal crossover that occurs in germ line cells, there is an astronomically huge number of possible unique combinations that can be made.

Of course, males generate many many sperm, so some of these are bound to be similar. But the number of sperm produced by any individual doesn't come anywhere close to the number of possible unique sperm that he could produce.

planet - Calculating RA/dec from JPL ephemeris data

I'm using JPL planetary ephemerides to calculate the position of planets. Using DE405 ephemeris (using a parser provided by Project Pluto with all tests passing). I am fetching the position of Mars with the observer set as the Earth (geocentric).

My first assumption is that the result is a set of geocentric equatorial coordinates in rectangular form (x, y, z). This may be incorrect.

My goal is to calculate RA/Dec. My second assumption is that I should use a formula converting from Cartesian to Spherical:

$r =sqrt(x^2+y^2+z^2)$
$ra =arctan(y/x)$
$dec = pi/2 - arccos(z/r)$

Using Julian day 2457134 (21st Apr 2015, noon UTC), and cross-checking the result with NASA's Horizons service which apparently uses the same ephemeris (DE405) gets me almost there but my results are a little off:

x 1.721427968227801 y 1.5802812301744067 z 0.6897426775298559

RA 02h50m12.51s Dec +16°26'41.37"

Horizons:

RA 02h50m11.52s Dec +16°26'36.5"

I'm not sure what I'm missing. Do I have to factor distance of the planet due to the time it takes for light to reach us? Am I not using the correct time? Are my assumptions wrong?

Why does the planet Saturn have numerous (62) moons compared to the rest of the planets in the Solar System?

Saturn and Jupiter have many moons for quite a few reasons, one of the main ones being that they have an absolutely immense gravitational pull. During the early stages of the formation of our solar system, there would of been many planet-like objects floating around which our gas giants would have attracted. Furthermore, these planets are so far out in the solar system water would if frozen (which explains Saturn's rings of ice). Infact, we can show that the ice can form moons by looking at some of the moons of Uranus, some of them are half made of ice!

A few of the outer moons of our planets are captured asteroids. Phoebe, which is a moon of Saturn, is believed to have been a captured asteroid.

I haven't heard anything about Saturn having more moons than jupiter.

orbit - Are there accurate equinox and solstice predictions for the distant past?

I wrote
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-13008.c
to find historical solstices and equinoxes. The full results are at:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/solstices-and-equinoxes.txt.bz2

Accuracy:

• I'm using the EARTH_IAU_1976 precession model and the
  EARTH_IAU_1980 nutation and obliquity models, which are
  the only models supported by the CSPICE library I'm
  using:

http://hesperia.gsfc.nasa.gov/ssw/stereo/gen/exe/icy64/doc/frames.req

This is the same library and the same models NASA uses to
do its own calculations, but the models are known to have
limited accuracy. Quoting "http://aa.usno.navy.mil/faq/docs/SpringPhenom.php":

The times given in the tables are accurate to within two or
three hours for 25 to 5 BCE, and one or two hours for 4 BCE
to 38 CE. The uncertainty in these times arises from the
stochastic, that is unpredictable, change in the Earth's
rotation rate.

The accuracy gets worse the further back OR the further
forward you go: not only don't we know precisely about the
Earth's rotation in the past, but we can't even predict the
Earth's rotation precisely for the future.

Sample output:

EQU 511720269.432607 A.D.   2016-03-20 04:30:01
SOL 519734120.174820 A.D.   2016-06-20 22:34:11
EQU 527826138.004142 A.D.   2016-09-22 14:21:09
SOL 535589116.137776 A.D.   2016-12-21 10:44:07

Format:

• The first column indicates whether this is a solstice or an equinox.




• The second column is the ephemeris time of the
  solstice/equinox. If you're doing serious astronomical
  work, this is the column you should use.




• The remaining columns indicate the UTC time of the
  solstice/equinox in a more human-readable format:

  
  
  
  • The CSPICE libraries assume that the Gregorian
    calendar reformation occurred on 4 October 1582
    (meaning the day after 4 October 1582 was 15 October
    1582). Looking at these lines:
  
  

SOL -13191695511.794357 A.D.   1581-12-11 20:07:27
EQU -13183992131.003845 A.D.   1582-03-10 23:57:07
SOL -13175951250.170158 A.D.   1582-06-12 01:31:48
EQU -13167875920.223862 A.D.   1582-09-13 12:40:38
SOL -13160138634.917915 A.D.   1582-12-22 01:55:23
EQU -13152434815.793312 A.D.   1583-03-21 05:52:23
SOL -13144394485.035870 A.D.   1583-06-22 07:17:53
EQU -13136319216.460808 A.D.   1583-09-23 18:25:42

you can see that the dates of the solstices/equinoxes jump
ahead 10 days per the reformation.

• The CSPICE libraries use the Julian calendar prior to
  4 October 1582. In reality, the Julian calendar was
  introduced in 46 BCE:
  https://en.wikipedia.org/wiki/Julian_calendar




• Prior to 46 BCE, there were other calendar systems in
  use, but the CSPICE libraries assume the Julian
  calendar goes back indefinitely:

https://en.wikipedia.org/wiki/Proleptic_Julian_calendar

My calculations go back to 13201 BCE (the limits of DE431,
the ephemeris I'm using), and it's possible human beings
weren't even using calendars regularly at the time: quoting
"https://en.wikipedia.org/wiki/History_of_calendars#Prehistory":

A mesolithic arrangement of twelve pits and an arc found in
Warren Field, Aberdeenshire, Scotland, dated to roughly
10,000 years ago, has been described as a lunar calendar
and dubbed the "world's oldest known calendar" in 2013.

Notes:

• It takes the Earth 365.256363004 days to revolve around
  the Sun with respect to the fixed stars, but the time
  between vernal equinoxes is slightly less (365.242190402
  days) because the position of the vernal equinox moves
  (precesses) with respect to the stars. Source:
  http://hpiers.obspm.fr/eop-pc/models/constants.html




• The Gregorian calendar's average day length of 365.2425
  is much closer to 365.242190402 days than the Julian
  calendar's 365.25 average day length, but it's still not
  perfect. As noted in
  Do solstices and equinoxes shift over time?
  if we continue using the Gregorian calendar in the far
  future, the equinoxes and solstices will drift
  backwards. By 17090 (the limit of DE431), they will look
  like this:

EQU 476198945887.238159 A.D.  17090-02-22 08:56:59
SOL 476207018540.040894 A.D.  17090-05-26 19:21:11
EQU 476214808218.146362 A.D.  17090-08-24 23:09:09
SOL 476222655067.609985 A.D.  17090-11-23 18:49:59

about a month behind their "regular" times.

MY EARLIER PARTIAL ANSWER FOR REFERENCE:

Since HORIZONS (http://ssd.jpl.nasa.gov/?horizons) and SPICE (http://naif.jpl.nasa.gov/naif/tutorials.html) can compute the ecliptic and solar position back that far, it should be possible to compute equinoxes and solstices with reasonable accuracy. However, I haven't been able to find a site that actually lists these dates (I'm pretty sure USNO did this at one point, but I can't find their list). Other possibly helpful sources/questions: