# VSOP (planets)

The Variations Séculaires of Orbite Planétaires ( VSOP, German "Secular variation of the planetary orbits ") is a planetary theory, a method for calculating the orbits of the planets of the solar system with very high accuracy. VSOP87 about reaching for the inner planets a maximum angular deviation of one arc second over the period from 2000 BC to 6000 AD.

It was founded in 1982 by Pierre Bretagnon, a member of the Bureau des Longitudes in Paris, published ( VSOP82 ), and has since been further developed: VSOP87, VSOP2000 and VSOP2002. It applies - with extensions - still today (2006 ) as a reference for the numerical modeling of the dynamics of the solar system.

## VSOP82

The VSOP82 - theory is a method of calculating the planetary positions for the planets Mercury to Neptune.

The elliptical orbit of a planet in the two-body system can be relatively easy to describe by specifying its six orbital elements. VSOP82 describes the orbits of the giant planets also by specifying the orbital elements. However, these orbital elements are variable in time. They describe that Keplerian orbit, the actual planet's orbit as possible at the given time conforms (so-called osculating train). These orbital elements are calculated via suitable power series.

## VSOP87

The VSOP87 is a development of VSOP82 theory, which was published in 1987 by Bretagnon and G. Francou. In her there is the possibility to reduce the computation complexity by eliminating rear Terme - of course at the expense of accuracy. It also provides direct calculation of the heliocentric coordinates.

There are several variants of the theory are available:

Besides the convenience, directly provide the desired coordinates, provide the variants A to E also has the advantage of being able to abort the calculation of the ranks at lower accuracy requirements, once the desired accuracy is reached. When using the VSOP87 itself it would be difficult to determine in this case, the accuracy with which the data supplied by this variant individual path elements must be calculated to obtain ultimately the resulting coordinates to the desired accuracy.

The VSOP87A -E is based on a power series expansion in the argument of time until the 5th power, their respective factors are broken down by a Fourier analysis. This is presented in tables descending contribution, so that using the coefficients of the contribution can be estimated to the total error.

## VSOP2000

For several years there has been an update that VSOP2000 of Xavier and Pierre Moisson Bretagnon which is more accurate than previous versions by a factor of 10-100 and error of nurmehr some 0.1 mas for Mercury, Venus and Earth for the interval 1900-2000 having.

## VSOP2002

Bretagnons last work was the implementation of relativistic effects, and a further increase by a factor of 10 - the VSOP2002 remained unfinished and shows weaknesses in Uranus and Neptune.

## Publication

Although the construction methods of VSOP82 and VSOP87 and their properties have been described in the astronomical literature, these theories are not included even in the publications. They could only be obtained on magnetic tape originally, but are now available over the Internet. For applications with lower accuracy requirements " Astronomical Algorithms" by Jean Meeus or the Austrian Astronomical Association excerpts of these lists periodic terms have been published in the book.

## Example

For the tropical year results