Inhaltsverzeichnis
Erde-Mond Baryzentrum EMB
mittlere Anomalien
| Tabelle 1 | |
|---|---|
| $M_2 =$ | $49\overset{\circ}{.}943016 + 58320\overset{\circ}{.}0 \cdot T + 197\overset{\circ}{.}493012 \cdot T$ |
| $M_3 =$ | $357\overset{\circ}{.}525576 + 35640\overset{\circ}{.}0 \cdot T + 359\overset{\circ}{.}049744 \cdot T$ |
| $M_4 =$ | $19\overset{\circ}{.}557000 + 19080\overset{\circ}{.}0 \cdot T + 59\overset{\circ}{.}977008 \cdot T$ |
| $M_5 =$ | $19\overset{\circ}{.}863000 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}582992 \cdot T$ |
| $M_6 =$ | $317\overset{\circ}{.}394000 + 1080\overset{\circ}{.}0 \cdot T + 141\overset{\circ}{.}793992 \cdot T$ |
Erde Mond Baryzentrum
Es folgt die Berechnung des EMB: \[\begin{align} \delta l &= + 6\overset{''}{.}454\sin(D) - 0\overset{''}{.}424\sin(D - A) + 0\overset{''}{.}177\sin(D + A) \\ &+ 0\overset{''}{.}172\sin(D - M_3) - 0\overset{''}{.}06\sin(D + M_3) \\ \delta b &= + 0\overset{''}{.}576 \sin(U) \\ \delta r &= + 30.76\text{ AE } \cos(D) - 3.06\text{ AE } \cos(D - A) + 0.85\text{ AE } \cos(D + A) \\ &+ 0.57\text{ AE } \cos(D - M_3) - 0.58\text{ AE } \cos(D + M_3) \end{align}\tag{1}\]
mit den Hilfswerten $A, D$ und $U$: \[\begin{align} A &= 134\overset{\circ}{.}964 + 477198\overset{\circ}{.}864\cdot T \\ D &= 297\overset{\circ}{.}864 + 445267\overset{\circ}{.}116\cdot T \\ U &= 93\overset{\circ}{.}276 + 483202\overset{\circ}{.}008\cdot T \end{align}\tag{2}\]
Tabellen
\[\begin{align} dl &= \sum_{n=1}^{6} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{6} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{6} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{3}\]
| Tabelle 2: Keplerterme | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $01$ | $-0.22$ | $6892.76$ | $0.00$ | $0.00$ | $-16707.37$ | $-0.54$ | $1$ | $0 $ | $0$ |
| $02$ | $-0.06$ | $-17.35 $ | $0.00$ | $0.00$ | $42.04 $ | $-0.15$ | $1$ | $0 $ | $1$ |
| $03$ | $-0.01$ | $-0.05 $ | $0.00$ | $0.00$ | $0.13 $ | $-0.02$ | $1$ | $0 $ | $2$ |
| $04$ | $0.00 $ | $71.98 $ | $0.00$ | $0.00$ | $-139.57 $ | $0.00 $ | $2$ | $0 $ | $0$ |
| $05$ | $0.00 $ | $-0.36 $ | $0.00$ | $0.00$ | $0.70 $ | $0.00 $ | $2$ | $0 $ | $1$ |
| $06$ | $0.00 $ | $1.04 $ | $0.00$ | $0.00$ | $-1.75 $ | $0.00 $ | $3$ | $0 $ | $0$ |
\[\begin{align} dl &= \sum_{n=7}^{52} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=7}^{52} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=7}^{52} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{4}\]
| Tabelle 3: Störterme der Planeten | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Störungen durch die Venus | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $07$ | $0.03 $ | $-0.07$ | $0.02 $ | $-0.02$ | $-0.16$ | $-0.07$ | $0$ | $-1$ | $0$ |
| $08$ | $2.35 $ | $-4.23$ | $0.00 $ | $0.00 $ | $-4.75$ | $-2.64$ | $1$ | $-1$ | $0$ |
| $09$ | $-0.10$ | $0.06 $ | $0.02 $ | $0.00 $ | $0.12 $ | $0.20 $ | $1$ | $-2$ | $0$ |
| $10$ | $-0.06$ | $-0.03$ | $0.02 $ | $-0.04$ | $0.09 $ | $0.12 $ | $2$ | $-1$ | $0$ |
| $11$ | $-4.70$ | $2.90 $ | $0.01 $ | $-0.01$ | $8.28 $ | $13.42$ | $2$ | $-2$ | $0$ |
| $12$ | $1.80 $ | $-1.74$ | $0.04 $ | $-0.06$ | $-1.44$ | $-1.57$ | $3$ | $-2$ | $0$ |
| $13$ | $-0.67$ | $0.03 $ | $0.01 $ | $0.00 $ | $0.11 $ | $2.43 $ | $3$ | $-3$ | $0$ |
| $14$ | $0.03 $ | $-0.03$ | $0.01 $ | $-0.01$ | $0.10 $ | $0.09 $ | $4$ | $-2$ | $0$ |
| $15$ | $1.51 $ | $-0.40$ | $0.18 $ | $-0.10$ | $-0.88$ | $-3.36$ | $4$ | $-3$ | $0$ |
| $16$ | $-0.19$ | $-0.09$ | $0.00 $ | $0.00 $ | $-0.38$ | $0.77 $ | $4$ | $-4$ | $0$ |
| $17$ | $0.76 $ | $-0.68$ | $0.01 $ | $0.00 $ | $0.30 $ | $0.37 $ | $5$ | $-3$ | $0$ |
| $18$ | $-0.14$ | $-0.04$ | $-0.03$ | $0.00 $ | $-0.11$ | $0.43 $ | $5$ | $-4$ | $0$ |
| $19$ | $-0.05$ | $-0.07$ | $0.00 $ | $0.00 $ | $-0.13$ | $0.21 $ | $5$ | $-5$ | $0$ |
| $20$ | $0.15 $ | $-0.04$ | $0.01 $ | $0.00 $ | $-0.06$ | $-0.21$ | $6$ | $-4$ | $0$ |
| $21$ | $-0.03$ | $-0.03$ | $-0.01$ | $0.00 $ | $-0.09$ | $0.09 $ | $6$ | $-5$ | $0$ |
| $22$ | $-0.05$ | $-0.07$ | $0.00 $ | $0.00 $ | $-0.13$ | $0.21 $ | $5$ | $-6$ | $0$ |
| $23$ | $-0.12$ | $-0.03$ | $-0.02$ | $-0.01$ | $-0.08$ | $0.31 $ | $7$ | $-5$ | $0$ |
| Störungen durch den Mars | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $24$ | $-0.22$ | $0.17 $ | $0.00$ | $0.00$ | $-0.21$ | $-0.27$ | $1$ | $-1$ | $0$ |
| $25$ | $-1.66$ | $0.62 $ | $0.00$ | $0.00$ | $0.16 $ | $0.28 $ | $1$ | $-2$ | $0$ |
| $26$ | $1.96 $ | $0.57 $ | $0.00$ | $0.01$ | $-1.32$ | $4.55 $ | $2$ | $-2$ | $0$ |
| $27$ | $0.40 $ | $0.15 $ | $0.00$ | $0.00$ | $-0.17$ | $0.46 $ | $2$ | $-3$ | $0$ |
| $28$ | $-0.53$ | $0.26 $ | $0.00$ | $0.00$ | $0.09 $ | $-0.22$ | $2$ | $-4$ | $0$ |
| $29$ | $0.05 $ | $0.12 $ | $0.00$ | $0.00$ | $-0.35$ | $0.15 $ | $3$ | $-3$ | $0$ |
| $30$ | $-0.13$ | $-0.48$ | $0.01$ | $0.00$ | $1.06 $ | $-0.29$ | $3$ | $-4$ | $0$ |
| $31$ | $-0.04$ | $-0.20$ | $0.00$ | $0.00$ | $0.20 $ | $-0.04$ | $3$ | $-5$ | $0$ |
| $32$ | $0.00 $ | $-0.03$ | $0.00$ | $0.00$ | $0.10 $ | $0.04 $ | $4$ | $-4$ | $0$ |
| $33$ | $0.05 $ | $-0.07$ | $0.00$ | $0.00$ | $0.20 $ | $0.14 $ | $4$ | $-5$ | $0$ |
| $34$ | $-0.10$ | $0.11 $ | $0.00$ | $0.00$ | $-0.23$ | $-0.22$ | $4$ | $-6$ | $0$ |
| $35$ | $-0.05$ | $0.00 $ | $0.00$ | $0.00$ | $0.01 $ | $-0.14$ | $5$ | $-7$ | $0$ |
| $36$ | $0.05 $ | $0.01 $ | $0.00$ | $0.00$ | $-0.02$ | $0.10 $ | $5$ | $-8$ | $0$ |
| Störungen durch den Jupiter | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $37$ | $0.01 $ | $0.07 $ | $0.00$ | $-0.02$ | $0.18 $ | $-0.02 $ | $-$1 | $-1$ | $0$ |
| $38$ | $-0.31$ | $2.58 $ | $0.02$ | $0.00 $ | $-0.52$ | $0.34 $ | $0$ | $-1$ | $0$ |
| $39$ | $-7.21$ | $-0.06$ | $0.00$ | $-0.02$ | $0.13 $ | $-16.27$ | $1$ | $-1$ | $0$ |
| $40$ | $-0.54$ | $-1.52$ | $0.01$ | $-0.17$ | $3.09 $ | $-1.12 $ | $1$ | $-2$ | $0$ |
| $41$ | $-0.03$ | $-0.21$ | $0.00$ | $-0.02$ | $0.38 $ | $-0.06 $ | $1$ | $-3$ | $0$ |
| $42$ | $-0.16$ | $0.05 $ | $0.01$ | $0.00 $ | $-0.18$ | $-0.31 $ | $2$ | $-1$ | $0$ |
| $43$ | $0.14 $ | $-2.73$ | $0.00$ | $0.00 $ | $9.23 $ | $0.48 $ | $2$ | $-2$ | $0$ |
| $44$ | $0.07 $ | $-0.55$ | $0.01$ | $0.00 $ | $1.83 $ | $0.25 $ | $2$ | $-3$ | $0$ |
| $45$ | $0.02 $ | $-0.08$ | $0.00$ | $0.00 $ | $0.25 $ | $0.06 $ | $2$ | $-4$ | $0$ |
| $46$ | $0.01 $ | $-0.07$ | $0.00$ | $0.00 $ | $0.16 $ | $0.04 $ | $3$ | $-2$ | $0$ |
| $47$ | $-0.16$ | $-0.03$ | $0.00$ | $0.00 $ | $0.08 $ | $-0.64 $ | $3$ | $-3$ | $0$ |
| $48$ | $-0.04$ | $-0.01$ | $0.00$ | $0.00 $ | $0.03 $ | $-0.17 $ | $3$ | $-4$ | $0$ |
| Störungen durch den Saturn | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $49$ | $0.00 $ | $0.32 $ | $0.00$ | $0.00 $ | $0.01 $ | $0.00 $ | $0$ | $-1$ | $0$ |
| $50$ | $-0.08$ | $-0.41$ | $0.00$ | $-0.01$ | $0.97 $ | $-0.18$ | $1$ | $-1$ | $0$ |
| $51$ | $0.04 $ | $0.10 $ | $0.00$ | $0.00 $ | $-0.23$ | $0.10 $ | $1$ | $-2$ | $0$ |
| $52$ | $0.04 $ | $0.10 $ | $0.00$ | $0.00 $ | $-0.35$ | $0.13 $ | $2$ | $-2$ | $0$ |
Heliozentrische Koordinaten
\[\begin{align} \Delta l &= + 6\overset{''}{.}40\sin(251\overset{\circ}{.}388 + 20\overset{\circ}{.}196\cdot T) + 1\overset{''}{.}87\sin(207\overset{\circ}{.}504 + 150\overset{\circ}{.}264\cdot T) \\ & + 0\overset{''}{.}27\sin(150\overset{\circ}{.}804 + 119\overset{\circ}{.}016\ T) + 0\overset{''}{.}2\sin(128\overset{\circ}{.}916 + 893\overset{\circ}{.}304\cdot T) \\ l_3 &= M_3 + 102\overset{\circ}{.}940308 + (6191\overset{''}{.}2\cdot T + 1\overset{''}{.}1\cdot T^2 + \Delta l + \delta l + \text{dl})/3600'' \\ b_3 &= - (\text{db} + \delta b)/3600'' \\ r_3 &= 1.0001398\text{ AE} - 7.0 \cdot 10^{-7}\text{ AE} \cdot T + 10^{-6}\text{ AE }(\text{dr} + \delta r) \end{align}\tag{5}\]