natural satellites - Is it possible that Mercury was originally the moon of Venus after a giant impact?

This was originally going to be a comment, but it ran too long, so I'm making it an answer.

Some models argue that the scenario of a satellite of Venus escaping like this is unlikely. Alemi & Stevenson (2006) have explored the possibility of a prior Venusian moon, starting from the assumption that Venus would not have been able to avoid a giant impact. Here's their sequence of events:

1. A large body collides with Venus in a similar manner to the proposed Earth-Theia collision.


2. Debris from the impact moves outwards into a disk surrounding Venus,


3. A moon coalesces from the disk, and begins to slowly recede because of tidal acceleration.


4. Another large body hits Venus. It reduces Venus's angular momentum, reversing its rotation.


5. The moon spirals into Venus as it undergoes tidal deceleration, finally colliding with it again.

One of the tricky things about testing this model is that the authors say that there would not necessarily have been drastic composition changes, meaning that it would be hard to analyze the planet's surface and see if there is evidence supporting the double impact hypothesis. So far, there have not been tests.

It is certainly true that Venus could have suffered other impacts - the model does not preclude that. There are a couple problems with Mercury arising from such a collision:

• Other impacts could have ended up with the same result as the original moon.


• The chances of many more impacts aren't too high.


• Solar tides would likely have destabilized the orbit of any moon larger than a few kilometers in diameter (see Sheppard & Trujillo (2009)).


• MESSENGER determined that Mercury has a high potassium/thorium ratio on its surface, which would seem to disprove any events involving extremely high temperatures, including any giant impact variant.

Of course, if we accept that Venus could have captured a moon, only the third objection remains - still a strong point against the survival of a satellite, even by itself.

observation - Parabolic or hyperbolic trajectories

Yes, and it is not uncommon for an orbit have an eccentricity close to one. The wikipedia site, linked in a comment above, notes C/1980 E1, which entered the inner solar system with an eccentricity close to one, but had a close encounter with jupiter and was accelerated. It left the inner solar system with a eccentricity of 1.05, and so is on a hyperbolic trajectory, and will escape from the sun's gravity

Orbits that are highly hyperbolic are very unlikely. Comets formed as part of the solar system.

They are not really harder to spot than any other comet. A comet takes many months to make its passage through the inner solar system. There is plenty of time for them to be spotted, especially if you have probes like SOHO or NEAT

How does gravity really work

First of all: "How gravity really works" is a deep question, and any serious scientist would quickly concede that all we have is an incomplete working model. You certainly have heard about General Relativity; the first image on the page is your trampoline.

Our working model, General Relativity, is working because it explains a lot of observations very nicely. (Careful, here is another deep question lingering: "Explains" means that we can predict some observations from other observations with the model of gravity we have in our mind. It does not necessarily mean that we understand the "real nature" of the underlying issues.) But we are very confident that the model is working over a wide range of observations. One of the last "first-time" observations which followed the predictions and thus gave us more confidence in the model was the two black holes colliding lately. Lately? Well, billions of years ago. We just learned about it lately. Here is a link to a New York Times article with an impressive video. (I think one can still read a limited number of Times articles for free, so try it out.)

Our model of gravity is incomplete because it doesn't connect well to the model of nature we have for other things (elementary particles, quantum physics). For a while (like 70 years or so) it didn't connect at all; Einstein himself completely failed to connect the dots, which was probably not encouraging since he had received the Nobel Price for laying one of the foundations of quantum physics and was the obvious authority about gravity. If he couldn't do it, who could?

If I'm not mistaken, the physicists today are making progress, slowly. This connection between quantum physics and gravity is one of the main unresolved problems in modern physics.

Last, let me address your concern about the planets spiraling into the sun. This idea probably comes from actual balls on an actual trampoline spiraling in, I suppose. You probably know that the balls lose speed due to friction, much the same way you slow down on your bike when you stop pedaling. Some of the kinetic energy is transformed into heat.

And you know what? You are right. Given enough time, the planets would eventually fall into the sun. Low-flying satellites fall back to earth after a few years, because there are still traces of atmosphere slowing them down out there. The reason is that there is "friction" in the wider sense involved in all large-scale processes in the universe. That is actually one of the fundamental physical principles making up the world we know. It's just that the near-vacuum between the planets doesn't provide that much friction, and the planets are fairly massive bodies with an enormous mass and kinetic energy. It will take a long long time for them to lose enough energy that they'll be so close as to touch the sun. (Perhaps too long to happen at all.) In fact, over human life times the planets, moons and stuff are almost perfect examples for movement without friction. But in the astronomical time scale -- billions of years --, there certainly is friction. For example, the moon is showing us always the same side because friction slowed its rotation so that the rotation is now "locked" with its orbit.

Bottom line: The idea that gravity bends space and time "explains" all large-scale observations so far; the "trampoline" is a good model for a 2-dimensional "space", i.e. a surface, if you ignore friction.

asteroids - How does large body gravity affect planet formation?

why didn't the sun's gravity keep the inner planets from forming?

The short answer is, the asteroid belt orbits the sun, it doesn't orbit Jupiter, and you shouldn't expect the same effect with 2 different relations.

The sun is the gravitational object that the Asteroid belt orbits. Jupiter is not and it has a stabilizing effect on the material that orbits around it. Jupiter has a (mostly) destabilizing effect on nearby material that orbits around the sun, though there is some stability with orbital resonance and trojan points. The reason why that is gets a little bit mathy, but I'll cover the basics.

When a solar system forms, probably out of a combination of strong solar wind from a supernova and a dense enough gas cloud, most of the solar-system material forms the young sun and maybe 2%-4% remains in orbit and over time, spirals and flattens out into a disk. (see cool video)

The sun's gravity stabilizes that disk. There's no reason for it to disburse it, though the young and usually strong solar wind can blast it and clear out the closer regions of smaller particles and any ices.

Jupiter is entirely different. Jupiter and other planets which form inteh disk, tends to eat everything in their path. That's one of the definitions of a planet. It clears out it's orbital area. These planets on their own would remain in orbit around the sun, but they can interact over time with each other. Pretty much anything in Jupiter's path, once Jupiter gets large enough, either gets eaten or gets thrown into a very different orbit, either further our or closer in.

The asteroid belt is (as Suhrid Mulay points out) a relatively low density region of space that doesn't have enough mass to coalesce into it's own planet, but it might not have always been that low density and that's probably only part of the reason. The other part of the reason is the proximity of Jupiter which tends to disrupt anything that orbits too close to it and Jupiter may have at one point, moved in quite a bit closer to Mars before moving back out. Tossing much of the material in that region far away.

Planets don't do well forming too close to other planets because they will gravitationally disturb each other. A planet the size of Jupiter had pretty significant reach when it comes to disturbing other planets and planet formation.

neuroscience - Why does regular exercise increase brain volume?

Well, Erickson et al (2011) attribute the increase in brain volume in the aerobic exercise group to brain-derived neurotrophic factor (BDNF).

Specifically (p. 3020):

In fact, we found here that changes in serum BDNF levels were
associated with changes in anterior hippocampal volume; an important
link because the hippocampus is rich in BDNF, and BDNF levels increase
with exercise treatments in both rodents and humans. BDNF is a
putative mediator of neurogenesis and contributes to dendritic
expansion and is also critical in memory formation. Our results suggest that
cell proliferation or increased dendritic branching might explain increased
hippocampal volume and improvements in memory after exercise

with the caveat:

however, increased vascularization (15, 16, 33) and dendritic
complexity (34) may also be contributing to increased volume

big bang theory - Calculating the age of the universe

The simplest assumption about the global properties of the Universe is that it looks the same outside the part that is observable to us, as it does inside. That is, we see a finite part of a Universe that is (probably) infinite in extend. If so, then the calculated age — which is finite — applies to all of the Universe, not just the observable part.

The age is calculated on the basis of the observed expansion rate, and the observed densities of the constituents of the Universe. It is possible to imagine a universe with the right mixture of constituents that has existed forever$^{dagger}$, but for our particular Universe, this just doesn't seem to be the case; it is ruled out by observations.

As a first-order approximation, you can simply take the age $t_mathrm{Uni}$ to be the reciprocal of the expansion rate $H_0 = 70,mathrm{km},mathrm{s}^{-1},mathrm{Mpc}^{-1} = 2times10^{-18}$ s. That is,

$$t_mathrm{Uni} sim frac{1}{H_0} = 14,mathrm{billion,years}.$$

However, this assumes that the Universe has been expanding at the same rate throughout its entire history, which is hasn't. More generally, the age is calculated from integrating (numerically except for simplified approximations) the Friedmann equation, yielding 13.819 billion years.

I should say that the calculated age is the time from the Big Bang till now. I guess the safest thing to say is that we don't know what happened the first tiny fraction of a second or so after creation, and in principle it could have existed before this instant, collapsed, and then re-expanded. But no observations I know of suggest this.

$^dagger$An example of a temporally infinite universe is one containing energy only in the form of a cosmological constant. In this case, the Friedmann equation reduces to $da/dt=aH_0$, with $a$ the scale factor ("size") of the universe, the solution of which is an exponential function with zero size only at $t = -infty$.

cosmology - Seeing a galaxy (quasar) greater than 46.6 billion light years away

The edge of the observable universe is actually 46.6 billion light years away, despite the Big Bang being only 13.8 Billion years ago. This is because the light which we are now receiving as the furthest visible stuff had to travel through ever expanding space in between, being redshifted down into what we call the Cosmic Microwave Background Radiation (CMBR). There is a little bit further than that which we are technically receiving, but it has been redshifted infinitely.

To see anything further away than 46.6 Bly, it would have had to existed literally before time itself, or travelled faster than the speed of light. Two highly improbable things