A "horseshoe orbit" is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body . The orbital period of the smaller body is very nearly the same as for the larger body, and its path appears to have a horseshoe shape in a rotating reference frame as viewed from the larger object.
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 the larger body's orbit over a long period of time. When the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, with the larger body between the 'horns'.
Asteroids in horseshoe orbits with respect to Earth include 54509 YORP, , and , and possibly . A broader definition includes 3753 Cruithne, which can be said to be in a compound and/or transition orbit, or and .
Saturn's moons Epimetheus and Janus occupy horseshoe orbits with respect to each other .
The following explanation relates to an asteroid which is in such an orbit around the Sun, and is also affected by the Earth.
The asteroid is in almost the same solar orbit as Earth. Both take approximately one year to orbit the Sun.
It is also necessary to grasp two rules of orbit dynamics:
#A body closer to the Sun completes an orbit more quickly than a body further away.
#If a body accelerates along its orbit, its orbit moves outwards from the Sun. If it decelerates, the orbital radius decreases.
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