Could the Earth Moon system capture another moon?

[Moontanman]

Is it possible the Earth Moon system could capture another moon? Plausibility of a Ceres sized body being captured by the Earth moon system and the possibility of the Earth Moon system capturing a small body say 20 kilometers in size.

Is it possible to calculate this mathematically? Is it possible but so unlikely the universe couldn't exist long enough kind of possible or reasonable?

Would the body, if captured, orbit the Earth or the moon? Could it orbit the moon? I am full of questions tonight I don't know how to answer.

[Przemyslaw.Gruchala]

There are known asteroids orbiting other asteroids.

In comparison to them Moon is giant.

NASA satellite orbiting Moon is example of such object at right velocity.

Too high velocity and it'll escape object.

Too low, and it'll be attracted to surface.

[ajb]

There are quasi-satellites which have orbits round the Sun that are similar to Earth's, but they are technically not true satellites of the Earth-Moon systems.

 

There is also one Trojan asteroid in the Earth's gravitationally stable L₄ Lagrangian point. Again, this technically orbits the Sun rather than the Earth.

 

Now, with all true gravitational bound objects they orbit their collective center of mass. This center of mass could lie inside one of the bodies, as it does for the Sun and the solar system. So for most purposes it is fine to say that we all orbit the Sun, but this is not quite the center of the Sun.

 

 

Graphic from Wikipedia

 

Anyway...

 

As far as we known there are no moons with moons. However there is nothing in principle stopping this.

 

There is the notion of a Hill sphere, which is the region in which a body dominates the attraction of satellites. To orbit a planet, a moon must lie inside the planet's Hill sphere. The satellite itself will have its own Hill sphere.

 

The Moon's Hill sphere has a a radius of about 60,000 km. That is about 1/6th or so of the distance between the Earth and Moon. If the Moon has a satellite, it would have to sit in the Hill sphere of the Moon otherwise it would orbit the Earth.

 

I doubt that any such orbit around the Moon would be very stable, there are strong tidal forces acting on the Earth-Moon system. Thus I would not really expect the Moon to capture an asteroid.

Edited February 16, 2013 by ajb

[Ophiolite]

Coincidentally I just purchased a copy of 'What if the Earth Had Two Moons' (St. Martins Press 2010 ISBN:978-0-312-59892-1). The author explores the effects of ten physically different Earths, introducing a variety of scientific principles along the way. In the opening piece, from which the title is derived, he explains how such a capture could take place.

[Moontanman]

Yes but I am writing a story that is about the earth moon system capturing another moon, i am thinking of a Ceres size body being nudged by humans until it is in orbit of the earth. i am thinking the safest orbit would be around the moon, but economically the orbit should be near the earth, maybe geosynchronous around the earth.
my first thought was a comet type body interacting with the earth and moon and being captured and how stable the orbits would be.

 

First of all is it possible for the earth moon system to capture a wayward asteroid naturally?

 

Would the size of the asteroid make any difference?

 

And last could a stable orbit around the moon by a Ceres sized object be possible?

 

My definition of stable is thousands of years at least.

 

Could we nudge such a large body into orbit in the Earth moon system if it couldn't occur naturally.

 

And finally would an orbit that enclosed both the earth and moon, say at a million miles from the earth be stable?

Edited February 16, 2013 by Moontanman

[Enthalpy]

Orbits around our Moon are said to be unstable and crash or escape within one year.

 

The difficulty with our own particular Moon is that its trajectory is very complicated. Its orbital plane is very tilted versus the ecliptic, and its big orbit radius makes it quite sensitive to the changes of the Sun's gravitation with distance, and to the change of centrifugal force as well.

 

As a consequence, Earth-Moon distance changes a lot, like +-20,000km over 380,000. The direction of the Moon's orbital plane also changes quickly versus the distant stars. To this, you must add that Earth's field changes a lot along an orbit around the Moon, as does the centrifugal force.

 

All added, a trajectory around our Moon is anything but a calm ellipse.

 

-----

 

Could an object be captured by the Moon in the first place? That's not very easy, because the object must lose energy (kinetic+gravitational) versus the Moon.

 

The simpler case is when the Moon's gravity brakes an object, permitting it to be captured by Earth. A slingshot suffices; the objet can't arrive too quickly because our Moon is a weak attractor. Much easier at Saturn or Jupiter, where man-made probes could use massive and fast moons to brake at little expense.

 

An immediate capture by the Moon would need some very lucky combination where Earth and the Sun influence the object and, once a time window has passed, the object that coud approach the Moon with some excess energy stays with a binding energy. Intuitively, it must be improbable for an object already captured by Earth, and impossible for any reasonable speed of a object coming from, say, the Asteroid Belt.

 

A delayed capture must be possible with luck: a Moon slingshot permits capture by Earth, and later the Moon captures the object. Until it loses it.

Edited February 17, 2013 by Enthalpy

[Bill Angel]

Yes but I am writing a story that is about the earth moon system capturing another moon, i am thinking of a Ceres size body being nudged by humans until it is in orbit of the earth. i am thinking the safest orbit would be around the moon, but economically the orbit should be near the earth, maybe geosynchronous around the earth.

Since your interest seems rather speculative, Steven Hawking in a talk mentions the idea of a mini black hole orbiting the earth:

. A black hole of the mass of a mountain, would give off x-rays and gamma rays, at a rate of about ten million Megawatts, enough to power the world's electricity supply. It wouldn't be easy however, to harnass a mini black hole. You couldn't keep it in a power station, because it would drop through the floor, and end up at the center of the Earth. About the only way, would be to have the black hole in orbit around the Earth.

See: http://www.hawking.org.uk/into-a-black-hole.html

 

Perhaps there is some way to utilize the gravitational fields of the Earth and the Moon together to get such a mini black hole into an orbit about the Earth?

[Moontanman]

Would any of these orbital problems be less pronounced if the bodies in question were moved via super technology into as perfect an orbit as possible?

 

Ceres orbiting the Earth between the Earth and the Moon, would closer to the Earth be better? Geosynchronous?

 

Ceres orbiting very close to the Moon 5000 miles or less

[Enthalpy]

Human-intended capture using our Moon must first bring the new object to a very accurate trajectory, yes, because the benefit of our Moon is small. So you may ask if the technology that brings the new object could also capture it in Earth orbit altogether. We're talking about saving possibly 100m/s over several km/s.

 

I using our Moon, the new object should be much lighter, unless this would change our Moon's orbit much, which is frankly undesireable. Ceres is already too heavy for such a scenario.

 

Lagrange's point is at 59,000km from Moon's center, so I feel - nothing more than an impression - that 10,000km is already too far, and that Earth's tides would destabilize the orbit. I've read that no Moon orbit is stable, not even over a few years, but have no opinion about it.

 

There is only one geosynchronous orbit and it's already used...

 

Shall the super technology be already existing, already feasible, or still fiction? I described there

http://www.scienceforums.net/topic/76627-solar-thermal-rocket/page-2#entry757109and following message

to bring an icy asteroid to Mars' orbit, leaving 11,500t of water there. Earth would be but more difficult. That's far from Ceres' mass, but is a very limited development from our present technology.

[J.C.MacSwell]

 

 

Now, with all true gravitational bound objects they orbit their collective center of mass. This center of mass could lie inside one of the bodies, as it does for the Sun and the solar system. So for most purposes it is fine to say that we all orbit the Sun, but this is not quite the center of the Sun.

 

 

Is this correct? Surely, say, Mercury is orbiting the Sun's centre more so than the collective centre of mass? Not that they (Sun's centre of mass vs solar system as a whole) would be very far apart(still near the centre of the Sun), and still influenced of course by the other planets but it would seem to me the inverse square law would reduce the influence of the more distant planets more than a linear mass balance, with the Sun.

Edited February 4, 2015 by J.C.MacSwell

[Moontanman]

Human-intended capture using our Moon must first bring the new object to a very accurate trajectory, yes, because the benefit of our Moon is small. So you may ask if the technology that brings the new object could also capture it in Earth orbit altogether. We're talking about saving possibly 100m/s over several km/s.

Probably not the best place to ask this question, but I already had this thread from a while back, but we are not talking about human technology, from our standpoint it might as well be magic, I am trying to outline a story i want to write.

 

 

I using our Moon, the new object should be much lighter, unless this would change our Moon's orbit much, which is frankly undesirable. Ceres is already too heavy for such a scenario.

Too heavy to orbit the Moon or too heavy to use the gravity capture which is not an issue?

 

Lagrange's point is at 59,000km from Moon's center, so I feel - nothing more than an impression - that 10,000km is already too far, and that Earth's tides would destabilize the orbit. I've read that no Moon orbit is stable, not even over a few years, but have no opinion about it.

I was thinking of a very close in orbit of the moon, just beyond the Roche limit of the moon.

 

There is only one geosynchronous orbit and it's already used...

Used by what?

 

Shall the super technology be already existing, already feasible, or still fiction? I described there

http://www.scienceforums.net/topic/76627-solar-thermal-rocket/page-2#entry757109and following message

to bring an icy asteroid to Mars' orbit, leaving 11,500t of water there. Earth would be but more difficult. That's far from Ceres' mass, but is a very limited development from our present technology.

The kicker here is this is not human technology, the story is about a super civilization coming into our solar system and moving stuff around without ever contacting us, we never see them, the only evidence of their existence is the effect on our solar system. (of course some people are going to think it's god others aliens and the drama is the conflict between those groups.

 

Thanks for the answers, I should have started another thread in the lounge...

Is this correct? Surely, say, Mercury is orbiting the Sun's centre more so than the collective centre of mass? Not that they (Sun's centre of mass vs solar system as a whole) would be very far apart(still near the centre of the Sun), and still influenced of course by the other planets but it would seem to me the inverse square law would reduce the influence of the more distant planets more than a linear mass balance, with the Sun.

http://en.wikipedia.org/wiki/Jupiter

 

Jupiter is the only planet that has a center of mass with the Sun that lies outside the volume of the Sun, though by only 7% of the Sun's radius.[64]

 

 

http://en.wikipedia.org/wiki/Barycentric_coordinates_%28astronomy%29

 

In astronomy, barycentric coordinates are non-rotating coordinates with origin at the center of mass of two or more bodies.

The barycenter (or barycentre; from the Greek βαρύ-ς heavy + κέντρ-ονcentre + -ic^[1]) is the point between two objects where they balance each other. For example, it is the center of mass where two or more celestial bodies orbiteach other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that is not at the center of the primary (the larger body). For example, the Moon does not orbit the exact center of theEarth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km below the surface of the Earth (4,661 km from Earth's center, ~74% of Earth's radius), where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun.

 

 

The barycenter is basically how they detect planets around other stars, this illustration shows how our Sun wobbles

 

[J.C.MacSwell]

Is this correct? Surely, say, Mercury is orbiting the Sun's centre more so than the collective centre of mass? Not that they (Sun's centre of mass vs solar system as a whole) would be very far apart(still near the centre of the Sun), and still influenced of course by the other planets but it would seem to me the inverse square law would reduce the influence of the more distant planets more than a linear mass balance, with the Sun.

To AJB:

 

My bolded is incorrect, as per Moontanmans link. Jupiter moves the center of mass close (outside) to the perimeter of the Sun...I don't believe Mercury orbits that point, but something much closer to the Sun's center of mass for reasons stated

Edited February 4, 2015 by J.C.MacSwell

[Enthalpy]

With non-human technology, the Earth can get an other moon. I suppose a Ceres size wouldn't destabilize our Moon if the added orbit differs enough from Moon's one - both would be abnormally big as compared to Earth, which has already the biggest moon relative to the planet, if we don't count Pluto here.

 

Our Moon wouldn't help much a capture, so the technology that brought Ceres to Earth would have to make the capture too. Reaching a low Earth orbit is about as costly as bringing Ceres near to Earth, so a high orbit is more economical - but with unknown technology this may not be a limit.

[John Cuthber]

From time to time, the moon has had moons.

Some of the Apollo missions for example.

[Enthalpy]

Yes!

 

But what I've read - and have no opinion about - is that orbits around our Moon drift over just a few decades to either crash on the Moon or leave its attraction, because the tides by the Earth and even the Sun are so strong. No worry with a spacecraft, more so with a Ceres or even a small asteroid.

[Robittybob1]

Yes!

 

But what I've read - and have no opinion about - is that orbits around our Moon drift over just a few decades to either crash on the Moon or leave its attraction, because the tides by the Earth and even the Sun are so strong. No worry with a spacecraft, more so with a Ceres or even a small asteroid.

How do the tides fit in within the picture? Can you explain your concept of it please?

[Enthalpy]

A nice place to put Ceres on an Earth orbit might be on the same orbit as our Moon, 60° before or after it. This makes a stable configuration, as is observed with planetoids on the same orbit as Jupiter (known as Trojans) or as Earth, and with moons on the same orbit as other moons around Jupiter and Saturn. That's one place where Nasa could put the asteroid they plan to bring back. Though, I don't know if it works with two moons of similar mass.

 

How do the tides fit in within the picture? Can you explain your concept of it please?

 

Call it gravity gradient if you prefer so. Nearer to the Earth or the Sun, the attraction increases, while the centrifugal force at identical revolution period decreases, and this is expressed as a gradient, which is responsible for tides on Earth and is also commonly called tidal effect in space technology.

 

This gradient affects the orbits: Sun's gradient affects our Moon and the satellites around the Earth, and Earth's gradient affect the satellites around the Moon. It's strong enough to be a technically important perturbation to geosynchronous satellites around the Earth, despite the Sun is so far away, and Earth's gradient is much worse for satellites around the Moon.

 

I have no piece of software for that. The ones that make sensible predictions work only when all masses differ enough from an other so that the lighter one doesn't influence the heavier, or so little that the effect is added afterwards. Even then, software predicts the position of satellites only to a few months.

 

The full "three bodies" or N-bodies problem, where masses can be similar, is not solved analytically (Poincaré told it couldn't), and for a century, it was believed that the solutions were unstable. Meanwhile, astronomers have observed planets around double stars where they weren't expected, both orbiting far from two close stars and orbiting near one star of a loose double system, so at least some solutions are stable at astronomical timescale.

 

Software consistently lets one body escape from a three-body system despite we see planets, and for long, people considered this represented the true behaviour, but it seems now to be software imperfection like rounding errors or step size. The worry is: how to prove it?

[Robittybob1]

Do we orbit the center of mass of the solar system or just the center of mass between the Sun and The Earth? It was discussed on one thread on another forum but I've lost track of it. So if the two biggest objects in our Solar System have a Barycenter outside of the radius of the Sun then would Mercury be orbiting this center of mass as well?

Maybe that is the solution to the 3 body problems - do we have to go back to the combined Center of mass and orbit that.

Edited February 6, 2015 by Robittybob1

[Moontanman]

I appreciate everyone's help, I like to have the science at least semi accurate but the story is more important, it looks like that Ceres would not be stable in orbit of the Earth, I wanted it to be inside the Moons orbit but close enough to the Earth so the Moons gravity would not make it unstable, maybe an orbit of a few days at most. Since the Moons has a significant effect on the Earth a Ceres sized body would be affected by both the Earth and the Moon, might make for some interesting tides but I would like the system to be stable over geologic time...

 

I have several stories roughed out and now that i have WP back on my computer I can get started on a couple at least. I have one that is almost finished, when i get it done I'll post it so you guys can "critique" it...

[Robittybob1]

Do we orbit the center of mass of the solar system or just the center of mass between the Sun and The Earth? It was discussed on one thread on another forum but I've lost track of it. So if the two biggest objects in our Solar System have a Barycenter outside of the radius of the Sun then would Mercury be orbiting this center of mass as well?

Maybe that is the solution to the 3 body problems - do we have to go back to the combined Center of mass and orbit that.

Please: I would still like someone to answer this question if possible.

[J.C.MacSwell]

Do we orbit the center of mass of the solar system or just the center of mass between the Sun and The Earth? It was discussed on one thread on another forum but I've lost track of it. So if the two biggest objects in our Solar System have a Barycenter outside of the radius of the Sun then would Mercury be orbiting this center of mass as well?

Maybe that is the solution to the 3 body problems - do we have to go back to the combined Center of mass and orbit that.

I was hoping to hear back from AJB, but I am fairly sure Earth (and Mercury, though I don't believe it is exactly the same point) orbit something much closer to the centre of the Sun than the centre of mass of the Solar System.

 

Taking the 3 body problem of Sun, Jupiter, and Mercury, If we placed Jupiter far enough away the barycenter would lie outside Mercury's orbit. I think Mercury would still be in stable orbit about the Sun in that case, though of course the Sun and Jupiter would still essentially orbit about the (new) barycenter.

[Mordred]

All planets orbit the barycenter. Here is a handy simulator

 

http://www.orbitsimulator.com/gravity/articles/ssbarycenter.html

Moving Jupiter closer to the sun would cause a greater change in the barycenter than moving Jupiter away from the sun. The closer Jupiter gets to the sun the stronger its gravitational influence.

[J.C.MacSwell]

All planets orbit the barycenter. Here is a handy simulator

 

http://www.orbitsimulator.com/gravity/articles/ssbarycenter.html

Moving Jupiter closer to the sun would cause a greater change in the barycenter than moving Jupiter away from the sun. The closer Jupiter gets to the sun the stronger its gravitational influence.

That seems to be more about the Sun orbiting the barycenter, and each planets contribution to it.

 

Moving Jupiter closer would move the barycenter closer to the Sun's centre. I agree with the bold, the period of orbit (or wobble) would get shorter

[Robittybob1]

All planets orbit the barycenter. Here is a handy simulator

 

http://www.orbitsimulator.com/gravity/articles/ssbarycenter.html

Moving Jupiter closer to the sun would cause a greater change in the barycenter than moving Jupiter away from the sun. The closer Jupiter gets to the sun the stronger its gravitational influence.

Which barycenter? The Sun Jupiter one or the combined SS barycenter? Looking at the equation for the position of a barycenter the further apart the masses are the further out from the heaviest mass is the barycenter.

Do you agree with that?

That seems to be more about the Sun orbiting the barycenter, and each planets contribution to it.

 

Moving Jupiter closer would move the barycenter closer to the Sun's centre. I agree with the bold, the period of orbit (or wobble) would get shorter

Which is surprising for if you take that to a limit and take Jupiter to an extreme distance so that its gravitation attraction on the Sun is minimal you would wonder why the Sun's wobble would be the greatest. But certainly the frequency of the wobble reduces the further out the planet is.

[Mordred]

Here is a good article covers the reduced two body to one body method as well as the two body.

 

http://web.mit.edu/8.01t/www/materials/modules/guide17.pdf

Gotta catch my flight