Papers and reference material contributing substantially to the programs on this web site.

Paper Index Paper Title - Author(s) and Journal or Publication Name.
Paper 1 Secular Terms of Classical Planetary Theories Using the Results of General Theory
J. Laskar
Astronomy and Astrophysics, 157, p59-p70 (1986)
Paper 2 Comparison of Bretagnon's VSOP82 Theory With Observations of Neptune
R.S. Gomes and S. Ferraz-Mello
Astronomy and Astrophysics, 185, p327-p331 (1987)
Paper 3 Planetary Theories In Rectangular and Spherical Variables. VSOP87 Solutions.
P. Bretagnon and G. Francou
Astronomy and Astrophysics, 202, p309-p315 (1988)

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Values marked with  *  are EXACT values or adopted standards.
Speed Of Light 299792458 m/s  * (NIST)
299792.458 km/s
186282.397 mi/s
1 Foot (ft) 0.3048 m  *
5280 ft  *
1 Statute Mile (mi) 1609.344 m  *
1.609344 km
1 Astronomical Unit  (AU) 149597871 km  * (IAU)
149597870.691 km ±0.030 (NASA/JPL)
92955807.267 mi
Light Time To Span 1 AU 499.0047838061356433 seconds
8 minutes and 19.004784 seconds
0.0057755183310895 day
Solar Radius 695508 km  *
432169 mi
Earth Radius 6356.755 km (Polar) 3949.904 mi
6367.448 km (Mean) 3956.549 mi
6373.140 km (Equatorial) 3960.086 mi
Lunar Radius 1736.0 km (Polar) 1078.7 mi
1737.1 km (Mean) 1079.4 mi
1738.1 km (Equatorial) 1080.0 mi
Geocentric Lunar Distance 363301 km (Min = Perigee) 225745 mi
384401 km (Mean) 238856 mi
405502 km (Max = Apogee) 251967 mi
Horizontal Parallax At 1 AU 8.79415"
Standard Julian Year 365.25 days  *
8766 hours
525960 minutes
31557600 seconds
Standard Gregorian Year 365.2425 days  *
31556952 seconds
1 Light Year (LY) 9460730472580.8 km
5878625373183.6 mi
63241.0770880709446742 AU
0.3066013952202032 pc
1 Parsec (pc) 30856775670468 km
206264.80624709635488 AU
3.2615637619058885 LY
Standard Earth Gravity
9.80665 m/s2  *
1.000 G  *
32.17405 ft/s2
Newtonian Constant Of Gravitation
0.0000000000667428 m3 / kg / s2
Stefan-Boltzmann Radiation Constant (σ)
0.000000056704 W / m2 / s / T4
Values marked with  *  are EXACT values or adopted standards.
Physical Constants - NIST   Planetary Fact Sheets - NASA

Planetary Theories in Rectangular and Spherical Variables
VSOP87 Solutions

Pierre Bretagnon, Gerard Francou
Astronomy and Astrophysics (1988)
Vol. 202, p309-p315

A scanned copy of this paper is available on this web site.

This source paper, by the original authors, Pierre Bretagnon and Gerard Francou, explains the derivation and mathematical foundations of the VSOP87 theory and how it all works.   Their extraordinary work lays the foundation upon which the long-term planetary positions programs on this web site are built, based on a full-precision implementation of the theory programmed in PHP 5x.

Astronomical Algorithms - 2nd Edition
Jean Meeus
Pub. Willmann-Bell, Inc. (1998)
ISBN 0-943396-61-1

Jean Meeus has published numerous valuable astronomical algorithms over the years, some of which have been adapted for use here and applied to the programming of this web site.

Secular Terms of Classical Planetary Theories Using the Results of General Theory
Astronomy and Astrophysics
Vol. 157, p68, Table 8 (1986)

J. Laskar

This is the source paper upon which the computation of the long-term obliquity of the ecliptic is based.   A scanned copy of this paper is available on this web site.

Explanatory Supplement to the Astronomical Almanac
U.S. Naval Observatory (1992)
ISBN 0-935702-68-7

This advanced reference book, published by the U.S. Naval Observatory, is a must-have for anyone interested in astro-computing.   It explains, in intricate detail, hundreds of the computations encountered in modern astronomy and used in the making of the published astronomical almanacs.

© Jay Tanner - PHP Science Labs - 2017