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Would it be possible that Mercury had a natural satellite but the gravitational pull from the Sun became so overwhelming from it growing over the years that it just sucked in Mercury's moon?

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The larger an object is and the further away it is from the Sun, the greater its Hill Sphere is. Mercury's is very small (only about $175000km$ in radius from what @userLTK said) and its "moon" would therefore be yanked away by the Sun relatively quickly. See this for more details.
The orbit of this moon would be highly unstable and therefore unpredictable, so it may hit the Sun.

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    $\begingroup$ Minor note, but it looks like you eyeballed the 300,000 km estimate. The calculation based on Mercury's perihelion of 46 million km, and the Sun's mass, about 3 million times Mercury, puts an estimate of about 1/262 of that distance or closer to 175,000 km and the stable region inside that is 1/3 to 1/2. For Mercury to have a reasonably stable satellite, it would need to be within 85,000 km, give or take. $\endgroup$ – userLTK Nov 30 '18 at 5:27
  • $\begingroup$ @userLTK Yes I did, thanks for the more precise calculations. $\endgroup$ – Tosic Nov 30 '18 at 9:11
  • $\begingroup$ An unpredictable orbit (although using strange attractor aka chaos theory we can put some boundaries) does not mean the angular momentum suddenly vanishes. So at best (or worst :-) ) the orbit would go elliptical to the point that the moon hits the sun, but the sun's gravity is not pulling the moon into itself. $\endgroup$ – Carl Witthoft Nov 30 '18 at 18:42
  • $\begingroup$ @CarlWitthoft Hitting the Sun is what I meant using this loose terminology, I'll correct that. $\endgroup$ – Tosic Nov 30 '18 at 20:24
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Would it be possible that Mercury had a natural satellite but the gravitational pull from the Sun became so overwhelming from it growing over the years that it just sucked in Mercury's moon?

Let me clarify a point, that the gravitational pull of a star doesn't "suck things in". One definition of an orbit is a balance between gravitational pull and tangential velocity. Mercury orbits the Sun at an average (tangential) velocity of about 47 km/s. If the Sun did pull a theoretical moon away from Mercury, which is absolutely possible, that Moon would exit Mercury's grasp with a similar tangential velocity to Mercury and it would enter a near-Mercury orbit. It wouldn't fall into the Sun.

Without getting too off-topic, a near-mercury orbit would be precarious because every time it flew past Mercury, which it would from time to time because the orbits would either cross or pass very close to one another, then with each near pass, it would get a push from Mercury, perhaps seeing an increase in eccentricity, or moving closer to the sun at points in it's orbit where it might begin to vaporize. There are no known objects with a smaller semi-major axis than Mercury, which implies that near-mercury orbits wouldn't be long-term stable.

As noted in the other answer, the region where a moon can continue to orbit a planet is the planet's Hill Sphere, but for long-term orbital stability, it's the true region of stability that matters, which is about 1/2 to 1/3rd of the Hill Radius. In the case of Mercury, using Mercury's closest point to the Sun of about 46,000 km, it's true region of stability is in the 60,000 km to 85,000 km distance. It's not an exact number, but inside that distance, a moon could theoretically orbit Mercury and be safe from the Sun's pull.

There's other potential problems though. Mercury isn't a perfect sphere, it's somewhat lumpy and a lumpy planet is less good for stable satellites. This lumpyness is called Mass Concentrations or Mascons NASA discovered that when they tried to orbit two satellites around the Moon. Our moon is unusually unballanced, so it's especially bad for orbits. Mercury is much more symmetrical than the Moon, so that's less of a problem, but it does have a heavy side and a lighter side which keeps it tidally locked in a 3/2 spin/orbit resonance, so it's not ideal for close orbits.

Another, potentially even bigger problem is that with a close orbiting Moon around a planet tends to be drawn in towards the planet due to creating a tidal bulge and tidal forces. Mercury has a very slow rotation, so any moon it might have had would almost certainly orbit ahead of it's tidal bulge and that interaction would draw the Moon closer to the planet over time. This is happening with Mars and Phobos. Phobos is also very small. A moon of more size would create a larger bulge in the planet which would cause it to spiral down faster.

It's worth noting that Mercury may, when it was much younger, have had a fast rotation that was slowed down over time by the sun, so there's some wiggle room on this point if you allow for a faster rotation in the distant past, but today, Mercury would have some trouble holding a Moon because it doesn't have a good window between too close and too far.

Nobody knows if Mercury ever had a moon, but there's some reason to believe it didn't. The 3 methods from which a planet can get a moon, Formation, Impact or Capture are all somewhat problematic for Mercury.

Formation moons require a fair amount of space where the planet forms, a lot of material and the most important factor, a considerable amount of angular momentum. There are no known rock planet formation moons and they would probably require a more massive planet to have a chance of forming at all. Mercury is too small.

Impact moons are also rare because to create an impact moon, the impact has to be very large and perhaps also hit the planet at the right angle. There's no such thing (to my knowledge) of a small impact moon. Individual bits of debris blown off a planet by impact would follow an elliptical orbit back to the planet. You need a critical mass of debris before the debris has enough of it's own gravitational field to coalesce. For that reason, impact of sufficient size and proper angle of impact are rare and the Moons, quite large relative to their planets. Our Moon and Charon are the only two known impact moons.

Captured moons tend to be small asteroids but could in theory be larger bodies. The difficulty with capture is that it requires a 3 body interaction. Mercury is deep in the Sun's gravity well, where objects orbit very fast and there's no significant 3rd body to assist with capture, and on top of that, Mercury's Hill sphere is small, so Mercury capturing a moon is unlikely.

Earth occasionally and temporarily captures a Moon, but Earth's Moon can act as a 3rd body, assisting in the capture, and then assisting in the later ejection of the same body and I use the word Moon pretty loosely in this case, as these are mostly small and very temporary bodies.

Mars is thought to have two captured asteroids/moons, Deimos and Phobos, but Mars is a fair bit further from the Sun and closer to the Asteroid belt. The point is that capture is rare. Sure, Jupiter has dozens of them, but Jupiter is a gravitational monster.

So, it's not just keeping a moon, but getting a moon in the first place can be a rare event for a rocky planet close to the sun. That's not your question, but I thought I'd put it out there.

I don't want to say never, because when the solar-system was very young, during the proto-planet stage or the late heavy bombardment . . . Mercury might have, theoretically had a moon by capture or impact, and if that was the case early enough, there might be no evidence of it today, especially since Mercury may have lost a significant percentage of it's crust.

But if Mercury had a moon today and if that Moon was in the right orbit, close to the outer edge of it's true region of stability, such a moon might orbit the planet for some time, perhaps millions of years, and it wouldn't get pulled away by the Sun, because it would more likely slowly spiral into Mercury eventually breaking up into a rocky ring system inside the Roche Limit, and over time, falling into the planet with some of the smaller bits of debris being deflected away from Mercury by the solar wind, radiative pressure and/or the Poynting-Robertson effect

Mercury window to have a stable or somewhat long term moon is the smallest of the 8 known planets in our solar-system. Further away from the Sun it becomes much easier.

I hope I didn't drift too off course in my answer. Pun intended.

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  • $\begingroup$ Your answer spiraled a bit before it precessed, but never drifted. Very nice! $\endgroup$ – uhoh Dec 1 '18 at 7:32

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