## Can the Earth have an asteroid stuck in permanent orbit like our moon?

Good morning,

I've searched about this case in the internet but just found things about asteriods sharing the same orbit as earth over the sun, but I wonder if an asteroid can get stuck in earth's orbit like the moon.

Thanks!

 I am not a scientist of any sort, just a huge fan of the universe that likes to read about it. I have just finished a book called Cosmos by Giles Sparrow and I have learned that large gas giants such as Jupiter and Saturn have irregularly shaped moons which are believed to be asteroids who have become trapped by the tremendous gravity of the large planets. With that being said I could not say for certain that an asteroid could become trapped in an orbit around Earth. I do not know the specific formulas to calculate gravitational effects on orbital patterns, however I imagine if an asteroid with a specific size and velocity came within a specific distance to the Earth it could be pulled into orbit. Probably very elliptical at first and over time would orbit in a more circular pattern. Anyone with actual knowledge of this please correct anything I said that is misleading or wrong.
 Mentor Blog Entries: 1 It's entirely plausible that an asteroid could fall into orbit around the world, given the right altitude and speed.

## Can the Earth have an asteroid stuck in permanent orbit like our moon?

 Quote by ryan_m_b It's entirely plausible that an asteroid could fall into orbit around the world, given the right altitude and speed.

Not wanting too much to ask. There is any software or math formula to calculate this?

I wonder what is the maximum size of this asteroid.

 Quote by TitanRZ Thanks for the fast answer! Not wanting too much to ask. There is any software or math formula to calculate this? I wonder what is the maximum size of this asteroid.
Maximum size would be one that's large enough to affect the orbits of Earth and Moon.

Note that all the planets outside Earth's orbit have two or more moons. There's little reason why Earth couldn't. An asteroid could happily orbit way out beyond the Moon.

It would have to be far out, really. The Moon is so large relative to Earth that they're effectively a binary system. Any asteroid would have to be far enough away so as to see the Earth-Moon system as essentially one gravitational point, otherwise the orbit is unstable.

 Recognitions: Gold Member The conditions has to be just right and it will only happen with some help from the Moon and perhaps also the atmosphere. In terms of everyday likelihoods, it would be an exceedingly rare event to have a significantly sized asteroid captured into Earth orbit. And then to have such an orbit being a stable orbit in the Earth-Moon system would be an even more rare event, as most orbits that gets anywhere near the Moon sooner or later will result in the object either impacting the Moon or Earth, or being ejected from the Earth-Moon system. Without doing the "math", I would venture a guess that you are most likely to live your whole life without such a stable capture of an asteroid ever occurring. See also http://earthsky.org/space/asteroids-accretion

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 Quote by TitanRZ ...Not wanting too much to ask. There is any software or math formula to calculate this? I wonder what is the maximum size of this asteroid.
If you have a Windows computer you can use Gravity Simulator, which is a program I wrote, to try out different capture scenerios: www.gravitysimulator.com

Asteroids can get captured through the L1 or L2 regions. This happened in 2006. Asteroid 2006 RH120 (aka 6R10DB9) was captured into Earth orbit in the L1 region. It orbited Earth for 15 months before escaping Earth orbit through the L2 region. This object is beleived to be 3-6 meters in diameter. For every object 3-6 meters in diameter, there are probably thousands of objects 3-6 cm in diameter. So I think it is highly likely that Earth has some meteoroids orbiting it now. Asteroids captured in this manner don't stay very long. They need to lose energy so the can't climb back out to the L1 or L2 regions.

Here's a link to a Gravity Simulator simulation I did with this object. You can download the simulation and run it on your own computer: http://www.orbitsimulator.com/cgi-bi...1182030550/0#0

The Moon can help capture an asteroid with a gravitational assist that robs the asteroid of energy. But such an asteroid would be in a Moon-crossing orbit, and would probably only complete a few orbits before the Moon ejects it.

An asteroid can also graze Earth's atmosphere, robbing it of energy and capturing it into Earth orbit. But such an asteroid would always have its perigee inside Earth's atmosphere, so it would sprial down before crashing into Earth. There was some speculation that this happened (10-20 years ago I think), when a group of observers saw a bright fireball that escaped back into space. Hours later, and hundreds of miles away another group of observers saw a bright fireball. This caused some to speculate that it was the same object. The first pass through the atmosphere captured it into an elliptical orbit. The second pass through destroyed it.

One possible way of capturing an asteroid into a stable orbit is to have a double asteroid pass through the Earth/Moon system. As it gets close to Earth, the pair of asteroids become unbound from each other, one gaining energy and one losing energy, with the one losing energy being left in a stable orbit. Some think that this is how Neptune captured Triton.

Stable prograde orbits can not exist beyond the Moon's orbit. The Moon would destabalize them. But stable retrograde orbits can exist beyond the Moon's orbit out to about 800,000 km.

Once asteroids get as large as Ceres, we stop calling them asteroids, and start calling them dwarf planets. Ceres, at 1/77 the mass of the Moon, is not massive enough to disrupt the Earth / Moon system. So the answer to "how big" is as big as you want.

 Thank you for the answers they were very enlightening! I hope you all have a good night.
 see 3753 Cruithne http://en.wikipedia.org/wiki/3753_Cruithne You get very complicated orbital dynamics between the earth, moon, and sun.
 Recognitions: Gold Member Science Advisor A small asteroid could get stuck in a Lagrange point.

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 Quote by Chronos A small asteroid could get stuck in a Lagrange point.
But for an asteroid to enter the Earth-Moon system and come "to rest" at a Lagrange point it must somehow loose some of its excess hyperbolic speed and it must do so very close to the point. In addition, all Lagrange points in the Earth-Moon system are unstable so the asteroid would eventually move away from the point again.

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 Quote by Filip Larsen But for an asteroid to enter the Earth-Moon system and come "to rest" at a Lagrange point it must somehow loose some of its excess hyperbolic speed and it must do so very close to the point. In addition, all Lagrange points in the Earth-Moon system are unstable so the asteroid would eventually move away from the point again.
L4 & L5 can be stable for millions of years. But you're right, coming to rest in these regions would be unusual.

 Mentor I'm not sure Cruithne is a very good example. Cruithne is a body in an orbit around the sun, more elliptical than the earth's, and with a similar period, so it appears to circle the earth in an earth-centered coordinate system. However, it never is gravitationally bound to the earth. A better example, although not one without its own problems is J002E3. This is an object which periodically is captured by the earth, orbits a few times, and then is ejected by gravitational perturbations from the sun and moon. It then orbits the sun until it falls back in to earth orbit. A close lunar approach could put it in permanent earth orbit - it would need to be a "reverse slingshot", where it loses velocity rather than gains it. The problem I alluded to is that J002E3 is almost certainly artificial, and the most likely candidate is the third stage of Apollo 12. The reason I say that it is artificial is because its surface is covered in paint.
 Mentor I'm not sure Cruithne is a very good example. Cruithne is a body in an orbit around the sun, more elliptical than the earth's, and with a similar period, so it appears to circle the earth in an earth-centered coordinate system. However, it never is gravitationally bound to the earth. A better example, although not one without its own problems is J002E3. This is an object which periodically is captured by the earth, orbits a few times, and then is ejected by gravitational perturbations from the sun and moon. It then orbits the sun until it falls back in to earth orbit. A close lunar approach could put it in permanent earth orbit - it would need to be a "reverse slingshot", where it loses velocity rather than gains it. The problem I alluded to is that J002E3 is almost certainly artificial, and the most likely candidate is the third stage of Apollo 12. The reason I say that it is artificial is because its surface is covered in paint.

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 Quote by Vanadium 50 ...A close lunar approach could put it in permanent earth orbit - it would need to be a "reverse slingshot", where it loses velocity rather than gains it...
But a close lunar approach would leave it in a lunar-crossing orbit. Interior to the Moon, it needs something to cause it to lose more energy so its apogee was well out of the Moon's grasp. Otherwise it would make a few orbits before the Moon ejected it.

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 Quote by TitanRZ Thanks for the fast answer! Not wanting too much to ask. There is any software or math formula to calculate this? I wonder what is the maximum size of this asteroid.
The size won't matter much.

It actually isn't that hard to calculate whether or not an asteroid would be captured by the Earth's gravity. You look at the object's relative velocity (relative to the Earth) and its distance from Earth and calculate it's specific energy (relative to Earth). If that specific energy is negative, then it will be captured by Earth's gravity. If that specific energy is 0 or greater, then the object won't be captured.

$\epsilon = \frac{v^2}{2} - \frac{\mu}{r}$

$\epsilon$ is the specific energy per unit of mass relative to Earth
$\mu$ is the geocentric gravitational constant (the universal gravitational constant times the Earth's mass)
v is object's speed relative to Earth
r is the object's distance from Earth

Essentially, you have an object orbiting the Sun in a fairly similar trajectory to the Earth's (otherwise, the relative velocity would surely be too large). The object is still orbiting the Sun (just as the Moon is), but with periodic perturbations that cause it to circle the Earth. In practice, from an Earth reference frame, the object is orbiting the Earth, but looking at it from outside the system might help to visualize just how the capture would happen and the limitations for it to occur (the fact that it has to be close to the same distance from the Sun as the Earth with a velocity close to the same as the Earth's).

As others mentioned, the object would also be affected by other objects besides the Earth - most significantly by the Moon. The chances of getting a stable orbit would be small, mainly because of the difficulty of getting a trajectory similar enough to Earth's to be captured in a fairly circular, stable orbit not disrupted by the Moon; but not in a trajectory so similar that Earth puts the object into a solar orbit similar to Cruithne's.

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