Kepler orbit

Kepler orbits are ideal web forms, on which a small celestial body moves around a larger one. It is the conic sections: circle, ellipse, parabola and hyperbola.

Parameter is the eccentricity, the relative path to the large axis distance between the ellipse center and focal points is in the closed Kepplerbahn Kepler ellipse. On Kepplerellipsen move as the planets around the sun and the moon around the earth.

The motion of two celestial bodies with each other is referred to as two-body problem. In general, this move both bodies. Kepler problem as a two-body problem is referred to, when one of the two bodies is substantially greater than the other. The movement of the larger body is ignored, its center of mass is assumed to be the center for the motion of the lower body.

Kepler orbits

Is a prerequisite for the adoption of a Keplerian orbit in an ideal form of an exact conic section, except that the two bodies in the two-body system there are no other celestial bodies or are far enough away to pose no interference of the movements in the two-body system. The ideal motion of a smaller celestial body by a larger (central star ) Kepler has described three laws, the first relates to the web form.

In polar coordinates with origin in the central star can be the geometric shape of the Kepler orbits described by the following formula:

This is the distance of the orbiting celestial body from the central star, he occupies at vorgebenem angle ( true anomaly ) between the lines connecting the central star - periapsis and central star luminaries.

The two constants ( eccentricity ) and (half- parameters) describe the shape of the Keplerian orbit:

The interval in which the angle is varied, depending on the type of the web and, in the case of the hyperbola, the eccentricity of:

Celestial bodies on parabolic orbits and hyperbolic orbits have the central star of a so-called unbound state. They approach the latter only once. Examples are some comets that disappear after a single approximation to the sun without recurrence of the solar system.

Kepler orbits can be described by so-called six orbital elements.

Disturbing forces

Due to irregular or more celestial bodies, however, the gravitational field is not spherically symmetric, thus perturbations arise. Even small retarding effects caused by gases or meteoroids, radiation pressure, and according to the theory of relativity contribute to them. Thus, the numerical values ​​of the six orbital elements change slowly.

It is this time-dependent effects or periodic basis by using the method " variation of the elements ", each instantaneous ( " osculating " ) Kepler ellipse merges continuously into the next. The perturbations can be long time (always in the same direction ) or periodically. In the vicinity of irregularly shaped celestial bodies or when flying through clouds of matter and irregular effects occur.

The path axes ( a) of the eight planets of our solar system remain practically constant, because their masses are large and the orbits are circular similar. Minor planets ( asteroids ) and comets can learn but serious changes if they come close to a planet. At low artificial satellites, the perturbations amount to a few tenths of a degree per hour or kilometers and some suggest the exact shape of the geoid.

Strictly speaking, exact Keplerian orbits are only valid for spherical bodies, but this condition for longer distances in astronomy adequately met. Also for the moon orbits around highly oblate planet (eg Jupiter's moons ) can be approximated with Kepler count formulas when the third Kepler law is supplemented by a small factor. De facto running this ( in addition to the path axis a) to a seventh path element for the circulation overtime.