Horseshoe orbit

The orbit of 2002 AA29 and the Earth. Image: JPL

A horseshoe orbit appears when a viewer on an orbiting body (like Earth) watches the movement of another orbiting body, whose orbit is skinnier (more eccentric), but has about the same period. As a result, the path appears to have the shape of a kidney bean.

The loop is not closed but will drift forward or backward slightly each time, so that the point it circles will appear to move smoothly along Earth's orbit over a long period of time. When the object approaches Earth closely at either end of its trajectory, gravitational exchange of energy changes the object's apparent direction. Over an entire cycle the loops will fill out a horseshoe shape, with the Earth in the horseshoe's gap.

Several asteroids (such as 3753 Cruithne and 2002 AA29) are known to occupy horseshoe orbits with respect to Earth. Saturn's moons Epimetheus and Janus occupy horseshoe orbits with respect to each other (in their case, there is no repeated looping: each one traces a full horseshoe with respect to the other).

Orbital cycle

In the following, "A" refers to the object that is tracing out the horseshoe with respect to the planet or moon. The primary is the object the planet/moon is itself orbiting.

If A's orbit is slightly inside the orbit of the planet/moon, A orbits slightly faster than that planet/moon. If A started in front of the planet, it would slowly drift ahead because it's orbiting faster.

Conversely, if A's orbit is slightly outside the orbit of the planet/moon, it orbits slightly slower. If A started a bit behind the planet, it will slowly drift behind because it's orbiting slower.

Starting from the high orbit (slower), A falls behind the planet and drifts away. But it is still in almost the same orbit. So eventually A drifts all the way around the orbit and approaches the planet from its front.

As A gets closer, the planet's gravitational pull increases. This reduces A's orbital velocity, so it drops inward with respect to the primary. The drop releases energy, so A speeds up as it settles in its new, faster, inner orbit. So A starts drifting away from the planet, because it is now moving faster.

A drifts around the orbit and catches up to the planet from behind. Now the planet's gravity increases A's velocity, which causes it to rise outward with respect to the primary. This absorbs energy, and A slows down as it settles in its new, slower, outer orbit. A now drifts away behind the planet (more accurately, the planet pulls away ahead of A).

If this cycle is observed from the Earth, it looks like the asteroid moves slowly toward the Earth over a period of years. Then it mysteriously starts moving toward or away from the Sun. Finally it starts moving away from the Earth, without ever going around the Earth.

The cycle happens over the span of hundreds of actual orbits around the Sun or other central body. But from the perspective of someone standing on the planet, it looks like the asteroid is traveling in a horseshoe shaped orbit.

Orbital cycle

See also