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