Variations séculaires des orbites planétaires

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The Variations séculaires des orbites planétaires ( VSOP , German " secular variations of the planet orbits ") is a planetary theory , a method for calculating the orbits for the planets of the solar system with very high accuracy. VSOP87 , for example, reaches a maximum angular deviation of one arc second for the inner planets 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 developed: VSOP87 , VSOP2000 and VSOP2002 . It is - with the 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 through Neptune .

The elliptical orbit of a planet in a two-body system can be described comparatively easily by specifying its six orbit elements . VSOP82 describes the orbits of the large planets by specifying the orbital elements. However, these path elements are variable over time. They describe the Kepler orbit that clings as closely as possible to the actual planetary orbit at the given point in time (so-called osculating orbit ). These path elements are calculated using suitable power series .

VSOP87

The VSOP87 is a further development of the VSOP82 theory published in 1987 by Bretagnon and G. Francou. With it, there is the possibility of reducing the computational effort by omitting rear terms - at the expense of accuracy, of course. It also offers direct calculation of the heliocentric coordinates.

There are several variants of the theory available:

VSOP87: Similar to the less precise predecessor version VSOP82, it contains series developments for the (variable) orbital elements of the planets. After determining the orbital elements valid for the desired point in time, the planetary position must then be calculated using the usual methods of ephemeris calculation.
VSOP87A: contains series expansions which directly provide the heliocentric Cartesian coordinates of the planets for the standard equinox J2000.0 .
VSOP87B: Series expansion of the heliocentric spherical coordinates ( ecliptical longitude , ecliptical latitude and radius vector ) of the planets for J2000.0.
VSOP87C: Series expansion of the heliocentric Cartesian coordinates for the equinox of the date
VSOP87D: Series expansion of the heliocentric spherical coordinates for the equinox of the date
VSOP87E: Series expansion of the barycentric Cartesian coordinates for J2000.0.

In addition to the convenience, to provide the desired coordinates directly, variants A to E have the advantage, with lower accuracy requirements to be able to abort the calculation of the rows when the desired accuracy is achieved. When using the VSOP87 itself, it would be difficult in this case to determine the accuracy with which the individual path elements supplied by this variant must be calculated in order to ultimately obtain the resulting coordinates with the desired accuracy.

The VSOP87A – E is based on a power series expansion in the argument of time up to the 5th power, the respective factors of which are broken down by a Fourier analysis . This is recorded in tables with decreasing contribution so that the contribution to the total error can be estimated using the coefficients.

VSOP2000

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

VSOP2002

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

publication

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

example

For the tropical year it results

  1. according to VSOP 87:
    365.242 189 623 - T × 0.000 061 522 - T 2 × 0.000 000 060 9 + T 3 × 0.000 000 265 25
  2. according to the VSOP2000:
    365.242 190 516 6 - T × 0.000 061 560 - T 2 × 0.000 000 068 4 + T 3 × 0.000 000 263 0 + T 4 × 0.000 000 003 2
T in Julian millennia (1000 × 365.25 days with respect to J2000.0 ), i.e. H. T = ( JD - 2,451,545.0) / 365,250.

Web links

  • The VSOP87 on the FTP server of the Institut de mécanique céleste et de calcul des éphémérides ( IMCCE ) (accessed on April 5, 2005)
  • The VSOP2010 on the FTP server of the IMCCE (accessed on January 2, 2015)
  • The VSOP2013 and the corresponding Chebyshev approximation on the FTP server of the IMCCE (accessed on January 2, 2015)

Individual evidence

  1. ^ P. Bretagnon, G. Francou: Planetary theories in rectangular and spherical variables. VSOP87 solutions . In: Astronomy & Astrophysics . No. 202 , 1988, pp. 309-315 , bibcode : 1982A & A ... 114..278B .
  2. ^ A b P. Bretagnon: Théorie du mouvement de l'ensemble des planètes. Solution VSOP82 . In: Astronomy and Astrophysics . No. 114 , 1982, pp. 278–288 , bibcode : 1982A & A ... 114..278B (English).
  3. ^ A b P. Bretagnon, G. Francou: Planetary theories in rectangular and spherical variables. VSOP87 solutions . In: Astronomy and Astrophysics . No. 202 , 1988, pp. 309–315 , bibcode : 1988A & A ... 202..309B (English).
  4. ^ X. Moisson, P. Bretagnon: Analytical Planetary solution VSOP2000 . In: Celestial Mechanics and Dynamical Astronomy . tape 80 , no. 3-4 . Springer, July 2001, p. 205-213 , doi : 10.1023 / A: 1012279014297 .
  5. ↑ A. Fienga, J.-L. Simon: Analytical and numerical studies of asteroid perturbations on solar system planet dynamics . In: Astronomy and Astrophysics . No. 429 , 2005, pp. 361–367 , doi : 10.1051 / 0004-6361: 20048159 (English, aanda.org [PDF; 1.7 MB ] c ESO 2004).
  6. ^ Jean Meeus: Astronomical Algorithms . 1st English edition. Willmann-Bell, Richmond, Va 1999, ISBN 0-943396-35-2 .
  7. ↑ Hermann Mucke: Wandelgestirnorte . In: Mucke (ed.): Modern astronomical phenomenology. 20th Sternfreunde Seminar, 1992/93 . Zeiss Planetarium of the City of Vienna and Austrian Astronomical Association, Vienna 1992, 2. Calculating the heliocentric location of the large planets Mercury to Neptune - The planetary theories VSOP82 and VSOP87, p. 1-23 .