Fundamental Astronomy

Table C.11. Osculating elements of planetary orbits
on JD 2451600.5 (Feb 24, 2000). a = semimajor axis,
e = eccentricity i = inclination, Ω = longitude of ascend-
C. Tables
ing node, ϖ = longitude of perihelion, L = men longitude,
Psid = mean sidereal orbital period (here 1 a means a Julian
year, or 365.25 days), Psyn = mean synodic period
a e i Ω ϖ L Psid Psyn
[AU] [10 6 km] [ ◦ ] [ ◦ ] [ ◦ ] [ ◦ ] [a] [d] [d]
Mercury 0.387 57.9 0.2056 7.01 48.3 77.5 119.4 0.2408 87.97 115.9
Venus 0.723 108.2 0.0068 3.39 76.7 131.9 270.9 0.6152 224.7 583.9
Earth 1.000 149.6 0.0167 0.00 143.9 102.9 155.2 1.0000 365.3 –
Mars 1.524 228.0 0.0934 1.85 49.6 336.1 24.5 1.8807 686.9 779.9
Jupiter 5.204 778.6 0.0488 1.30 100.5 15.5 39.0 11.8565 4,330.6 398.9
Saturn 9.582 1433.4 0.0558 2.49 113.6 89.9 51.9 29.4235 10,747 378.1
Uranus 19.224 2875.8 0.0447 0.77 74.0 170.3 314.1 83.747 30,589 369.7
Neptune 30.092 4501.7 0.0112 1.77 131.8 39.5 305.5 163.723 59,800 367.5
Table C.12. Mean elements of planets with respect to the
equator and equinox of J2000.0. The variable t is the time in
days since J2000.0 and T is the same time in Julian centuries:
t = J − 2451545.0, T = t/36525. L is the mean longitude,
L = M + ϖ. The elements do not contain periodic terms,
and the accuracy of the positions computed from them is
of the order of a few minutes of arc. The values are from the
Explanatory Supplement to the Astronomical Almanac. The
elements of the Earth describe the orbit of the barycentre of
the Earth–Moon system
Mercury a = 0.38709893 + 0.00000066T e= 0.20563069 + 0.00002527T
i = 7.00487 ◦ − 23.51 ′′ T Ω = 48.33167 ◦ − 446.30 ′′ T
ϖ = 77.45645 ◦ + 573.57 ′′ T L = 252.25084 ◦ + 4.09233880 ◦ t
Venus a = 0.72333199 + 0.00000092T e= 0.00677323 − 0.00004938T
i = 3.39471 ◦ − 2.86 ′′ T Ω = 76.68069 ◦ − 996.89 ′′ T
ϖ = 131.53298 ◦ − 108.80 ′′ T L = 181.97973 ◦ + 1.60213047 ◦ t
Earth + Moon a = 1.00000011 − 0.00000005T e= 0.01671022 − 0.00003804T
i = 0.00005 ◦ − 46.94 ′′ T Ω =−11.26064 ◦ − 18,228.25 ′′ T
ϖ = 102.94719 ◦ + 1198.28 ′′ T L = 100.46435 ◦ + 0.98560910 ◦ t
Mars a = 1.52366231 − 0.00007221T e= 0.09341233 + 0.00011902T
i = 1.85061 ◦ − 25.47 ′′ T Ω = 49.57854 ◦ − 1020.19 ′′ T
ϖ = 336.04084 ◦ + 1560.78 ′′ T L = 355.45332 ◦ + 0.52403304 ◦ t
Jupiter a = 5.20336301 + 0.00060737T e= 0.04839266 − 0.00012880T
i = 1.30530 ◦ − 4.15 ′′ T Ω = 100.55615 ◦ + 1217.17 ′′ T
ϖ = 14.75385 ◦ + 839.93 ′′ T L = 34.40438 ◦ + 0.08308676 ◦ t
Saturn a = 9.53707032 − 0.00301530T e= 0.05415060 − 0.00036762T
i = 2.48446 ◦ + 6.11 ′′ T Ω = 113.71504 ◦ − 1591.05 ′′ T
ϖ = 92.43194 ◦ − 1948.89 ′′ T L = 49.94432 ◦ + 0.03346063 ◦ t
Uranus a = 19.19126393 + 0.00152025T e= 0.04716771 − 0.00019150T
i = 0.76986◦ − 2.09 ′′ T Ω = 74.22988◦ + 1681.40 ′′ T
ϖ = 170.96424◦ + 1312.56 ′′ T L = 313.23218◦ + 0.01173129◦t Neptune a = 30.06896348 − 0.00125196T e= 0.00858587 + 0.00002514T
i = 1.76917◦ − 3.64 ′′ T Ω = 131.72169◦ − 151.25 ′′ T
ϖ = 44.97135◦ − 844.43 ′′ T L = 304.88003◦ + 0.00598106◦t 449