Inhaltsverzeichnis

Saturn

mittlere Anomalien

Tabelle 1
$M_5 =$	$20\overset{\circ}{.}351304 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}906668 \cdot T$
$M_6 =$	$317\overset{\circ}{.}875212 + 1080\overset{\circ}{.}0 \cdot T + 142\overset{\circ}{.}116768 \cdot T$
$M_7 =$	$142\overset{\circ}{.}903332 + 360\overset{\circ}{.}0 \cdot T + 68\overset{\circ}{.}493096 \cdot T$
$M_8 =$	$259\overset{\circ}{.}505028 + 0\overset{\circ}{.}0 \cdot T + 218\overset{\circ}{.}470428 \cdot T$

Tabellen

\[\begin{align} dl &= \sum_{n=1}^{8} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{8} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{8} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\]

Tabelle 2: Keplerterme
n	$a_n['']$	$b_n['']$	$c_n['']$	$d_n['']$	$e_n['']$	$f_n['']$	$p_n$	$s_n$	$t_n$
$01$	$-348.3$	$22907.7$	$-3266.5$	$8314.4$	$-52915.5$	$-752.2$	$1$	$0$	$0$
$02$	$-225.2$	$-146.2 $	$79.6 $	$17.4 $	$337.7 $	$521.3 $	$1$	$0$	$1$
$03$	$1.3 $	$-1.4 $	$0.1 $	$-0.4 $	$3.2 $	$2.9 $	$1$	$0$	$2$
$04$	$44.2 $	$724.0 $	$-188.7 $	$459.1 $	$-1464.3 $	$-34.7 $	$2$	$0$	$0$
$05$	$-17.0 $	$-11.3 $	$1.0 $	$-3.7 $	$18.9 $	$-28.6 $	$2$	$0$	$1$
$06$	$6.5 $	$30.5 $	$-11.6 $	$28.1 $	$-61.1 $	$0.4 $	$3$	$0$	$0$
$07$	$-1.2 $	$-0.7 $	$-0.2 $	$-0.6 $	$1.1 $	$-1.8 $	$3$	$0$	$1$
$08$	$0.6 $	$1.4 $	$-0.6 $	$1.6 $	$-3.0 $	$-0.2 $	$4$	$0$	$0$

\[\begin{align} dl &= \sum_{n=9}^{71} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \\ db &= \sum_{n=9}^{71} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \\ dr &= \sum_{n=9}^{71} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \end{align}\tag{2}\]

Tabelle 3: Störterme der Planeten
Störungen durch den Jupiter
n	$a_n['']$	$b_n['']$	$c_n['']$	$d_n['']$	$e_n['']$	$f_n['']$	$p_n$	$s_n$	$t_n$
$09$	$12.0 $	$-1.4 $	$1.2 $	$-1.8 $	$-13.9 $	$6.4 $	$0 $	$-1$	$0$
$10$	$0.0 $	$-0.2 $	$0.0 $	$-0.1 $	$-0.9 $	$1.0 $	$0 $	$-2$	$0$
$11$	$0.9 $	$0.4 $	$0.2 $	$0.2 $	$-1.8 $	$1.9 $	$1 $	$1 $	$0$
$12$	$-1.0 $	$-30.7 $	$-3.6 $	$-9.3 $	$108.6 $	$-815.0$	$1 $	$-1$	$0$
$13$	$-2.0 $	$-2.7 $	$-0.1 $	$-0.4 $	$-2.1 $	$-11.9 $	$1 $	$-2$	$0$
$14$	$0.1 $	$0.2 $	$0.0 $	$0.0 $	$-1.0 $	$0.3 $	$2 $	$1 $	$0$
$15$	$-3.5 $	$-426.6 $	$-1.6 $	$-2.7 $	$-546.5$	$-26.5 $	$2 $	$-1$	$0$
$16$	$3.5 $	$-2.2 $	$0.0 $	$0.0 $	$-2.6 $	$-4.3 $	$2 $	$-1$	$1$
$17$	$10.5 $	$-30.9 $	$-1.9 $	$0.2 $	$-130.5$	$-52.5 $	$2 $	$-2$	$0$
$18$	$-0.2 $	$-0.4 $	$-0.1 $	$0.0 $	$-1.2 $	$-0.1 $	$2 $	$-3$	$0$
$19$	$29.0 $	$-40.2 $	$3.2 $	$-9.4 $	$98.2 $	$45.3 $	$3 $	$-1$	$0$
$20$	$0.6 $	$0.6 $	$0.0 $	$0.0 $	$-1.0 $	$1.3 $	$3 $	$-1$	$1$
$21$	$-27.0 $	$-21.1 $	$-19.8$	$5.4 $	$-68.5 $	$8.1 $	$3 $	$-2$	$0$
$22$	$0.9 $	$-0.5 $	$-0.1 $	$-0.8 $	$-0.4 $	$-2.0 $	$3 $	$-2$	$1$
$23$	$-5.4 $	$-4.1 $	$-0.1 $	$-0.1 $	$-19.1 $	$26.2 $	$3 $	$-3$	$0$
$24$	$1.5 $	$-2.5 $	$1.0 $	$-1.1 $	$12.4 $	$4.7 $	$4 $	$-1$	$0$
$25$	$-821.9 $	$-9.6 $	$-70.5$	$-4.4 $	$-26.0 $	$1873.6$	$4 $	$-2$	$0$
$26$	$4.1 $	$-21.9 $	$0.7 $	$-3.0 $	$-50.3 $	$-9.9 $	$4 $	$-2$	$1$
$27$	$-2.0 $	$-4.7 $	$-0.1 $	$-0.3 $	$-19.3 $	$8.2 $	$4 $	$-3$	$0$
$28$	$-1.5 $	$1.3 $	$0.0 $	$0.0 $	$6.5 $	$7.3 $	$4 $	$-4$	$0$
$29$	$-2627.6$	$-1277.3$	$-13.8$	$-4.3 $	$117.4 $	$-344.1$	$5 $	$-2$	$0$
$30$	$63.0 $	$-98.6 $	$0.1 $	$-0.2 $	$12.7 $	$6.7 $	$5 $	$-2$	$1$
$31$	$1.7 $	$1.2 $	$0.0 $	$0.0 $	$-0.2 $	$0.3 $	$5 $	$-2$	$2$
$32$	$0.4 $	$-3.6 $	$0.0 $	$-0.3 $	$-11.3 $	$-1.6 $	$5 $	$-3$	$0$
$33$	$-1.4 $	$0.3 $	$-0.1 $	$0.0 $	$1.5 $	$6.3 $	$5 $	$-4$	$0$
$34$	$0.3 $	$0.6 $	$0.0 $	$0.0 $	$3.0 $	$-1.7 $	$5 $	$-5$	$0$
$35$	$-146.7 $	$-73.7 $	$-43.6$	$-46.7$	$166.4 $	$-334.3$	$6 $	$-2$	$0$
$36$	$5.2 $	$-6.8 $	$1.7 $	$-1.0 $	$15.1 $	$11.4 $	$6 $	$-2$	$1$
$37$	$1.5 $	$-2.9 $	$0.1 $	$-0.1 $	$-2.2 $	$-1.3 $	$6 $	$-3$	$0$
$38$	$-0.7 $	$-0.2 $	$0.0 $	$0.0 $	$-0.7 $	$2.8 $	$6 $	$-4$	$0$
$39$	$0.0 $	$0.5 $	$0.0 $	$0.0 $	$2.5 $	$-0.1 $	$6 $	$-5$	$0$
$40$	$0.3 $	$-0.1 $	$0.0 $	$0.0 $	$-0.3 $	$-1.2 $	$6 $	$-6$	$0$
$41$	$-9.6 $	$-3.9 $	$-4.7 $	$-5.3 $	$9.6 $	$-18.6 $	$7 $	$-2$	$0$
$42$	$0.4 $	$-0.5 $	$0.3 $	$-0.1 $	$1.0 $	$0.9 $	$7 $	$-2$	$1$
$43$	$3.0 $	$5.3 $	$0.0 $	$0.0 $	$7.5 $	$-3.5 $	$7 $	$-3$	$0$
$44$	$0.2 $	$0.4 $	$0.0 $	$0.0 $	$1.6 $	$-1.3 $	$7 $	$-4$	$0$
$45$	$-0.1 $	$0.2 $	$0.0 $	$0.0 $	$1.0 $	$0.5 $	$7 $	$-5$	$0$
$46$	$0.2 $	$0.0 $	$0.0 $	$0.0 $	$0.2 $	$-1.0 $	$7 $	$-6$	$0$
$47$	$-0.7 $	$-0.2 $	$-0.4 $	$-0.4 $	$0.6 $	$-1.2 $	$8 $	$-2$	$0$
$48$	$0.5 $	$1.0 $	$0.1 $	$0.2 $	$-2.0 $	$1.5 $	$8 $	$-3$	$0$
$49$	$0.4 $	$1.3 $	$0.0 $	$-0.1 $	$3.6 $	$-0.9 $	$8 $	$-4$	$0$
$50$	$4.0 $	$-8.7 $	$0.2 $	$-0.4 $	$-19.9 $	$-9.9 $	$9 $	$-4$	$0$
$51$	$0.5 $	$0.3 $	$0.0 $	$0.0 $	$0.8 $	$-1.8 $	$9 $	$-4$	$1$
$52$	$21.3 $	$-16.8 $	$0.2 $	$-0.2 $	$3.3 $	$3.3 $	$10$	$-4$	$0$
$53$	$1.0 $	$1.7 $	$0.0 $	$0.0 $	$-0.4 $	$0.4 $	$10$	$-4$	$1$
$54$	$1.6 $	$-1.3 $	$0.8 $	$-0.2 $	$3.0 $	$3.7 $	$11$	$-4$	$0$
Störungen durch den Uranus
n	$a_n['']$	$b_n['']$	$c_n['']$	$d_n['']$	$e_n['']$	$f_n['']$	$p_n$	$s_n$	$t_n$
$55$	$1.0 $	$0.7 $	$0.1 $	$0.0 $	$0.4 $	$-1.5 $	$0$	$-1$	$0$
$56$	$0.0 $	$-0.4 $	$-0.1$	$-0.1$	$-1.1 $	$0.1 $	$0$	$-2$	$0$
$57$	$-0.9 $	$-1.2 $	$-0.5$	$-0.3$	$-2.7 $	$2.1 $	$0$	$-3$	$0$
$58$	$7.8 $	$-1.5 $	$0.0 $	$0.0 $	$2.3 $	$12.7 $	$1$	$-1$	$0$
$59$	$-1.1 $	$-8.1 $	$-0.3$	$-0.3$	$5.2 $	$-0.3 $	$1$	$-2$	$0$
$60$	$-16.4$	$-21.0$	$0.4 $	$0.0 $	$-2.1 $	$0.0 $	$1$	$-3$	$0$
$61$	$0.6 $	$-0.1 $	$0.1 $	$0.0 $	$0.1 $	$1.2 $	$2$	$-1$	$0$
$62$	$-4.9 $	$-11.7$	$0.0 $	$-0.2$	$31.5 $	$-13.3$	$2$	$-2$	$0$
$63$	$19.1 $	$10.0 $	$0.1 $	$-1.1$	$-22.1$	$42.1 $	$2$	$-3$	$0$
$64$	$0.9 $	$-0.1 $	$0.0 $	$0.0 $	$0.1 $	$1.4 $	$2$	$-4$	$0$
$65$	$-0.4 $	$-0.9 $	$0.0 $	$-0.3$	$1.7 $	$-0.8 $	$3$	$-2$	$0$
$66$	$2.3 $	$0.0 $	$0.3 $	$0.3 $	$1.0 $	$5.7 $	$3$	$-3$	$0$
$67$	$0.3 $	$-0.7 $	$0.0 $	$0.0 $	$2.0 $	$0.7 $	$3$	$-4$	$0$
$68$	$-0.1 $	$-0.4 $	$0.0 $	$0.0 $	$1.1 $	$-0.3 $	$3$	$-5$	$0$
Störungen durch den Neptun
n	$a_n['']$	$b_n['']$	$c_n['']$	$d_n['']$	$e_n['']$	$f_n['']$	$p_n$	$s_n$	$t_n$
$69$	$-1.3$	$-1.2$	$0.0$	$0.0$	$2.3 $	$-2.5$	$1$	$-1$	$0$
$70$	$1.0 $	$-0.1$	$0.0$	$0.0$	$0.1$	$1.4$	$1$	$-2$	$0$
$71$	$1.1 $	$-0.1$	$0.0$	$0.0$	$0.2 $	$3.3 $	$2$	$-2$	$0$

\[\begin{align} dl &= \sum_{n=72}^{75} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=72}^{75} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=72}^{75} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{3}\]

Tabelle 4: Störungen durch den Jupiter und den Uranus
n	$a_n['']$	$b_n['']$	$c_n['']$	$d_n['']$	$e_n['']$	$f_n['']$	$p_n$	$s_n$	$t_n$
$72$	$-0.8$	$-0.1$	$0.3 $	$0.5$	$-0.2$	$1.8 $	$5$	$-2$	$-3$
$73$	$2.4 $	$27.8$	$0.0 $	$0.0$	$2.1 $	$-0.2$	$6$	$-2$	$-3$
$74$	$-0.7\cdot T$	$-0.4\cdot T$	$0.0 $	$0.0$	$0.0 $	$0.0 $	$6$	$-2$	$-3$
$75$	$0.1 $	$1.6 $	$-0.2$	$0.6$	$-3.6$	$0.3 $	$7$	$-2$	$-3$

Heliozentrische Koordinaten

\[\begin{align} l_6 &= M_6 + 92\overset{\circ}{.}200896 + (5018\overset{''}{.}6\cdot T + 1\overset{''}{.}9\cdot T^2 + \text{dl})/3600'' \\ b_6 &= (+ 175\overset{''}{.}1 - 10\overset{''}{.}2\cdot T + \text{db})/3600'' \\ r_6 &= 9.557584\text{ AE} + 1.86 \cdot 10^{-4}\text{ AE} \cdot T + 10^{-5}\text{ AE dr} \end{align}\tag{4}\]