Horseshoe orbit

The horseshoe orbit of the horseshoe orbit or even the horseshoe path is a special orbit of a co-orbital object that orbits a central star along with a second (usually much larger ) body in the same or a very similar orbit. In normal rest frame the orbit of the co-orbital companion like a regular elliptical Kepler orbit looks. From the movement of the larger object to the central star comoving system ( in which the larger celestial body seems to rest ) one then sees only the relative motion of the co-orbital companion. The co-orbital companion describes of this reference system as seen along the orbit of the larger body a wide berth, which he periodically back and swings. The shape of the sheet resembles a horseshoe, hence the name horseshoe orbit.

Stability

Because of their very similar orbits co-orbital objects have the same mean orbital period around the central star as the larger celestial body. You are in gravitational interaction with the larger celestial bodies and are due to the same average orbital period in a so-called 1:1 orbital resonance. Such orbits are stable only under certain conditions, one of which is the most important in the normal case where the co-orbital companion in relation to the larger body has a vanishingly small mass (so-called restricted three-body problem ).

However body on a horseshoe orbit must have non-negligible mass to assume a stable orbit (see Examples section ).

Explanation

The left figure shows a possible horseshoe orbit an object in the Sun-Earth system: Both earth and the object will rotate in unison counterclockwise around the sun. In this case, the object is sometimes more, sometimes less distant from the earth. This position relative to the sun and the earth changes with time, and describes the horseshoe path shown.

Suppose that the object is in front of the earth at the point E in a circular orbit. Since this sheet is lower (by the sun ), its rotational speed is a little higher than that of the earth, and it slowly moves away from it. On this track the object remains until it orbits the Sun once almost.

At point A, the object is again close to the earth ( now, however, behind her ). The object is now attracted by the gravitational force of the earth and accelerated along the revolving path (that is anticlockwise). Due to the increased centrifugal force as it drifts outwards until its orbital speed is again smaller than that of the earth (from point B) and it starts to fall back behind the earth.

After some time the object is again outside the sphere of influence of the Earth's gravity is no longer accelerated and is back on a circular path on which it continues to drift away from the Earth ( point C). On this path, it moves again to the sun (this time in the opposite direction).

In point D of the gravitational influence of the earth begins to act, however of "rear" pulls this time, and decelerates the object, so that the centrifugal force is decreased again and it falls into a lower orbit whereby its rotational speed again increases to the point where it the influence of the earth leaves again. Here at point E, the orbit starts anew.

Transition to Trojans

The transition from a trojan to a horseshoe track is fluid: If the distance of a Trojan for the Lagrange point L4 or L5 is too large, then it is even on the orbit exceed the larger celestial body opposite point and then move towards the other Lagrange point and thus in a big bow back and swing.

Examples

So far, few objects are known only on horseshoe orbits. Remarkably, the two previously known co-orbital companion of the Earth, asteroid 2002 AA29 are (an object with less than 100 m in diameter ) and about 300 m wide in 2010 SO16. A quasi- satellite of the Earth was in the years 1996 to 2006, the small asteroid 2003 YN107, since the same again describes a horseshoe orbit along the Earth's orbit. Two other co-orbital objects in unusual horseshoe orbits are the small, almost equal to Saturn's large moons Janus and Epimetheus, which rotate on very similar orbits Saturn, every four years are very close and share their orbits.