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Mean orbital elements of Sun & principal planets
Article compiled: c. 1984-85, posted: 1st March, 2004 Copyright © 2004 Abdul Ahad. All rights reserved. They are all stated as of epoch 1900 January 0.5 Ephemeris Time (epoch 1900.0) [Julian date 241 5020.0] and I have excluded terms in T^3 and higher in order to keep calculations simple yet yielding reasonable levels of rigorousness. If JD= Julian date at the instant for which one requires to calculate planetary positions (the "ephemeris date"), then the following time arguments will fix the relevant intervals between the ephemeris date and epoch 1900.0: d= JD-241 5020.0 (number of days since the epoch) T=d/36525 (number of Julian centuries from the epoch) D=3.6525*T Sun Mean longitude: L=279.69668+0.9856473354*d+0.00002267*D^2 +... Mean anomaly: g=358.47583+0.9856003*d+... [Modified by me to fit current values] Eccentricity: e=0.01675104-0.000 04180*T-0.000 000126*T^2 -... Obliquity of ecliptic: e=23.452294-0.0130125*T-0.000 00164*T^2 -... Mercury i=7.002881+0.0018608*T-0.000 0183*T^2+... W=47.14594+1.1852083*T+0.0001739*T^2+... p=75.89970+1.5554889*T+0.0002947*T^2+... a=0.3870986 e=.20561421+0.00002046*T-0.000 000 030*T^2+... L=178.179078+4.0923770233*d+0.000 0226*D^2+... Apparent Diam (arc secs)= 6.72/distance (AUs) Venus i=3.393631+0.0010058*T-0.000 0010*T^2+... W=75.77965+0.899850*T+0.000 410*T^2+... p=130.16383+1.4080361*T-0.000 9764*T^2+... a=0.7233322 e=0.00682069-0.000 04774*T+0.000 000 091*T^2+... L=342.767053+1.6021687039*d+0.000 023212*D^2+... Apparent Diam (arc secs) = 16.68/distance (AUs) Mars i=1.850333-0.000 6750*T+0.000 0126*T^2+... W=48.78644+0.7709917*T-0.000 0014*T^2+... p=334.21820+1.8407583*T+0.000 1299*T^2+... a=1.5236915 e=0.09331290+0.000 092 064*T-0.000 000 077T^2+... L=293.747628+0.5240711638*d+0.000 023 287*D^2+... Apparent Diam (arc secs) = 9.36/distance (AUs) Jupiter i=1.30875-0.00565*T W=99.4378+1.0111*T p=12.7114+1.6113*T a=5.2028039 e=0.048338+0.000162*T L=238.0495+3036.3028*T Apparent Eq. Diam (arc secs)= 196.88/distance (AUs) Saturn i=2.49238-0.0041*T W=112.7837+0.8730*T p=91.0888+1.9595*T a=9.5388437 e=0.055890-0.000 347*T L=266.5652+1223.5103*T Apparent Eq. Diam (arc secs) = 165.46/distance (AUs) Uranus i=0.77268+0.00063*T W=73.4899+0.5106*T p=169.035+1.627*T a=19.18228-0.000565*T e=0.047046+0.000272*T L=243.3584+429.911*T Apparent Eq. Diam (arc secs) = 70.04/distance (AUs) Neptune i=1.77927-0.0092*T W=130.6786+1.102*T p=43.746+0.88*T a=30.057053+0.001210*T e=0.008528+0.000 0785*T L=85.0277+219.8553*T Apparent Eq. Diam (arc secs)= 67.00/distance (AUs) All angular elements are expressed in degrees and relate to the mean equinox of date 
Main text on calculating planetary positions Copyright © 1984 to 2004 Abdul Ahad. All rights reserved.
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