Inhaltsverzeichnis
Venus
mittlere Anomalien
| Tabelle 1 | |
|---|---|
| $M_1 =$ | $175\overset{\circ}{.}011516 + 149400\overset{\circ}{.}0 \cdot T + 72\overset{\circ}{.}661500 \cdot T$ |
| $M_2 =$ | $50\overset{\circ}{.}407092 + 58320\overset{\circ}{.}0 \cdot T + 197\overset{\circ}{.}803872 \cdot T$ |
| $M_3 =$ | $357\overset{\circ}{.}989508 + 35640\overset{\circ}{.}0 \cdot T + 359\overset{\circ}{.}359488 \cdot T$ |
| $M_4 =$ | $20\overset{\circ}{.}026692 + 19080\overset{\circ}{.}0 \cdot T + 60\overset{\circ}{.}286716 \cdot T$ |
| $M_5 =$ | $20\overset{\circ}{.}413008 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}982988 \cdot T$ |
| $M_6 =$ | $317\overset{\circ}{.}899404 + 1080\overset{\circ}{.}0 \cdot T + 142\overset{\circ}{.}099416 \cdot T$ |
Tabellen
\[\begin{align} dl &= \sum_{n=1}^{6} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{6} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{6} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\]
| Tabelle 2: Keplerterme | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $01$ | $2.37 $ | $2793.23$ | $9995.27$ | $7027.22$ | $-4899.07$ | $0.11$ | $1$ | $0$ | $0$ |
| $02$ | $0.10 $ | $-19.65 $ | $64.95 $ | $-86.10 $ | $34.40 $ | $0.22$ | $1$ | $0$ | $1$ |
| $03$ | $0.06 $ | $0.04 $ | $-0.55 $ | $-0.07 $ | $-0.07 $ | $0.11$ | $1$ | $0$ | $2$ |
| $04$ | $-170.42$ | $73.13 $ | $67.71 $ | $47.56 $ | $-16.59 $ | $0.00$ | $2$ | $0$ | $0$ |
| $05$ | $0.93 $ | $2.91 $ | $-0.03 $ | $-0.92 $ | $0.23 $ | $0.00$ | $2$ | $0$ | $1$ |
| $06$ | $-2.31 $ | $0.90 $ | $0.04 $ | $2.09 $ | $-0.08 $ | $0.00$ | $3$ | $0$ | $0$ |
\[\begin{align} dl &= \sum_{n=7}^{42} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=7}^{42} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=7}^{42} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{2}\]
| Tabelle 3: Störterme der Planeten | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Störungen durch den Merkur | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $07$ | $0.00 $ | $0.00 $ | $0.01 $ | $0.00 $ | $0.06 $ | $-0.09$ | $1$ | $-1$ | $0$ |
| $08$ | $0.25 $ | $-0.09$ | $0.00 $ | $0.00 $ | $-0.09$ | $-0.27$ | $2$ | $-1$ | $0$ |
| $09$ | $-0.07$ | $-0.08$ | $-0.01$ | $-0.01$ | $-0.14$ | $0.14 $ | $4$ | $-2$ | $0$ |
| $10$ | $-0.35$ | $0.08 $ | $0.00 $ | $0.00 $ | $0.02 $ | $0.09 $ | $5$ | $-2$ | $0$ |
| Störungen durch die Erde | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $11$ | $-2.38$ | $-4.27$ | $0.00 $ | $0.00 $ | $3.27 $ | $-1.82 $ | $1$ | $-1$ | $0$ |
| $12$ | $0.09 $ | $0.00 $ | $-0.02$ | $-0.25$ | $-0.08$ | $0.05 $ | $1$ | $-2$ | $0$ |
| $13$ | $-9.57$ | $-5.93$ | $-0.01$ | $-0.01$ | $8.57 $ | $-13.83$ | $2$ | $-2$ | $0$ |
| $14$ | $-2.47$ | $-2.40$ | $0.16 $ | $0.24 $ | $0.83 $ | $-0.95 $ | $2$ | $-3$ | $0$ |
| $15$ | $-0.09$ | $-0.05$ | $-0.28$ | $0.12 $ | $0.08 $ | $-0.13 $ | $3$ | $-2$ | $0$ |
| $16$ | $7.12 $ | $0.32 $ | $-0.07$ | $0.01 $ | $-0.62$ | $13.76 $ | $3$ | $-3$ | $0$ |
| $17$ | $-0.65$ | $-0.17$ | $0.10 $ | $0.05 $ | $0.18 $ | $-0.73 $ | $3$ | $-4$ | $0$ |
| $18$ | $-1.08$ | $-0.95$ | $-0.03$ | $-0.03$ | $-0.17$ | $0.22 $ | $3$ | $-5$ | $0$ |
| $19$ | $0.06 $ | $0.00 $ | $0.14 $ | $-0.18$ | $-0.01$ | $0.08 $ | $4$ | $-3$ | $0$ |
| $20$ | $0.93 $ | $-0.46$ | $-0.01$ | $0.01 $ | $1.06 $ | $2.13 $ | $4$ | $-4$ | $0$ |
| $21$ | $-1.53$ | $0.38 $ | $0.27 $ | $0.00 $ | $-0.64$ | $-2.54 $ | $4$ | $-5$ | $0$ |
| $22$ | $-0.17$ | $-0.05$ | $0.02 $ | $0.00 $ | $0.03 $ | $-0.11 $ | $4$ | $-6$ | $0$ |
| $23$ | $0.18 $ | $-0.28$ | $-0.02$ | $0.04 $ | $0.71 $ | $0.47 $ | $5$ | $-5$ | $0$ |
| $24$ | $0.15 $ | $-0.14$ | $-0.04$ | $0.03 $ | $0.30 $ | $0.31 $ | $5$ | $-6$ | $0$ |
| $25$ | $-0.08$ | $0.02 $ | $0.01 $ | $0.00 $ | $-0.03$ | $-0.11 $ | $5$ | $-7$ | $0$ |
| $26$ | $-0.23$ | $0.00 $ | $0.00 $ | $0.00 $ | $0.01 $ | $-0.04 $ | $5$ | $-8$ | $0$ |
| $27$ | $0.01 $ | $-0.14$ | $0.00 $ | $-0.01$ | $0.39 $ | $0.04 $ | $6$ | $-6$ | $0$ |
| $28$ | $0.02 $ | $-0.05$ | $-0.01$ | $0.01 $ | $0.12 $ | $0.04 $ | $6$ | $-7$ | $0$ |
| $29$ | $0.10 $ | $-0.10$ | $-0.02$ | $0.02 $ | $0.19 $ | $0.19 $ | $6$ | $-8$ | $0$ |
| $30$ | $-0.03$ | $-0.06$ | $0.00 $ | $0.00 $ | $0.18 $ | $-0.08 $ | $7$ | $-7$ | $0$ |
| $31$ | $-0.03$ | $-0.02$ | $0.00 $ | $0.00 $ | $0.06 $ | $-0.08 $ | $8$ | $-8$ | $0$ |
| Störungen durch den Mars | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $32$ | $-0.65$ | $1.02$ | $-0.02$ | $0.00$ | $-0.04$ | $-0.02$ | $1$ | $-3$ | $0$ |
| $33$ | $-0.05$ | $0.04$ | $0.00 $ | $0.00$ | $-0.09$ | $-0.10$ | $2$ | $-2$ | $0$ |
| $34$ | $-0.50$ | $0.45$ | $0.01 $ | $0.03$ | $-0.79$ | $-0.89$ | $2$ | $-3$ | $0$ |
| Störungen durch den Jupiter | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $35$ | $-2.62$ | $1.40 $ | $0.02 $ | $0.03 $ | $-2.35$ | $-4.40$ | $-1$ | $-1$ | $0$ |
| $36$ | $-0.47$ | $-0.08$ | $0.04 $ | $-0.18$ | $0.12 $ | $-0.76$ | $-1$ | $-2$ | $0$ |
| $37$ | $-0.05$ | $1.56 $ | $-0.08$ | $-0.04$ | $0.16 $ | $0.04 $ | $0 $ | $-1$ | $0$ |
| $38$ | $-0.73$ | $-0.51$ | $-0.01$ | $0.01 $ | $1.27 $ | $-1.82$ | $2 $ | $-2$ | $0$ |
| $39$ | $-0.14$ | $-0.10$ | $0.00 $ | $0.00 $ | $0.25 $ | $-0.34$ | $2 $ | $-3$ | $0$ |
| $40$ | $-0.01$ | $0.04 $ | $0.00 $ | $0.00 $ | $-0.11$ | $-0.02$ | $3 $ | $-3$ | $0$ |
| Störungen durch den Saturn | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $41$ | $-0.11$ | $-0.14$ | $0.01$ | $0.00$ | $0.24$ | $-0.20$ | $1$ | $-1$ | $0$ |
| $42$ | $0.00 $ | $0.21 $ | $0.00$ | $-0.01$ | $0.00$ | $0.00 $ | $0$ | $-1$ | $0$ |
Heliozentrische Koordinaten
\[\begin{align} \Delta l &= 2\overset{''}{.}74\sin(27\overset{\circ}{.}504 + 150\overset{\circ}{.}264\ T) + 0\overset{''}{.}27\sin(331\overset{\circ}{.}236 + 119\overset{\circ}{.}052\cdot T) \\ l_2 &= M_2 + 131\overset{\circ}{.}572188 + (1\overset{''}{.}9 + 5073\overset{''}{.}0\cdot T + 1\overset{''}{.}1\cdot T^2 + \text{dl} + \Delta l)/3600'' \\ b_2 &= (- 67\overset{''}{.}70 + 0\overset{''}{.}04\cdot T + 0\overset{''}{.}01\cdot T^2 + \text{db})/3600'' \\ r_2 &= 0.7233482\text{ AE} - 2.0 \cdot 10^{-7}\text{ AE} \cdot T + 10^{-6}\text{ AE dr} \end{align}\tag{3}\]