Is it possible for something that size to go into an orbit at some altitude?
Or are there speed and size contraints?
Sure. Mars is considerably smaller than the Earth, but both its moons, Phobos and Deimos, are believed to be captured asteroids. All that matters is that the asteroid or comet have the right trajectory and velocity with respect to the Earth in order to achieve a stable orbit.
It could happen, but it would be very very rare. The comet/asteroid would be orbiting the sun, so its velocity relative to the earth is probably going to be much greater than the speed of any orbit around the earth. Almost all orbits are going to be hyperbolic with respect to the earth, the body would have to be in precisely the right place with precisely the right velocity to be captured, and even then it’s likely to be in an extremely elliptical orbit.
And even if it’s captured temporarily, I don’t think there are many places where it can achieve a stable orbit. The earth has an enormous moon, and its gravity would disturb other objects that try to orbit the earth.
Given that the Earth already has a moon (and quite a sizeable one at that), it would be possible for us to capture very large comets, asteroids, and the like. Without the moon, though, it would be impossible: Anything that started off not captured would end up either not captured, or smacking into the surface (not what most folks would consider an “orbit”).
I beleive that is only true of a 2 mass system. If you add in other masses or better yet collisions you can get into a semi-stable orbit (semi = 1,000,000 of years).
Almost impossible; a near Earth asteroid that happened to be moving under escape velocity could be captured, and in fact there are likely to be several in resonant orbits. Here’s an article on Cruithne, a second very tiny “Moon” of Earth. Such orbits are ultimately unstable, of course, unless they get a close pass by the Moon that circularizes the orbit, but the Earth can capture small asteroids indefinitely.
Comets, on the other hand, which come from the outsystem (likely the Oort Cloud) would almost certainly be moving too fast to be captured.
Stranger
On further thought could frame shifting allow a 2 mass system to ‘capture’ each other.
I wouldn’t describe an object in a horseshoe orbit as “captured” by the Earth. Captured by the Sun, sure (presumably with the Earth’s help, just as the Moon could help the Earth capture something). But if the Earth suddenly ceased to exist, Cruithne wouldn’t even notice until it came time to exchange momentum, at which point it’d just continue on a normal elliptical orbit around the Sun.
I should add to my previous answer, by the way, that anything captured by an n-body system will be in an unstable orbit. It may last a very long time, but if an object can go from free to a particular orbit, it can also go from that orbit to free (that is to say, get ejected from the system). This has practical implications for launching non-time-critical spacecraft (unmanned probes to other planets, for instance), because if you can get into one of those unstable orbits, a very small amount of fuel can suffice to nudge you into being ejected, in the direction you want to go.
Not really. If an object isn’t in orbit around earth to begin with, by definition it’s above escape velocity. If it happens to “fall” towards earth it would gain speed. Its speed would always be above escape velocity unless it hits a third object (or influenced by the gravity of a third object) and loses speed.
I stand corrected.
Stranger