Seeing the Earth circles the sun and our Moon circles the Earth, why would a comet or asteroid, passing closer to Earth than the Moon, maintain its orbit and not get captured into Earth’s orbit?
The reason, quite simply, is one of speed. The comet or asteroid is moving too fast to be captured into orbit around the Earth.
To see why, imagine a satellite orbiting the Earth. It’s moving in its orbit at some speed. If we make it go a little faster, the highest point in each orbit (the apogee) will be a little higher. If we keep making the satellite move faster and faster, eventually the high point in the orbit will be so far from the Earth that the satellite will experience a greater gravitational attraction from the Sun than from the Earth. When this occurs, the satellite will be in orbit around the Sun, rather than the Earth. The speed necessary to reach this point is called the “escape velocity.”
Just as an object needs to be moving faster than escape velocity to escape the Earth and enter orbit around the Sun, any object that follows the reverse path – that is, it is in orbit around the Sun but passes near the Earth – must also be moving at faster than escape velocity. Thus, we can see that if a comet or an asteroid passes close to the Earth, it is simply moving too fast to be captured into orbit – always moving at faster than the escape velocity, it will pass near the Earth and then escape into orbit around the Sun once more. This will occur regardless of whether it passes closer to the Earth than the Moon, or farther away; as it falls closer to the Earth it will speed up, always remaining above escape velocity.
In order to be captured into orbit around the Earth, the comet or asteroid would need to slow down to below escape velocity. But, out in the vacuum of space, there is really nothing that can slow the comet or asteroid, and so it will continue on its way, out into solar orbit again.