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Are there orbits with long-term stability (astronomical time scales) around Earth? Low altitude orbits will decay due to friction with Earth's atmosphere. Inside Earth's Roche limit, a Moon could not form anyway due tidal forces. At altitudes closer to that of the Moon, the Moon would presumably destabilize an orbit such that the object would either collide with Earth or the Moon or be ejected.

Many of the other planets in our solar system have multiple natural satellites; where this occurs, they are always vastly smaller than the primary - think of Jupiter, Saturn, and even Mars. On the other hand Earth, and apparently Pluto, each has only one natural satellite, relatively large in comparison to the primary. Is this because a large satellite will tend to clear the entire "sphere of influence" around its primary of any other material?

So my question is: does the existence of our Moon effectively prevent the formation or capture of any other natural satellite around Earth? (Considering only true satellites, not "companion" objects or quasi-satellites)

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    $\begingroup$ Pluto has 5 natural satellites. $\endgroup$ – Keith Thompson Sep 25 '16 at 8:29
  • $\begingroup$ According to an article I once read in a publication the earth one had two moons ( Both made up of the same Earth-Theia material ) but both of them crashed together to form the one we see today. $\endgroup$ – Suhrid Mulay Sep 25 '16 at 12:14
  • $\begingroup$ In a practical sense the answer to the question in the final paragraph is "yes" though in a theoretical sense is possibly "no". The Earth - Moon system has been around for a few billion years and that is long enough to capture another satellite if it was going to happen. $\endgroup$ – adrianmcmenamin Sep 25 '16 at 18:37
  • $\begingroup$ @adrianmcmenamin your "no" answer is statistically invalid. The random probability of capturing some wayward object doesn't change with time -- it always was a small number and always will be (unless some interesting event floods the Solar System with space rocks). $\endgroup$ – Carl Witthoft Sep 26 '16 at 14:01
  • $\begingroup$ The increased length of time is a good test of "long-term stability" which features in the first line of the question. There's nothing there. $\endgroup$ – adrianmcmenamin Sep 26 '16 at 21:28
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Short answer: It might be impossible "long term". It's problematic because of the size of the Moon and the proximity to the Sun.

Long answer:

The Earth-Moon system in empty space could hold several more moons (like the Pluto-Charon system). The problem is proximity to the sun in addition to the size of the Moon. Planets closer to their star have a harder time holding onto moons in part cause the Hill sphere is smaller, in part cause the tidal forces are that much bigger (and those 2 factors may go hand in hand, not in addition to). But it's not just coincidence that Mercury and Venus don't have moons, they're also less likely to hold onto Moons.

Mars has a smaller Hill Sphere than Earth due to it's lower mass but it's 2 moons are very tiny. Also, one of Mars 2 moons might not be there that much longer. It may crash into Mars in as little as 100 million years.

Earth's proximity to the Sun gives the Earth a Hill Sphere of about 1.5 million km, and the true region of stability (long term) is about 1/3 to 1/2 of that, so about 500-750,000 km which isn't all that much further out than the Moon is currently.

Our Moon's average distance is 384,000 km, but our moon has a slightly eccentric orbit so it's distance varies between about 363,100 and 405,700 km. Source.

The 2nd factor is the relative mass between the Moon and the planet. Mars has 2 moons but it's moons are very small and they have very little gravitational effect on each other. Our Moon is 1/81st the mass of the Earth which is the largest Moon to planet ratio in our solar-system.

Using the simplified hill sphere formula, the cube root of (the ratio of the masses/3). Basically the cube root of (1/243) gives Earth's moon's a hill sphere of about 16% it's distance to the Earth. Any Earth orbiting object that passes within the Moon's hill sphere is obviously not going to be in a stable orbit. In fact the region of instability probably extends well past that 16%. How far past, I'm not sure, but I can safely say that anything even remotely close to the Moon's orbit couldn't orbit the Earth for any period of time.

Using 16%, the clearly unstable region is between 300,000 km and 470,000 KM. It would be impossible for an object to orbit the Earth at a greater distance than the Moon. Solar and Lunar perturbations would be too big.

If it's possible for Earth to have a 2nd moon at all, it would need to orbit quite close to the Earth. Probably well inside 300,000 KM. The closer to the Earth the more the Earth's gravitation would be dominant, so if I was to guess, I think the Moon would need to be quite close, maybe in the 50,000 km range - but that's just a guess.

For comparison, Jupiter's 3 moons in orbital resonance; Ganymede, the largest of the 3 has a hill sphere is about 3% it's distance from Jupiter. The 1:2:4 orbital resonance works out to the 1.5th root of 2 or about a 1.59 to 1 orbital distance ratio. Those 3 moons also have very nearly circular orbits. If the Moon's orbit was nearly circular, there might be a stable resonance 1.59 times closer to the Earth, but because of the Moon's orbit is measurably eccentric, I don't believe the 2:1 orbital period ratio would be long term stable because there's too many wobbles in it. I think your best bet for a stable orbit for a 2nd moon would be very close to the Earth, probably in the 50-100,000 KM range (but that's a rough guess).

It's worth noting that "long term stable" isn't a precise term cause there's no clear cut-off. A thousand orbits? A million? A billion? Lifespan of the Sun?

I realize that "maybe, maybe not" isn't an answer, but I wanted to touch on some of why it's difficult. A captured satellite couldn't get captured into a relatively circular near earth orbit because the incoming velocity is too great. In theory, if there was enough debris, a satellite could form close to the Earth and perhaps be stable for relatively long term, but the Moon would to some extent prevent such a formation in a similar way that Jupiter prevents the asteroid belt from coalescing into a tiny planet. (the low mass of the asteroid belt plays a role in that too, perhaps a bigger role), but Jupiter is a factor. Article here

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A few hundred kilometers beyond geosynchronous is the satellite graveyard orbit, which distance is also a function of satellite size. One could place an asteroid into such a orbit to be a quite visible moon. One can argue that since we do not have such a moon, that it is therefore improbable. However, as below, no moon is forever, and most assuredly in the past we had lots of little moons. Earth more or less has a sort of a second moon, and will for centuries so "can't have" is doubtful.enter image description here

I do not buy the "I do not like the complicated orbit small temporary natural satellite argument." Using that argument, Phobos would not be a moon of Mars as its orbit will terminally decay in 30 million years. Our Luna will eventually escape due tidal braking, so, I would prefer to say that no satellite is forever. The next problem is that if 2016HO3 above is not a 'moon' or 'satellite' then Earth is not a 'planet,' as planets 'clear their own orbits' as point 3 of the IAU definition of planet.

enter image description here

The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The region of stability for retrograde orbits at a large distance from the primary, is larger than the region for prograde orbits at a large distance from the primary. This was thought to explain the preponderance of retrograde moons around Jupiter; however, Saturn has a more even mix of retrograde/prograde moons so the reasons are more complicated...The Hill sphere of (66391) 1999 KW$_4$, a Mercury-crosser asteroid that has a moon (S/2001 (66391) 1), measures 22 km in radius.

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  • $\begingroup$ An interesting object, but it is not a true satellite of Earth. It is described as a "companion of Earth" and quasi-satellite because it orbits the Sun outside of Earth's Hill sphere. I've edited my question accordingly. $\endgroup$ – Anthony X Sep 26 '16 at 2:08
  • $\begingroup$ @AnthonyX sorry I didn't get back to this. In the total number of asteroid impacts on Earth, the Moon is negligible. It's too small (1/81st the Earth's mass) to significantly increase asteroid attraction by gravitation and it's too far away in size to act like a good shield (1/2 of 1% of the sky by diameter). Where the moon can have an effect is it can push near misses one direction or another with both it's dance that moves the Earth slightly and it's gravitation, so individually the Moon can affect a hit or a miss but on aggregate, the Moon doesn't have much effect. $\endgroup$ – userLTK Oct 5 '16 at 0:03
  • $\begingroup$ Will the Moon "escape" prior to the time it takes for the Earth/Moon system to mutually lock so that they continually have the same faces turned to each other? Once a mutual lock is in place, I believe the moon would stop moving away. $\endgroup$ – Michael Richardson Mar 15 '17 at 17:02
  • $\begingroup$ @MichaelRichardson The only predictions I am aware of, are for escape. That may indeed be before tidal locking occurs, as anyone who would bother modelling the Earth/Moon system would most likely include the momentum of both the Earth's rotation and the Moon's orbit. $\endgroup$ – Carl Mar 15 '17 at 17:44

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