Orbit

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An orbit is the path that an object makes around another object under the influence of gravity.

The classical example is that of the solar system, where the Earth, other planets, asteroids, comets, and smaller pieces of rubble are in orbit around the Sun; and moons are in orbit around planets. These days, many artificial satellites are in orbit around the Earth.

For a system of only 2 bodies that are only influenced by their mutual gravity, their orbits can be exactly calculated according to the laws of motion and gravity of Newton. In this case, the orbit is a flat curve. Moreover, it is convenient to describe the motion in a coordinate system that is centered on the heavier body, and we can say that the lighter body is in orbit around the heavier body. The orbit can be open or closed, depending on the total kinetic+potential energy of the system.

  • An open orbit has the shape of a hyperbola (or in the limiting case, a parabola): the bodies approach each other for a while, curve around each other around the time of their closest approach, and then separate again forever. This is often the case with comets that occasionally approach the Sun.
  • A closed orbit has the shape of an ellipse (or in the limiting case, a circle). The bodies repeat their path after a constant period of time. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows:
  1. The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of the ellipse. Therefore the orbit lies in a plane, called the orbital plane. The point on the orbit closest to the Sun is called perihelion, the point most distant from the Sun is called aphelion. For the Moon and artificial satellites in orbit around the Earth, these points are called perigee and apogee respectively.
  2. As the planet moves around its orbit for a specific amount of time, the line from Sun to planet sweeps a constant area of the orbital plane, irrespective of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area.
  3. For each planet, the ratio of the 3rd power of its average distance to the Sun, to the 2nd power of its period, is the same constant value for all planets.

Except for special cases like Lagrangian points, for a system of 3 or more bodies the equations of motion can not be exactly solved mathematically: but they can be approached with arbitrary high accuracy. The expressions usually take the pure elliptic motion as a basis, and add perturbation terms to account for the gravitational influence of multiple bodies.

Because a body moving in a 3-dimensional space has 6 degrees of freedom (3 for its position in the 3-dimensional space, and 3 for its velocity in that space), its orbit is exactly determined by 6 independent parameters. Usually the following orbital parameters are used:

  1. mean axis
  2. eccentricity
  3. inclination
  4. longitude of the perihelion
  5. longitude of the ascending node
  6. mean anomaly at the epoch