Inhaltsverzeichnis
Mars
mittlere Anomalien
| Tabelle 1 | |
|---|---|
| $M_2 =$ | $49\overset{\circ}{.}759488 + 58320\overset{\circ}{.}0 \cdot T + 197\overset{\circ}{.}371512 \cdot T$ |
| $M_3 =$ | $357\overset{\circ}{.}343488 + 35640\overset{\circ}{.}0 \cdot T + 358\overset{\circ}{.}928496 \cdot T$ |
| $M_4 =$ | $19\overset{\circ}{.}387908 + 19080\overset{\circ}{.}0 \cdot T + 59\overset{\circ}{.}858496 \cdot T$ |
| $M_5 =$ | $19\overset{\circ}{.}761984 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}461996 \cdot T$ |
| $M_6 =$ | $317\overset{\circ}{.}202012 + 1080\overset{\circ}{.}0 \cdot T + 141\overset{\circ}{.}669000 \cdot T$ |
Tabellen
\[\begin{align} dl &= \sum_{n=1}^{12} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{12} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{12} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\]
| Tabelle 2: Keplerterme | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $001$ | $-5.32$ | $38481.97$ | $-6321.67$ | $1876.89$ | $-141856.04$ | $0.40 $ | $1$ | $0$ | $0$ |
| $002$ | $-1.12$ | $37.98 $ | $37.28 $ | $117.48 $ | $-138.67 $ | $-2.93$ | $1$ | $0$ | $1$ |
| $003$ | $-0.32$ | $-0.03 $ | $1.04 $ | $-0.40 $ | $0.12 $ | $-1.19$ | $1$ | $0$ | $2$ |
| $004$ | $28.28$ | $2285.80 $ | $-589.35 $ | $174.81 $ | $-6608.37 $ | $0.00 $ | $2$ | $0$ | $0$ |
| $005$ | $1.64 $ | $3.37 $ | $2.89 $ | $11.10 $ | $-12.93 $ | $0.00 $ | $2$ | $0$ | $1$ |
| $006$ | $0.00 $ | $0.00 $ | $0.10 $ | $-0.03 $ | $0.00 $ | $0.00 $ | $2$ | $0$ | $2$ |
| $007$ | $5.31 $ | $189.29 $ | $-61.98 $ | $18.53 $ | $-461.81 $ | $0.00 $ | $3$ | $0$ | $0$ |
| $008$ | $0.31 $ | $0.35 $ | $0.25 $ | $1.19 $ | $-1.36 $ | $0.00 $ | $3$ | $0$ | $1$ |
| $009$ | $0.81 $ | $17.96 $ | $-6.88 $ | $2.08 $ | $-38.26 $ | $0.00 $ | $4$ | $0$ | $0$ |
| $010$ | $0.05 $ | $0.04 $ | $0.02 $ | $0.14 $ | $-0.15 $ | $0.00 $ | $4$ | $0$ | $1$ |
| $011$ | $0.11 $ | $1.83 $ | $-0.79 $ | $0.24 $ | $-3.48 $ | $0.00 $ | $5$ | $0$ | $0$ |
| $012$ | $0.02 $ | $0.20 $ | $-0.09 $ | $0.03 $ | $-0.34 $ | $0.00 $ | $6$ | $0$ | $0$ |
\[\begin{align} dl &= \sum_{n=13}^{106} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=13}^{106} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=13}^{106} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{2}\]
| Tabelle 3: Störterme der Planeten | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Störungen durch die Venus | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $013$ | $-0.01$ | $-0.03$ | $0.00 $ | $0.00 $ | $0.10 $ | $-0.04$ | $0$ | $-1$ | $0$ |
| $014$ | $0.05 $ | $0.10 $ | $0.00 $ | $0.00 $ | $-2.08$ | $0.75 $ | $1$ | $-1$ | $0$ |
| $015$ | $-0.25$ | $-0.57$ | $0.00 $ | $0.00 $ | $-2.58$ | $1.18 $ | $2$ | $-1$ | $0$ |
| $016$ | $0.02 $ | $0.02 $ | $0.00 $ | $0.00 $ | $0.13 $ | $-0.14$ | $2$ | $-2$ | $0$ |
| $017$ | $3.41 $ | $5.38 $ | $0.01 $ | $-0.01$ | $1.87 $ | $-1.15$ | $3$ | $-1$ | $0$ |
| $018$ | $0.02 $ | $0.02 $ | $0.00 $ | $0.00 $ | $0.11 $ | $-0.13$ | $3$ | $-2$ | $0$ |
| $019$ | $0.32 $ | $0.49 $ | $-0.07$ | $0.07 $ | $-1.88$ | $1.21 $ | $4$ | $-1$ | $0$ |
| $020$ | $0.03 $ | $0.03 $ | $0.00 $ | $0.00 $ | $0.12 $ | $-0.14$ | $4$ | $-2$ | $0$ |
| $021$ | $0.04 $ | $0.06 $ | $-0.01$ | $0.01 $ | $-0.17$ | $0.11 $ | $5$ | $-1$ | $0$ |
| $022$ | $0.11 $ | $0.09 $ | $-0.01$ | $0.01 $ | $-0.35$ | $0.43 $ | $5$ | $-2$ | $0$ |
| $023$ | $-0.36$ | $-0.28$ | $0.00 $ | $0.00 $ | $-0.20$ | $0.25 $ | $6$ | $-2$ | $0$ |
| $024$ | $-0.03$ | $-0.03$ | $0.00 $ | $-0.01$ | $0.11 $ | $-0.13$ | $7$ | $-2$ | $0$ |
| Störungen durch die Erde | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $025$ | $0.09 $ | $0.06 $ | $0.02 $ | $-0.02$ | $0.14 $ | $-0.22 $ | $-1$ | $-1$ | $0$ |
| $026$ | $0.72 $ | $0.49 $ | $0.12 $ | $-0.10$ | $1.55 $ | $-2.31 $ | $0 $ | $-1$ | $0$ |
| $027$ | $7.00 $ | $4.92 $ | $0.08 $ | $-0.13$ | $13.93$ | $-20.48$ | $1 $ | $-1$ | $0$ |
| $028$ | $13.08$ | $4.89 $ | $-0.05$ | $0.13 $ | $-4.53$ | $10.01 $ | $2 $ | $-1$ | $0$ |
| $029$ | $0.14 $ | $0.05 $ | $0.01 $ | $0.14 $ | $0.48 $ | $-2.66 $ | $2 $ | $-2$ | $0$ |
| $030$ | $1.38 $ | $0.56 $ | $-0.01$ | $0.19 $ | $-2.00$ | $4.85 $ | $3 $ | $-1$ | $0$ |
| $031$ | $-6.85$ | $2.68 $ | $0.00 $ | $0.03 $ | $8.38 $ | $21.42 $ | $3 $ | $-2$ | $0$ |
| $032$ | $-0.08$ | $0.20 $ | $0.00 $ | $0.00 $ | $1.20 $ | $0.46 $ | $3 $ | $-3$ | $0$ |
| $033$ | $0.16 $ | $0.07 $ | $-0.01$ | $0.05 $ | $-0.19$ | $0.47 $ | $4 $ | $-1$ | $0$ |
| $034$ | $-4.41$ | $2.14 $ | $-0.07$ | $-0.09$ | $-3.33$ | $-7.21 $ | $4 $ | $-2$ | $0$ |
| $035$ | $-0.12$ | $0.33 $ | $-0.03$ | $-0.02$ | $2.22 $ | $0.72 $ | $4 $ | $-3$ | $0$ |
| $036$ | $-0.04$ | $-0.06$ | $0.00 $ | $0.00 $ | $-0.02$ | $0.23 $ | $4 $ | $-4$ | $0$ |
| $037$ | $-0.44$ | $0.21 $ | $-0.06$ | $-0.07$ | $-0.70$ | $-1.46 $ | $5 $ | $-2$ | $0$ |
| $038$ | $0.48 $ | $-2.60$ | $0.00 $ | $0.00 $ | $-7.25$ | $-1.37 $ | $5 $ | $-3$ | $0$ |
| $039$ | $-0.09$ | $-0.12$ | $0.00 $ | $0.00 $ | $-0.66$ | $0.50 $ | $5 $ | $-4$ | $0$ |
| $040$ | $0.03 $ | $0.00 $ | $0.00 $ | $0.00 $ | $0.01 $ | $-0.17 $ | $5 $ | $-5$ | $0$ |
| $041$ | $-0.05$ | $0.03 $ | $-0.01$ | $-0.01$ | $-0.07$ | $-0.15 $ | $6 $ | $-2$ | $0$ |
| $042$ | $0.10 $ | $-0.96$ | $0.04 $ | $0.00 $ | $2.36 $ | $0.30 $ | $6 $ | $-3$ | $0$ |
| $043$ | $-0.17$ | $-0.20$ | $0.02 $ | $-0.02$ | $-1.09$ | $0.94 $ | $6 $ | $-4$ | $0$ |
| $044$ | $0.05 $ | $0.00 $ | $0.00 $ | $0.00 $ | $0.00 $ | $-0.30 $ | $6 $ | $-5$ | $0$ |
| $045$ | $0.01 $ | $-0.10$ | $0.02 $ | $0.00 $ | $0.32 $ | $0.04 $ | $7 $ | $-3$ | $0$ |
| $046$ | $0.86 $ | $0.77 $ | $0.01 $ | $-0.01$ | $1.86 $ | $-2.01 $ | $7 $ | $-4$ | $0$ |
| $047$ | $0.09 $ | $-0.01$ | $0.00 $ | $0.00 $ | $-0.05$ | $-0.44 $ | $7 $ | $-5$ | $0$ |
| $048$ | $-0.01$ | $0.02 $ | $0.00 $ | $0.00 $ | $0.10 $ | $0.08 $ | $7 $ | $-6$ | $0$ |
| $049$ | $0.20 $ | $0.16 $ | $-0.01$ | $0.02 $ | $-0.53$ | $0.64 $ | $8 $ | $-4$ | $0$ |
| $050$ | $0.17 $ | $-0.03$ | $0.00 $ | $0.01 $ | $-0.14$ | $-0.84 $ | $8 $ | $-5$ | $0$ |
| $051$ | $-0.02$ | $0.03 $ | $0.00 $ | $0.00 $ | $0.16 $ | $0.09 $ | $8 $ | $-6$ | $0$ |
| $052$ | $-0.55$ | $0.15 $ | $0.00 $ | $0.00 $ | $0.30 $ | $1.10 $ | $9 $ | $-5$ | $0$ |
| $053$ | $-0.02$ | $0.04 $ | $0.00 $ | $0.00 $ | $0.20 $ | $0.10 $ | $9 $ | $-6$ | $0$ |
| $054$ | $-0.09$ | $0.03 $ | $0.00 $ | $-0.01$ | $-0.10$ | $-0.33 $ | $10$ | $-5$ | $0$ |
| $055$ | $-0.05$ | $0.11 $ | $-0.01$ | $0.00 $ | $0.48 $ | $0.21 $ | $10$ | $-6$ | $0$ |
| $056$ | $0.10 $ | $-0.35$ | $0.00 $ | $0.00 $ | $-0.52$ | $-0.15 $ | $11$ | $-6$ | $0$ |
| $057$ | $-0.01$ | $-0.02$ | $0.00 $ | $0.00 $ | $-0.10$ | $0.07 $ | $11$ | $-7$ | $0$ |
| $058$ | $0.01 $ | $-0.04$ | $0.01 $ | $0.00 $ | $0.18 $ | $0.04 $ | $12$ | $-6$ | $0$ |
| $059$ | $-0.05$ | $-0.07$ | $0.01 $ | $0.00 $ | $-0.29$ | $0.20 $ | $12$ | $-7$ | $0$ |
| $060$ | $0.23 $ | $0.27 $ | $0.00 $ | $0.00 $ | $0.25 $ | $-0.21 $ | $13$ | $-7$ | $0$ |
| $061$ | $0.02 $ | $0.03 $ | $0.00 $ | $0.00 $ | $-0.10$ | $0.09 $ | $14$ | $-7$ | $0$ |
| $062$ | $0.05 $ | $0.01 $ | $0.00 $ | $0.00 $ | $0.03 $ | $-0.23 $ | $14$ | $-8$ | $0$ |
| $063$ | $-1.53$ | $0.27 $ | $0.00 $ | $0.00 $ | $0.06 $ | $0.42 $ | $15$ | $-8$ | $0$ |
| $064$ | $-0.14$ | $0.02 $ | $-0.01$ | $-0.02$ | $-0.10$ | $-0.55 $ | $16$ | $-8$ | $0$ |
| $065$ | $0.03 $ | $-0.06$ | $0.00 $ | $0.00 $ | $-0.25$ | $-0.11 $ | $16$ | $-9$ | $0$ |
| Störungen durch den Jupiter | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $066$ | $0.05 $ | $0.03 $ | $0.01 $ | $-0.01$ | $0.08 $ | $-0.14 $ | $-2$ | $-1$ | $0$ |
| $067$ | $0.39 $ | $0.27 $ | $-0.03$ | $-0.06$ | $0.92 $ | $-1.50 $ | $-1$ | $-1$ | $0$ |
| $068$ | $-0.16 $ | $0.03 $ | $-0.01$ | $0.06 $ | $0.13 $ | $0.67 $ | $-1$ | $-2$ | $0$ |
| $069$ | $-0.02 $ | $0.01 $ | $0.00 $ | $0.01 $ | $0.05 $ | $0.09 $ | $-1$ | $-3$ | $0$ |
| $070$ | $3.56 $ | $1.13 $ | $-0.25$ | $-0.24$ | $-5.41 $ | $-7.18 $ | $0 $ | $-1$ | $0$ |
| $071$ | $-1.44 $ | $0.25 $ | $0.02 $ | $0.31 $ | $1.24 $ | $7.96 $ | $0 $ | $-2$ | $0$ |
| $072$ | $-0.21 $ | $0.11 $ | $0.01 $ | $0.05 $ | $0.55 $ | $1.04 $ | $0 $ | $-3$ | $0$ |
| $073$ | $-0.02 $ | $0.02 $ | $0.01 $ | $0.01 $ | $0.11 $ | $0.11 $ | $0 $ | $-4$ | $0$ |
| $074$ | $16.67 $ | $-19.15$ | $-0.06$ | $-0.07$ | $61.00 $ | $53.36 $ | $1 $ | $-1$ | $0$ |
| $075$ | $-21.64$ | $3.18 $ | $-0.31$ | $0.50 $ | $-7.77 $ | $-54.64$ | $1 $ | $-2$ | $0$ |
| $076$ | $-2.82 $ | $1.45 $ | $0.01 $ | $0.07 $ | $-2.53 $ | $-5.73 $ | $1 $ | $-3$ | $0$ |
| $077$ | $-0.31 $ | $0.28 $ | $0.00 $ | $0.00 $ | $-0.34 $ | $-0.51 $ | $1 $ | $-4$ | $0$ |
| $078$ | $2.15 $ | $-2.29 $ | $0.33 $ | $0.19 $ | $7.04 $ | $6.94 $ | $2 $ | $-1$ | $0$ |
| $079$ | $-15.69$ | $3.31 $ | $-0.17$ | $0.25 $ | $-15.70$ | $-73.17$ | $2 $ | $-2$ | $0$ |
| $080$ | $-1.73 $ | $1.95 $ | $0.02 $ | $-0.03$ | $-9.19 $ | $-7.20 $ | $2 $ | $-3$ | $0$ |
| $081$ | $-0.01 $ | $0.33 $ | $0.01 $ | $-0.01$ | $-1.42 $ | $0.08 $ | $2 $ | $-4$ | $0$ |
| $082$ | $0.03 $ | $0.03 $ | $0.00 $ | $0.00 $ | $-0.13 $ | $0.12 $ | $2 $ | $-5$ | $0$ |
| $083$ | $0.26 $ | $-0.28 $ | $0.08 $ | $0.04 $ | $0.73 $ | $0.71 $ | $3 $ | $-1$ | $0$ |
| $084$ | $-2.06 $ | $0.46 $ | $-0.13$ | $-0.25$ | $-1.61 $ | $-6.72 $ | $3 $ | $-2$ | $0$ |
| $085$ | $-1.28 $ | $-0.27 $ | $-0.04$ | $-0.02$ | $2.21 $ | $-6.90 $ | $3 $ | $-3$ | $0$ |
| $086$ | $-0.22 $ | $0.08 $ | $0.00 $ | $0.01 $ | $-0.44 $ | $-1.25 $ | $3 $ | $-4$ | $0$ |
| $087$ | $-0.02 $ | $0.03 $ | $0.00 $ | $0.00 $ | $-0.15 $ | $0.08 $ | $3 $ | $-5$ | $0$ |
| $088$ | $0.03 $ | $-0.03 $ | $0.01 $ | $0.01 $ | $0.08 $ | $0.08 $ | $4 $ | $-1$ | $0$ |
| $089$ | $-0.26 $ | $0.06 $ | $-0.03$ | $-0.05$ | $-0.17 $ | $-0.70 $ | $4 $ | $-2$ | $0$ |
| $090$ | $-0.20 $ | $-0.05 $ | $-0.01$ | $-0.02$ | $0.22 $ | $-0.79 $ | $4 $ | $-3$ | $0$ |
| $091$ | $-0.11 $ | $-0.14 $ | $0.00 $ | $0.00 $ | $0.93 $ | $-0.60 $ | $4 $ | $-4$ | $0$ |
| $092$ | $-0.04 $ | $-0.02 $ | $0.00 $ | $0.00 $ | $0.09 $ | $-0.23 $ | $4 $ | $-5$ | $0$ |
| $093$ | $-0.02 $ | $-0.03 $ | $0.00 $ | $0.00 $ | $0.13 $ | $-0.09 $ | $5 $ | $-4$ | $0$ |
| $094$ | $0.00 $ | $-0.03 $ | $0.00 $ | $0.00 $ | $0.21 $ | $0.01 $ | $5 $ | $-5$ | $0$ |
| Störungen durch den Saturn | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $095$ | $0.03 $ | $0.13 $ | $0.02 $ | $0.00 $ | $0.48 $ | $-0.13 $ | $-1$ | $-1$ | $0$ |
| $096$ | $0.27 $ | $0.84 $ | $0.01 $ | $-0.01$ | $0.40 $ | $-0.43 $ | $0 $ | $-1$ | $0$ |
| $097$ | $0.12 $ | $-0.04 $ | $-0.01$ | $-0.02$ | $-0.33 $ | $-0.55 $ | $0 $ | $-2$ | $0$ |
| $098$ | $0.02 $ | $-0.01 $ | $0.00 $ | $0.00 $ | $-0.07 $ | $-0.08 $ | $0 $ | $-3$ | $0$ |
| $099$ | $1.12 $ | $0.76 $ | $-0.01$ | $0.01 $ | $-2.66 $ | $3.91 $ | $1 $ | $-1$ | $0$ |
| $100$ | $1.49 $ | $-0.95 $ | $0.04 $ | $-0.05$ | $3.07 $ | $4.83 $ | $1 $ | $-2$ | $0$ |
| $101$ | $0.21 $ | $-0.18 $ | $0.00 $ | $0.00 $ | $0.55 $ | $0.64 $ | $1 $ | $-3$ | $0$ |
| $102$ | $0.12 $ | $0.10 $ | $-0.01$ | $0.02 $ | $-0.29 $ | $0.34 $ | $2 $ | $-1$ | $0$ |
| $103$ | $0.51 $ | $-0.36 $ | $0.03 $ | $0.01 $ | $1.61 $ | $2.25 $ | $2 $ | $-2$ | $0$ |
| $104$ | $0.10 $ | $-0.10 $ | $0.00 $ | $0.00 $ | $0.50 $ | $0.43 $ | $2 $ | $-3$ | $0$ |
| $105$ | $0.01 $ | $-0.02 $ | $0.00 $ | $0.00 $ | $0.11 $ | $0.05 $ | $2 $ | $-4$ | $0$ |
| $106$ | $0.07 $ | $-0.05 $ | $0.01 $ | $0.01 $ | $0.16 $ | $0.22 $ | $3 $ | $-2$ | $0$ |
Heliozentrische Koordinaten
\[\begin{align} \Delta l &= + 52\overset{''}{.}49\sin(67\overset{\circ}{.}248 + 19\overset{\circ}{.}764\cdot T) + 0\overset{''}{.}61\sin(331\overset{\circ}{.}92 + 119\overset{\circ}{.}052\cdot T) \\ & + 0\overset{''}{.}32\sin(170\overset{\circ}{.}316 + 773\overset{\circ}{.}46\cdot T) + 0\overset{''}{.}28\sin(340\overset{\circ}{.}812 + 40\overset{\circ}{.}788\cdot T) \\ l_4 &= M_4 + 336\overset{\circ}{.}045276 + (0\overset{''}{.}14 + 6616\overset{''}{.}37\cdot T + 0\overset{''}{.}99\cdot T^2 + \Delta l + \text{dl})/3600'' \\ b_4 &= (+ 596\overset{''}{.}32 - 2\overset{''}{.}92\cdot T - 0\overset{''}{.}10\cdot T^2 + \text{db})/3600'' \\ r_4 &= 1.5303352\text{ AE} + 1.31 \cdot 10^{-5}\text{ AE} \cdot T + 10^{-6}\text{ AE dr} \end{align}\tag{3}\]