Inhaltsverzeichnis
Jupiter
mittlere Anomalien
| Tabelle 1 | |
|---|---|
| $M_5 =$ | $20\overset{\circ}{.}351304 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}906668 \cdot T$ |
| $M_6 =$ | $317\overset{\circ}{.}875212 + 1080\overset{\circ}{.}0 \cdot T + 142\overset{\circ}{.}116768 \cdot T$ |
| $M_7 =$ | $142\overset{\circ}{.}903332 + 360\overset{\circ}{.}0 \cdot T + 68\overset{\circ}{.}493096 \cdot T$ |
Tabellen
\[\begin{align} dl &= \sum_{n=1}^{7} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{7} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{7} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\]
| Tabelle 2: Keplerterme | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $01$ | $-113.1$ | $19998.6$ | $-4670.7$ | $288.9$ | $-25208.2$ | $-142.2$ | $1$ | $0$ | $0$ |
| $02$ | $-76.1 $ | $66.9 $ | $21.6 $ | $29.4 $ | $-84.2 $ | $-95.8 $ | $1$ | $0$ | $1$ |
| $03$ | $-0.5 $ | $-0.3 $ | $0.1 $ | $-0.1 $ | $0.4 $ | $-0.7 $ | $1$ | $0$ | $2$ |
| $04$ | $-3.4 $ | $632.0 $ | $-226.8 $ | $12.7 $ | $-610.6 $ | $-6.5 $ | $2$ | $0$ | $0$ |
| $05$ | $-4.2 $ | $3.8 $ | $0.2 $ | $0.6 $ | $-4.1 $ | $-4.5 $ | $2$ | $0$ | $1$ |
| $06$ | $-0.1 $ | $28.0 $ | $-12.5 $ | $0.7 $ | $-22.1 $ | $-0.2 $ | $3$ | $0$ | $0$ |
| $07$ | $0.0 $ | $1.4 $ | $-0.6 $ | $0.0 $ | $-1.0 $ | $0.0 $ | $4$ | $0$ | $0$ |
\[\begin{align} dl &= \sum_{n=8}^{50} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \\ db &= \sum_{n=8}^{50} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t)) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=8}^{50} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \end{align}\tag{2}\]
| Tabelle 3: Störterme der Planeten | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Störungen durch den Saturn | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $08$ | $-0.2 $ | $1.4 $ | $0.1 $ | $-0.2 $ | $2.0 $ | $0.6 $ | $-1$ | $-1 $ | $0$ |
| $09$ | $9.4 $ | $8.9 $ | $-0.4 $ | $-1.4 $ | $3.9 $ | $-8.3 $ | $0 $ | $-1 $ | $0$ |
| $10$ | $5.6 $ | $-3.0 $ | $-2.0 $ | $0.0 $ | $-5.4 $ | $-5.7 $ | $0 $ | $-2 $ | $0$ |
| $11$ | $-4.0 $ | $-0.1 $ | $0.0 $ | $0.0 $ | $0.0 $ | $5.5 $ | $0 $ | $-3 $ | $0$ |
| $12$ | $3.3 $ | $-1.6 $ | $-0.5 $ | $-1.2 $ | $-1.6 $ | $-3.1 $ | $0 $ | $-5 $ | $0$ |
| $13$ | $78.8 $ | $-14.5 $ | $-0.2 $ | $0.2 $ | $11.5 $ | $64.4 $ | $1 $ | $-1 $ | $0$ |
| $14$ | $-2.0 $ | $-132.4 $ | $-1.7 $ | $0.4 $ | $28.8 $ | $4.3 $ | $1 $ | $-2 $ | $0$ |
| $15$ | $-1.1 $ | $-0.7 $ | $0.0 $ | $0.0 $ | $0.2 $ | $-0.3 $ | $1 $ | $-2 $ | $1$ |
| $16$ | $-7.5 $ | $-6.8 $ | $0.6 $ | $-0.9 $ | $-0.4 $ | $-1.1 $ | $1 $ | $-3 $ | $0$ |
| $17$ | $0.7 $ | $0.7 $ | $0.0 $ | $-0.2 $ | $0.6 $ | $-1.1 $ | $1 $ | $-4 $ | $0$ |
| $18$ | $51.5 $ | $-26.0 $ | $-4.9 $ | $-12.4$ | $-32.5 $ | $-64.4 $ | $1 $ | $-5 $ | $0$ |
| $19$ | $-1.2 $ | $-2.2 $ | $-0.4 $ | $0.3 $ | $-2.7 $ | $1.5 $ | $1 $ | $-5 $ | $1$ |
| $20$ | $5.3 $ | $-0.7 $ | $0.2 $ | $1.1 $ | $0.7 $ | $6.1 $ | $2 $ | $-1 $ | $0$ |
| $21$ | $-76.4 $ | $-185.1 $ | $1.6 $ | $0.0 $ | $260.2 $ | $-108.0$ | $2 $ | $-2 $ | $0$ |
| $22$ | $66.7 $ | $47.8 $ | $0.9 $ | $0.3 $ | $-51.4 $ | $69.8 $ | $2 $ | $-3 $ | $0$ |
| $23$ | $0.6 $ | $-1.0 $ | $0.0 $ | $0.0 $ | $1.0 $ | $0.6 $ | $2 $ | $-3 $ | $1$ |
| $24$ | $17.0 $ | $1.4 $ | $0.0 $ | $-0.1 $ | $-1.8 $ | $9.6 $ | $2 $ | $-4 $ | $0$ |
| $25$ | $1066.2$ | $-518.3 $ | $1.8 $ | $-0.3 $ | $-1.3 $ | $-23.9 $ | $2 $ | $-5 $ | $0$ |
| $26$ | $-25.4 $ | $-40.3 $ | $0.0 $ | $0.0 $ | $-0.9 $ | $0.3 $ | $2 $ | $-5 $ | $1$ |
| $27$ | $-0.7 $ | $0.5 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.0 $ | $2 $ | $-5 $ | $2$ |
| $28$ | $-5.0 $ | $-11.5 $ | $2.1 $ | $-1.0 $ | $11.7 $ | $-5.4 $ | $3 $ | $-2 $ | $0$ |
| $29$ | $16.9 $ | $-6.4 $ | $-0.5 $ | $0.8 $ | $13.4 $ | $26.9 $ | $3 $ | $-3 $ | $0$ |
| $30$ | $7.2 $ | $-13.3 $ | $0.1 $ | $-0.1 $ | $20.9 $ | $10.5 $ | $3 $ | $-4 $ | $0$ |
| $31$ | $68.5 $ | $134.3 $ | $7.1 $ | $15.2 $ | $-166.9 $ | $86.5 $ | $3 $ | $-5 $ | $0$ |
| $32$ | $3.5 $ | $-2.7 $ | $0.5 $ | $-0.4 $ | $3.4 $ | $4.3 $ | $3 $ | $-5 $ | $1$ |
| $33$ | $0.6 $ | $1.0 $ | $0.0 $ | $0.0 $ | $-0.9 $ | $0.5 $ | $3 $ | $-6 $ | $0$ |
| $34$ | $-1.1 $ | $1.7 $ | $0.0 $ | $0.0 $ | $-0.4 $ | $-0.2 $ | $3 $ | $-7 $ | $0$ |
| $35$ | $-0.3 $ | $-0.7 $ | $0.2 $ | $-0.1 $ | $0.4 $ | $-0.2 $ | $4 $ | $-2 $ | $0$ |
| $36$ | $1.1 $ | $-0.6 $ | $0.1 $ | $0.2 $ | $0.9 $ | $1.2 $ | $4 $ | $-3 $ | $0$ |
| $37$ | $3.2 $ | $1.7 $ | $0.2 $ | $0.1 $ | $-4.1 $ | $5.8 $ | $4 $ | $-4 $ | $0$ |
| $38$ | $6.7 $ | $8.7 $ | $-1.1 $ | $1.6 $ | $-9.3 $ | $8.7 $ | $4 $ | $-5 $ | $0$ |
| $39$ | $1.5 $ | $-0.3 $ | $0.0 $ | $0.0 $ | $0.6 $ | $2.4 $ | $4 $ | $-6 $ | $0$ |
| $40$ | $-1.9 $ | $2.3 $ | $0.0 $ | $-0.1 $ | $-3.2 $ | $-2.7 $ | $4 $ | $-7 $ | $0$ |
| $41$ | $0.4 $ | $-1.8 $ | $0.0 $ | $0.0 $ | $1.9 $ | $0.5 $ | $4 $ | $-8 $ | $0$ |
| $42$ | $-0.2 $ | $-0.5 $ | $0.0 $ | $0.0 $ | $0.3 $ | $-0.1 $ | $4 $ | $-9 $ | $0$ |
| $43$ | $-8.6 $ | $-6.8 $ | $0.0 $ | $0.0 $ | $-0.4 $ | $0.1 $ | $4 $ | $-10$ | $0$ |
| $44$ | $-0.5 $ | $0.6 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.0 $ | $4 $ | $-10$ | $1$ |
| $45$ | $-0.1 $ | $1.5 $ | $-0.1 $ | $0.1 $ | $-2.5 $ | $-0.8 $ | $5 $ | $-5 $ | $0$ |
| $46$ | $0.1 $ | $0.8 $ | $0.0 $ | $0.0 $ | $-1.6 $ | $0.1 $ | $5 $ | $-6 $ | $0$ |
| $47$ | $-0.5 $ | $-0.1 $ | $0.0 $ | $0.0 $ | $0.1 $ | $-0.8 $ | $5 $ | $-9 $ | $0$ |
| $48$ | $2.5 $ | $-2.2 $ | $0.1 $ | $-0.2 $ | $2.8 $ | $3.1 $ | $5 $ | $-10$ | $0$ |
| Störungen durch den Uranus | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $49$ | $0.4 $ | $0.9 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.0 $ | $1$ | $-1$ | $0$ |
| $50$ | $0.4 $ | $0.4 $ | $0.0 $ | $0.0 $ | $-0.4 $ | $0.3 $ | $1$ | $-2$ | $0$ |
\[\begin{align} dl &= \sum_{n=51}^{52} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=51}^{52} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=51}^{52} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{3}\]
| Tabelle 4: Störungen durch den Saturn und den Uranus | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $51$ | $-0.8 $ | $8.5 $ | $0.0 $ | $0.0 $ | $-0.1 $ | $0.0 $ | $2$ | $-6$ | $3$ |
| $52$ | $0.4 $ | $0.5 $ | $-0.1 $ | $0.0 $ | $-0.7 $ | $0.5 $ | $3$ | $-6$ | $3$ |
Heliozentrische Koordinaten
\[\begin{align} l_5 &= M_5 + 14\overset{\circ}{.}00076 + (5025\overset{''}{.}2\cdot T + 0\overset{''}{.}8\cdot T^2 + \text{dl})/3600'' \\ b_5 &= (+ 227\overset{''}{.}3 - 0\overset{''}{.}3\cdot T + \text{db})/3600'' \\ r_5 &= 5.208873\text{ AE} + 4.1 \cdot 10^{-5}\text{ AE} \cdot T + 10^{-5}\text{ AE dr} \end{align}\tag{4}\]