# Feasibility of extra-lunar capture

Using our own Earth and Moon as a template is it possible for a second large body (One quarter to a third of the Moon’s Size) drifting close by to be captured in a stable and permanent orbit? Can we predict what that orbit would look like? The mass of the object is irrelevant, whether it sits slightly closer or further away from the existing moon is also irrelevant, all that matters is that the orbit be stable and that the body be large and visible enough so that anyone on the planet surface that is effected can clearly see where the blame lies.

• By irrelevant I mean to say that it is a ‘variable’ that can change depending on what you believe could work. – Darius Arcturus Nov 30 '19 at 20:59
• we have satellites orbiting either the Moon or Earth. So, what is your question? – L.Dutch - Reinstate Monica Nov 30 '19 at 21:05
• Classically meteors that get close enough (<300,000km) seemed doomed to collide with us. Is it possible something so large could establish an orbit without colliding with the moon or planet. Or is it really just unpredictable chance? – Darius Arcturus Nov 30 '19 at 21:09
• I’m thinking of something that could be several thousand kilometres across. – Darius Arcturus Nov 30 '19 at 21:10
• @DariusArcturus 100% of meteors are doomed to collide because a meteor is the term for a space rock visible in our atmosphere. Aka a shooting star. Asteroids regularly come within as little as 15,000 km without impacting. They're going too fast to be captured. en.m.wikipedia.org/wiki/… – Schwern Nov 30 '19 at 21:19

# This is absolutely possible

It's all a question of scale. NASA has brainstormed an Asteroid Recovery Mission, a plan to send a small(ish) probe out to an asteroid to tow it out of the asteroid belt and into an intercept course with the Earth-Moon system. A gravitational slingshot around in front of the moon will transfer energy and momentum from the asteroid (which has a surplus, coming from the outer solar system) to the moon, to stabilise the asteroid in orbit around the moon, slightly increasing the speed of the moon's orbit around the Earth. A similar operation around the earth could take energy from the Earth's orbit around the sun instead.

This operation can be done with any object, coming into any orbit, as long as the incoming energy and momentum is not large enough to destabilise the existing system, throwing the moon off the Earth or the Earth off the Sun.

The total orbital energy of a bound object of mass $$m$$ orbiting at radius $$r$$ around the sun (of mass $$M_\odot$$) is given by

$$E = - \frac{GmM_\odot}{2r}$$

So the orbital energy 'thrown off' by the body in coming in from its radius $$r_0$$ to Earth's orbital radius $$r_\oplus$$ is:

$$E = \frac{GmM_\odot}{2}\frac{(r_\oplus - r_0)}{r_0 r_\oplus} = \frac{Gm_\oplus M_\odot}{2r_\oplus}\frac{\mu(r_\oplus - r_0)}{r_0}$$

Where the first fraction is actually the orbital energy of the earth and $$\mu$$ in the dimensionless second fraction is the mass of the new object as a fraction of the Earth's. The trouble with bringing in our new object from the asteroid belt (orbital radius 2-3.5 times that of the earth) is that we already know that the whole belt in total has less than 4% of the mass of the moon, with half of that taken up in the four largest asteroids. Ceres, the largest at 950km diameter, is just big enough to qualify as your object, while Vesta, Pallas and Hygiea are all far too small. We could steal Tethys or Dione from Saturn, but that would be mechanically complicated; a much richer source of suitably-sized objects is the Kuiper belt, where we know there are definitely some objects in the right range (Quaoar, Sedna, etc), and there may be many others. With orbital radii in the 40-80AU range, $$\frac{(r_\oplus - r_0)}{r_0} \approx 1$$, so you just need $$\mu$$ to be "small" in order to ensure that the newly-added energy is also "small".

Fortunately for an object a-third-to-a-quarter the radius of the moon which is itself a-third-to-a-quarter the radius of the Earth, $$\mu$$ is always going to be small (0.0002 for Quaoar, for instance, or 0.000183 for Tethys). At this scale, the amount of surplus energy the new object brings to the party is actually pretty tiny.

Without any active propulsion or navigation the chances of a Kuiper belt object being knocked out of its existing orbit in such a way as to interact with Earth with exactly the right orbital parameters to be captured is infinitesimal. Physically, however, it's perfectly possible.

It is possible for multiple stars to orbit each other

Systems containing up to 7 stars are known to exist but are very rare

By analogy it would seem likely that 3 planetary sized bodies could orbit each other. However in order to be stable the orbits would need to be specifically arranged such that one pair approximated to a single entity from the gravitational perspective of the third. In this way a three body problem can be approximated as a two body problem and form a stable orbit. The closer to this ideal the longer lived the system will be. Conversely the greater the difference in interaction between the three different bodies the greater the instability.

Exactly what size of objects would form stable orbits for what period of time is not easy to calculate. However given the fact that you only need a semi stable orbit and are flexible about orbit and mass I suggest that such a situation could occur, however it would be an unlikely scenario.

• I think the question is more asking whether a stable moon-planet orbit can become a planet-with-two-moons orbit without destabilizing the original. – SRM Nov 30 '19 at 23:46
• The orbit of the third body would have to be sufficiently far away from the Earth Moon system that the Earth Moon system can be approximated to a single body cantered on the Earth Moon centre on rotation. How far that is and how quickly the system destabilises are difficult to judge. Unlikely but possible IMO. The gravitational examples are for stars rather than planets but the same principle should apply at a smaller scale for planets. In fact the Sun, Earth, Moon system is a stable triplet gravitationally. – Slarty Dec 1 '19 at 10:20