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