planetary formation - Why haven't asteroid belts turned into new large bodies?

From Wikipedia:
http://en.wikipedia.org/wiki/Asteroid_belt#Formation

Planetesimals within the region which would become the asteroid belt were too strongly perturbed by Jupiter's gravity to form a planet. Instead they continued to orbit the Sun as before, and occasionally colliding.[27] In regions where the average velocity of the collisions was too high, the shattering of planetesimals tended to dominate over accretion,[28] preventing the formation of planet-sized bodies. Orbital resonances occurred where the orbital period of an object in the belt formed an integer fraction of the orbital period of Jupiter, perturbing the object into a different orbit; the region lying between the orbits of Mars and Jupiter contains many such orbital resonances. As Jupiter migrated inward following its formation, these resonances would have swept across the asteroid belt, dynamically exciting the region's population and increasing their velocities relative to each other.[29]

Magnitude, satellite flare and the Heavens Above app

The astronomy "magnitude" scale works backwards: smaller numbers indicate brighter objects. Back in the days before precision measurements of brightness, stars were categorized by eye, with the brightest being "stars of the first magnitude". When more precise measurement became possible, this scale was retained, and extended into the negative numbers for very bright objects like Venus, the Sun, and a few of the brightest stars.

The Iridium satellites have enormous, mirror-like antenna arrays. When one of them is angled correctly, it will reflect sunlight straight at you, producing an incredibly bright flare visible even in broad daylight. Very few other satellites have large reflective surfaces other than their solar panels, and solar panels are kept pointed straight at the Sun, so they never generate flares.

To give some points of comparison, the Iridum flare listed in your screenshot, at magnitude -5.2, is comparable to Venus at its brightest, visible during daylight if you know where to look. The other satellites listed, with magnitudes in the 2-3.5 range, have brightnesses between that of Polaris, and that of the dimmer stars making up Ursa Minor.

human biology - How does laser surgery correct accommodation problems?

Laser eye surgery works by altering the shape of the cornea. The cornea works together with the lens to focus rays of light onto the retina. The cornea accounts for two-thirds of the optical power of the eye (1) (i.e. the eyes capability to focus light), however unlike the lens is of fixed power. It is the lens that changes is shape by the action of suspensory ligaments and ciliary muscles in order to focus light by the correct amount depending on how far away the light originated from (and consequently the angle of incidence with the cornea). I'm sure that you are aware of all this, however for the benefit of future readers this is fully explained diagrammatically on this webpage.

Three forms of accommodation problems can be treated by laser surgery:

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Hypermetropia (long-sight) is where light focusses behind the retina:

Laser treatment is used to make the cornea thicker, resulting in a greater degree of refraction of light and correction of the focus.

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Myopia (short-sight) is where light focusses before the retina:

Laser treatment is used to make the cornea thinner, resulting in a reduced degree of refraction of light and correction of the focus.

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Astigmatism is where the cornea is not the correct shape - it is closer to a rugby ball rather than the sweeping curve demonstrated in the first diagram. This results in multiple focal points therefore a blurred image.

Laser eye surgery is used to alter the shape of the cornea until it is more normal.

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Presbyopia is an age related condition where the lens becomes more rigid and is less able to change its shape to accommodate the light.

As this is a problem with the lens rather than the cornea, it can not be treated with laser eye surgery. It must be corrected with glasses, as shown in the above diagram.

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(1) Cassin, B. and Solomon, S. Dictionary of Eye Terminology. Gainsville, Florida: Triad Publishing Company, 1990.

gravity - What is spacetime 'made' of?

General relativity is often explained as saying spacetime is curved by gravity, what does this mean?

It means that general relativity can be formulated in a way in which its mathematics have a very direct analogue to differential geometry on a curved four-dimensional manifold. In other words, the way test particles would behave under the influence of only gravitational forces is exactly how they would behave if moving freely on a curved four-dimensional manifold. The mathematics have a direct correspondence: nothing more, nothing less.

Electromagnetism has a description in which the electromagnetic field strength is the curvature of a connection on a line bundle. I realize that this statement is very cryptic to someone who hasn't studied gauge theory, but it's important to realize that an essentially geometric description is not special to gravity. What's special to gravity is that it couples to all stress-energy-momentum equally, and gravitational freefall of a test particle is completely independently of composition.

Because of this universality, it is possible to interpret the properties of the gravitational field as properties of spacetime, i.e. as property of the arena on which everything else happens. We don't have to do so, and indeed there are some presentations of general relativity (e.g., Weinberg's) in which the geometric interpretation is relegated to an unimportant side note, but we can--and geometry is how general relativity was originally developed.

How could we perceive a curve in spacetime when there is no external "straight" reference frame for instance?

We could measure it.

As a conceptually (but not practically) simple way to do so, we could set up a small ball consisting of initially comoving test particles. With no curvature of the gravitational field, every such ball would keep the same shape and volume because they're all the test particles are moving in the same direction with the same speed. But if the gravitational field has Ricci curvature, the volume of the ball would either start shrinking or expanding. Similarly, changes in the shape of the ball would give information about Weyl curvature.

This is the same kind of answer as in the case of electromagnetism: the field strength is also a kind of curvature (though not of spacetime), but how do we perceive it? Well, we could measure it by seeing how test charges behave.

cosmology - How to disentangle a very distant star's relative velocity vs. redshift distance

Conrad is almost right. It is true generally that if a Galaxy is close enough to take spectra of individual stars (e.g. luminous supergiants) then it is not far enough away to be regarded as part of the "Hubble flow" and so applying Hubble's law to this star, or its host galaxy, would not yield a reliable distance in any case, but would reflect the "peculiar motion" of that galaxy.

To put some numbers on this. Galaxy peculiar motions tend to be a few 100 km/s, as do the individual velocities of stars with respect to their galaxies. Taking a Hubble constant of 70 km/s per Mpc, we see that we need to be at distances of 15 Mpc before Hubble recession velocities ($v = H_0 d$) become large compared with peculiar motions. At these distances we cannot observe individual stars - they are too faint and unresolved from the bulk of the Galactic light.

The exceptions are supernovae. The redshifts of individual supernovae, that briefly outshine their galaxies, can be measured right across the universe. Here you are correct that the measured redshift is a combination of cosmological redshift due to the expansion of the universe and a velocity of the star relative to the Hubble flow at that distance. There is no way to distinguish between these two unless velocity measurements could be obtained for other objects in the same galaxy. Given the rarity of supernovae, we might wait a long time for this.

But does it matter? Even if we look at a "low redshift" supernova at $z=0.1$, its Hubble recession velocity is 30,000 km/s and far in excess of any peculiar velocity contribution at the level of $sim 1$%.

supermassive black hole - Time according to the gravity of Sagittarius A?

Not at all a dumb question. As you have heard, it is true that time is affected by gravity. The stronger the gravitational field, the slower time passes. If you're far from any gravitating matter, time passes "normally".

But to answer your question, we must specify what is meant by "the black holes's time" (let's call the black hole $mathrm{BH}_mathrm{Sgr,A^*}$; see note below on the nomenclature), since it depends on how far from Sgr A* we are talking. The time pace at a distance $r$ from the center of a BH is given by
$$t = t_infty sqrt{1 - frac{r_mathrm{S}}{r}},$$
where $t_infty$ is the time "at infinity", i.e. far from the BH, and
$$r_mathrm{S} equiv frac{2GM}{c^2} simeq 3,mathrm{km},times left( frac{M}{M_odot}right)$$
is the so-called Schwarzschild radius (the "surface" of the BH), which is where not even light can escape. Here, $G$ is the gravitational constant, $M$ is the mass of the BH, $c$ is the speed of light, and $M_odot$ is the mass of the Sun.

The last equality shows that a BH with the mass of the Sun would have a radius of 3 km. The mass of $mathrm{BH}_mathrm{Sgr,A^*}$ is some 4.1 million Solar masses, so its radius is $r_mathrm{S} = 12.4$ million km.

Plugging in the other numbers, we can see that at a distance from $mathrm{BH}_mathrm{Sgr,A^*}$ of

1. 1 lightyear, time runs slower by a factor of 1.0000006557, i.e. unnoticeably.


2. 1 astronomical unit (the distance from Earth to the Sun), time runs 17% slower.


3. 1 million km from the surface, time runs slower by a factor of 3.7.


4. 1000 km from the surface, time runs slower by a factor of 111.


5. 1 km from the surface, time runs slower by a factor of ~3500.


6. 1 m from the surface, time runs more than a million times slower.


7. At the surface, time stops.

Note that this time dilation is what a distant observer (i.e. the guy with the $t_infty$ time) would measure for an observer at the distance $r$. The person at $r$ would just measure his/her own time as usual. For instance, according to point 5 above, if you were hovering 1 km from the surface, waving your hand every second, then I, choosing to stay at a safe distance of 1 lightyear but with a magically powerful telescope, would see you wave approximately once every hour. And when you run out of fuel and plummet into the BH, then when you cross the surface you wouldn't notice anything particular, but I would see you frozen in time. This is the concept of relativity.

Finally, let me use this chance to clarify something that people, including myself, often have gotten wrong: Sagittarius A (without an asterisk) is a radio source in the center of the Milky Way. It consists of three parts: Sagittarius A East (a supernova remnant), Sagittarius A West (dust and gas clouds), and Sagittarius A*, or Sgr A*, which is a very bright and compact radio source believed to be formed by a supermassive BH. Sgr A* isn't actually the BH itself. I think the BH doesn't really have a name, so I'll call it $mathrm{BH}_mathrm{Sgr,A^*}$. Maybe that's a bad name…

botany - How long will a vegetable live for after being harvested?

The short answer is that as long as the vegetable/fruit is fresh looking - i.e. the cells have not disintegrated - they will be respiring, many cells will be functioning quite normally, and the plant is still technically alive. In cases where the part of the plant we treat as a vegetable is a part intended for reproduction (e.g. a seed, or a tuber like a potato) the plant will keep growing.

The point at which the plant dies is not clearly defined like it is in animals, but generally if you can still eat it, it's still alive.

Death in plants is quite different from that in animals - we refer to it as senescence. The key difference is that it happens to tissues and organs which can die and separate from the organism. Individual leaves can die without the plant's health being affected. Once this has happened to all the parts, the organism is considered dead, but if there is any respiring tissue left, it's still alive.