Monday, 9 April 2012

What does the surface of Mercury look like?

The MESSENGER probe was able to take many true-color pictures of Mercury. A full list can be found on JPL's Photojournal. It is clear that Mercury is light grey in color.









In terms of the actual surface, Mercury is very similar to the Moon. It's surface is speckled with craters, with some smaller craters inside them, as can be seen in some of the images above. The smoothness varies - note the inside of the larger crater in the first picture. It's quite smooth, save the smaller crater inside it.



See also this pdf.

Thursday, 5 April 2012

Is there an objective difference between space expansion and reduction in speed of light

In physics the "speed" of anything depends on the coordinate system you choose, since speed is measured as change in coordinate position in some interval of coordinate time. Even in the special theory of relativity, which doesn't take into account gravity and hence involves no spacetime curvature, the notion that the speed of light is always equal to the same constant (labeled $c$ in physics and astronomy) would only true in a special class of coordinate systems known as inertial frames, it is quite possible to define a "non-inertial" coordinate system in special relativity such as Rindler coordinates in which the speed of light does not have the same value $c$. In the general theory of relativity, which models gravity in terms of mass/energy curving spacetime, you can only have "local inertial frames" defined on very small patches of spacetime (specifically, the limit as the size approaches zero)--see this article on the "equivalence principle" for the conceptual details of how local inertial frames can be defined by observers in freefall measuring events in their immediate neighborhood (like an observer looking at events within an elevator in freefall). Such observers will always measure the local speed of light within a vacuum in their local region to be equal to $c$, regardless of the larger-scale properties of the spacetime they're embedded in, like the "expansion of space".



But if you try to define a global coordinate system on a large region of curved spacetime, this coordinate system is always a non-inertial one, so there is no guarantee that the coordinate speed of light in this coordinate system will be equal to $c$, and indeed the coordinate speed of light may vary from one region of spacetime to another depending on what coordinate system you choose (the equations of general relativity work in all smooth coordinate systems, as long as you define the metric correctly relative to your chosen coordinate system). In the basic model of curved spacetime in cosmology (the FLRW model), the simplifying assumption is made that matter is a sort of uniform fluid filling all of space, so that if you pick the right definition of simultaneity (multiple definitions are always possible in relativity due to the relativity of simultaneity), you will find that the density of this fluid is identical at every point in space at any given moment of cosmic time. This obviously isn't completely true to life, but it's expected that on large scales the density of matter is close to uniform at any given cosmic time, so it's seen as a reasonable approximation. The expansion of space basically means that the density of the fluid gets lower as time passes, and that if two objects are at rest relative to the local fluid in their immediate neighborhood, then the proper distance between them will grow with time (proper distance corresponds to what you would measure if you laid a bunch of short rulers end-to-end between the two objects at a particular moment in time, and then added up the distances).



As it happens, this cosmological model has a further nice feature (as discussed in the 'proper distance' link above which is based on this paper, see p. 99 of the 'Full Refereed Journal' link). The most "natural" coordinate system to use in this model is one in which the time coordinate corresponds to the proper time measured by a set of observers who have been at rest relative to the cosmic fluid since the big bang, and the spatial coordinate is such that the coordinate distance between any such observers at a given time corresponds to their proper distance at that time. If you use such a system, it works out that the overall coordinate velocity of any object can be broken down into a sum of two velocities:



  1. The "recession velocity" at any given space, which is the velocity that an observer at rest relative to the cosmic fluid would be moving (the rate that their proper distance from the origin of the coordinate system is growing as a function of time, where we can assume the origin corresponds to our own location in space).


  2. The "peculiar velocity" of any object which is not at rest relative to the cosmic fluid, which is just the same as the velocity of that object as measured in the local inertial frame of an observer at the same location who is at rest relative to the cosmic fluid. So, the peculiar velocity of a light ray must always be $c$.


So, if we know the recession velocity $v_{rec}$ at some distant location in space, then a light ray emitted directly towards us from that location will have an overall velocity $v_{rec} - c$ in this coordinate system, and a light ray emitted directly away from us will have an overall velocity $v_{rec} + c$. So from the perspective of this coordinate system, it makes sense to say as a shorthand that the light itself always travels at $c$, but space is also expanding away from us and this accounts for why the light is redshifted, and also why light originally emitted at distance $d$ won't necessarily take a time of $d/c$ to reach our own location. But this neat way of describing things is specific to both the cosmological model being assumed and the coordinate system used, things may not work out so neatly in other choices of spacetime or other coordinate systems. The only really general statement you can make about the speed of light is the one I mentioned earlier, that regardless of what global coordinate system you use and what the speed of a light ray works out to be in that system, it's always true that in a local inertial frame defined on a small patch of spacetime, light traveling through that patch always has a speed of $c$ as measured in that local frame.

Wednesday, 4 April 2012

genetics - Why can't we breed watermelons without any remaining seeds in the flesh?

Watermelon is just starting to come in season in the northeastern U.S., and having a seedless watermelon is convenient. The only downside is, the "seedless" almost always still have the immature, sterile white seeds in them.



What is the mechanism for breeding these watermelons so that only these white seeds remain? What is the genotype that results? Could the genetics be modified so that there are virtually no seeds (short of any minor aberrations) left in the flesh of the fruit?

Tuesday, 3 April 2012

solar system - 9th planet location?

It's too dim to be seen during a normal survey during the majority of its
orbit.



Update: Scientists at the University of Bern have modeled a hypothetical 10 Earth mass planet in the proposed orbit to estimate its detectability with more precision than my attempt below.



The takeaway is that NASAs WISE mission would have probably spotted a planet of at least 50 Earth masses in the proposed orbit and that none of our current surveys would have had a chance to find one below 20 earth masses in most of its orbit. They put the planets temperature at 47K due to residual heat from formation; which would make is 1000x brighter in infrared than it is in visible light reflected from the sun.



It should however be within reach of the LSST once it is completed (first light 2019, normal operations beginning 2022); so the question should be resolved within a few more years even if its far enough from Batygin and Brown's proposed orbit that their search with the Subaru telescope comes out empty.



My original attempt to handwave an estimate of detectability is below.
The paper gives potential orbital parameters of $400-1500~textrm{AU}$ for the semi major axis, and $200-300~textrm{AU}$ for perihelion. Since the paper doesn't give a most-likely case for orbital parameters, I'm going to go with the extreme case that makes it most difficult to find. Taking the most eccentric possible values from that gives an orbit with a $1500~textrm{AU}$ semi-major axis and a $200~textrm{AU}$ perihelion has a $2800~textrm{AU}$ aphelion.



To calculate the brightness of an object shining with reflected light, the proper scaling factor is not a $1/r^2$ falloff as could be naively assumed. That is correct for an object radiating its own light; but not for one shining by reflected light; for that case the same $1/r^4$ scaling as in a radar return is appropriate. That this is the correct scaling factor to use can be sanity checked based on the fact that despite being similar in size, Neptune is $sim 6x$ dimmer than Uranus despite being only $50%$ farther away: $1/r^4$ scaling gives a $5x$ dimmer factor vs $2.25$ for $1/r^2$.



Using that gives a dimming of 2400x at $210~textrm{AU};.$ That puts us down $8.5$ magnitudes down from Neptune at perihelion or $16.5$ magnitude. $500~textrm{AU}$ gets us to $20$th magnitude, while a $2800~textrm{AU}$ aphelion dims reflected light down by nearly $20$ magnitudes to $28$ magnitude. That's equivalent to the faintest stars visible from an 8 meter telescope; making its non-discovery much less surprising.



This is something of a fuzzy boundary in both directions. Residual energy from formation/radioactive material in its core will be giving it some innate luminosity; at extreme distances this might be brighter than reflected light. I don't know how to estimate this. It's also possible that the extreme cold of the Oort Cloud may have frozen its atmosphere out. If that happened, its diameter would be much smaller and the reduction in reflecting surface could dim it another order of magnitude or two.



Not knowing what sort of adjustment to make here, I'm going to assume the two factors cancel out completely and leave the original assumptions that it reflects as much light as Neptune and reflective light is the dominant source of illumination for the remainder of my calculations.



For reference, data from NASA's WISE experiment has ruled out a Saturn-sized body within $10,000~textrm{AU}$ of the sun.



It's also likely too faint to have been detected via proper motion; although if we can pin its orbit down tightly Hubble could confirm its motion.



Orbital eccentricity can be calculated as:



$$e = frac{r_textrm{max} - r_textrm{min}}{2a}$$



Plugging in the numbers gives:



$$e = frac{2800~textrm{AU} - 200~textrm{AU}}{2cdot 1500~textrm{AU}} = 0.867$$



Plugging $200~textrm{AU}$ and $e = 0.867$ into a cometary orbit calculator gives a $58,000$ year orbit.



While that gives an average proper motion of $ 22~textrm{arc-seconds/year};,$ because the orbit is highly eccentric its actual proper motion varies greatly, but it spends a majority of its time far from the sun where its values are at a minimum.



Kepler's laws tell us that the velocity at aphelion is given by:



$$v_a^2 = frac{ 8.871 times 10^8 }{ a } frac{ 1 - e }{ 1 + e }$$



where $v_a$ is the aphelion velocity in $mathrm{m/s};,$ $a$ is the semi-major axis in $mathrm{AU},$ and $e$ is orbital eccentricity.



$$v_a = sqrt{frac{ 8.871 times 10^8 }{ 1500 } cdot frac{ 1 - 0.867 }{ 1 + 0.867 }} = 205~mathrm{m/s};.$$



To calculate the proper motion we first need to convert the velocity into units of $textrm{AU/year}:$



$$205 mathrm{frac{m}{s}}; mathrm{frac{3600 s}{1 h}} cdot mathrm{frac{24 h}{1 d}} cdot mathrm{frac{365 d}{1 y}} cdot mathrm{frac{1; AU}{1.5 times 10^{11}m}} = 0.043~mathrm{frac{AU}{year}}$$



To get proper motion from this, create a triangle with a hypotenuse of $2800~textrm{AU}$ and a short side of $0.043~textrm{AU}$ and then use trigonometry to get the narrow angle.



$$sin theta = frac{0.044}{2800}\ implies theta = {8.799×10^{-4}}^circ = 3.17~textrm{arc seconds};.$$



This is well within Hubble's angular resolution of $0.05~textrm{arc seconds};$ so if we knew exactly where to look we could confirm its orbit even if its near its maximum distance from the sun. However its extreme faintness in most of its orbit means that its unlikely to have been found in any survey. If we're lucky and it's within $sim 500~textrm{AU},$ it would be bright enough to be seen by the ESA's GAIA spacecraft in which case we'll located it within the next few years. Unfortunately, it's more likely that all the GAIA data will do is to constrain its minimum distance slightly.



Its parallax movement would be much larger; however the challenge of actually seeing it in the first place would remain.

gravity - What if we throw two solid objects parallel in space? Do those two objects have any chance to collide with each other?

It all depends on the direction you "throw them" and the space-time they find themselves in.



Case 1 - in a perfectly empty universe (other than your footballs) the two would eventually collide. It doesn't matter what initial velocity you give them. The only thing that matters is there separation and their mass. You can just use Newtonian gravity to compute the two footballs' acceleration toward one another -- and hence the time for them to collide.



Such an 'empty' universe as above is called a Minkowsky space-time.



If you put these footballs on a trajectory into our real universe, well we know that space-time is curved by the matter/energy (just energy density in general) that occupies it. Hence a trajectory that starts out parallel will invariably end up "not parallel". The balls will either collide or diverge depending on the geometry of the space-time they find themselves in. The "geometry of the space-time" is (again) completely dependent on the distribution of "stuff" (matter/energy) in the universe as related to the location of the footballs.



In short, the footballs will follow the geometry of the space-time they find themselves in. That geometry (in our real universe) means they will not remain on parallel paths.

Monday, 2 April 2012

water - Can a comet orbit a planet?

Its very unlikely for a comet to become a satellite of an inner solar system planet. Much less likely than it is for an asteroid. Most asteroids are on fairly circular orbits, and so the relative velocity between asteroids and planets is quite low. In comparison comets have very elliptical orbits, and their relative velocities to the planets are much larger.



For an asteroid to be captured it must lose momentum. This is possible, though rare. For example, a binary asteroid can be captured if it is separated by tidal forces. For an comet with much more momentum, the chance of being captured is much much lower. Asteroids are captured by the Earth moon system, but not into stable orbits, they don't stay long.



If it did occur, the comet would still be active, with a coma of gas, which would be visible just like a very nearby comet. It wouldn't be particularly bright, since the surface brightness of a comet doesn't depend on distance from the Earth.



Over time the comet would run out of volatiles and become more or less indistinguishable from a captured asteroid. If it were in the Earth's orbit it probably wouldn't last that long, as there are not many orbits that are stable in the long term around the Earth, due to perturbations from the moon.



The dust and gas, including water vapour, will initally remain in orbit, forming a faint ring. It will, over time, be disrupted, and either end up in the atmosphere, on the moon, or ejected from the system. A comet doesn't contain enough water to make a difference to the Earth's ecosystem.

Sunday, 1 April 2012

planet - Is there any real evidence to prove or disprove the existence of alien civilizations?


Is there any REAL proof that alien civilizations exist in outer space?




No.




What if someone would say that Earth is the only inhabited planet in the whole Universe, how would you respond?




Depends on what their goal is. If their goal is to convince me of that, I'd just try to avoid the conversation. If their goal is to come to an understanding of the current body of scientific knowledge on the matter, I'd talk about how we don't know that that statement is true.




I need to write a 5 paragraph argumentative essay to prove that alien civilizations exist. I need to write an introduction, 3 paragraphs supporting my statement that aliens exist, and a conclusion. In each of the three "body" paragraphs I need to describe in detail a piece of evidence supporting my claim.




That will be difficult, given that there is no such proof. Best you could do is argue that alien civilizations likely exist, given a certain set of assumptions.




I don't even know where to start. I mean, I want to find out the opinion of some scientists who think that we are alone, and then disprove their claim in my essay.




That is not a good goal for an essay. Don't start with the goal of disproof. Start with the goal of understanding.




I need to know the latest scientific evidence on the existence of alien civilizations. I don't mean like alien abduction stories or any of that science fiction stuff. I need some real proof that will be convincing and not undermine my argument.




Look at the Drake Equation and recent research that concludes that there are many planets in the galaxy.




How can you know for sure if there are alien civilizations in outer space?




You would need observational evidence.




What do they look like? On which planets do they live? What kind of technology do they use?




All unknown.




Why are we not alone in the Universe?




This question presumes the conclusion that we are not alone. We might be alone.




What evidence disproves the claims of Earth chauvinists?




None.