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Planetary Positions

Tab.4 gives the 6 orbital elements $a, e, \lambda, \varpi,i, \Omega$ and their time development for the 7 major planets and the Earth-Moon barycentre (EMB), where $\varpi=\Omega+\omega$ is the longitude of the periapsis. Values are reduced to a relative precision of $10^{-7}$ from Tab.5.8 in Simon et al. (1994). This precision is sufficient for the calculation of planetary positions to the highest precision possible with a single set of mean elements for the period 1950-2050. The resulting precisions in relation to the DE200 ecliptic position are given in Tab.5. The positions are calculated from the mean elements by determining the true anomaly from eqn.26 and applying eqns.30. The last three columns of Tab.5 are not corrected for disturbances by Jupiter and Saturn, while these disturbances are included in the first four columns using Tab.6 of Simon et al. (1994). As one can see from Tab.5 it is - at least for the outer planets - recommendable to apply these corrections. To save space we do not give the numerical values in this paper but refer the reader to Simon et al. (1994) or to our web-page (cited above). The last row of Tab.5 gives the loss in precision when using mean elements (not solving eqn.26) instead of true elements for the EMB: mean and true position differ by up to $2^\circ.7$.


Table 4: Heliocentric mean orbital elements of the planets in $HAE_{J2000}$ to a precision of $10^{-7}$ or $1''$ for 1950-2050 after Simon et al. (1994). The elements are semi-major axis $a$ [1 AU = 149 597 870 km], eccentricity $e$, mean longitude $\lambda $, longitude of periapsis $\varpi $, inclination $i$, and ascending node $\Omega $. The time parameter $T_0$ is scaled in Julian centuries of 36525 days from J2000.0. EMB denotes the Earth-Moon barycentre. The first column $\mu $ gives the IAU1976 mass ratio Sun/planet.
  $\mu $ $a$[AU] $e[10^{-7}]$ $\lambda[^\circ]$
Mercury 6023600 0.38709831 2056318+204$T_0$ 252.2509055+149472.6746358$T_0$
Venus 408523.5 0.72332982 67719-478$T_0$ 181.9798009+58517.8156760$T_0$
EMB 328900.5 1.0000010 167086-420$T_0$ 100.4664568+35999.3728565$T_0$
Mars 3098710 1.5236793 934006+905$T_0$ 355.4329996+19140.2993039$T_0$
Jupiter 1047.355 5.2026032 484979+1632$T_0$ 34.3515187+3034.9056606$T_0$
Saturn 3498.5 9.5549092 555481-3466$T_0$ 50.0774443+1222.1138488$T_0$
Uranus 22869 19.2184461 463812-273$T_0$ 314.0550051+428.4669983$T_0$
Neptune 19314 30.1103869 94557+60$T_0$ 304.3486655+218.4862002$T_0$

  $\varpi[^\circ]$ $i[^\circ]$ $\Omega[^\circ]$
Mercury 77.4561190+0.1588643$T_0$ 7.0049863-0.0059516$T_0$ 48.3308930-0.1254227$T_0$
Venus 131.5637030+0.0048746$T_0$ 3.3946619-0.0008568$T_0$ 76.6799202-0.2780134$T_0$
EMB 102.9373481+0.3225654$T_0$ 0.0 +0.0130548$T_0$ 174.8731758-0.2410908$T_0$
Mars 336.0602340+0.4439016$T_0$ 1.8497265-0.0081477$T_0$ 49.5580932-0.2950250$T_0$
Jupiter 14.3312069+0.2155209$T_0$ 1.3032670-0.0019877$T_0$ 100.4644070+0.1767232$T_0$
Saturn 93.0572375+0.5665415$T_0$ 2.4888788+0.0025514$T_0$ 113.6655025-0.2566722$T_0$
Uranus 173.0052911+0.0893212$T_0$ 0.7731969-0.0016869$T_0$ 74.0059570+0.0741431$T_0$
Neptune 48.1202755+0.0291866$T_0$ 1.7699526+0.0002256$T_0$ 131.7840570-0.0061651$T_0$



Table 5: Precision of planetary positions derived from orbital elements (Tab.4) for the period 1950-2060 compared to DE200 positions on the ecliptic of date. Maximal differences are given for heliocentric ecliptic latitude $\beta $, longitude $\lambda $, and distance $r$ and orbital velocity $v$. Values 'With Disturbances' use the corrections given in Tab.6 of Simon et al. (1994).
  With Disturbances Without Disturbances
  $\delta \beta ['']$ $\delta \lambda ['']$ $\delta r $[1000km] $\delta v $[m/s] $\delta \beta ['']$ $\delta \lambda ['']$ $\delta r $[1000km]
Mercury 0.8 6.0 0.51 1.2 3.2 26 1.6
Venus 0.9 5.5 1.0 1.8 1.6 28 5.0
EMB 0.6 7.6 1.2 1.9 0.6 29 7.0
Mars 1.0 26 8.1 4.5 4.3 160 39
Jupiter 5.5 46 71 15 20 830 990
Saturn 14 81 170 37 62 2100 6700
Uranus 4.9 86 510 27 44 3600 8800
Neptune 1.7 10 170 22 69 2400 11000
Earth 1.0 7.9 1.8 3.6 1.1 29 7.2
Moon 51 64 62 180 51 84 67
Earth$_{approx}$ 1.1 16 8.6 260 1.1 34 8.6
Earth-EMB 1.1 14 5.8 14 1.1 29 7.2
EMB$_{mean}$ 1.1 6900 2500        




Subsections
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Next: Position of Earth and Up: Planetary Systems Previous: Planetary Orbits
Markus Fraenz 2002-03-12