Inhaltsverzeichnis
Uranus
mittlere Anomalien
| Tabelle 1 | |
|---|---|
| $M_5 =$ | $20\overset{\circ}{.}320992 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}904004 \cdot T$ |
| $M_6 =$ | $317\overset{\circ}{.}865996 + 1080\overset{\circ}{.}0 \cdot T + 142\overset{\circ}{.}112988 \cdot T$ |
| $M_7 =$ | $142\overset{\circ}{.}816212 + 360\overset{\circ}{.}0 \cdot T + 68\overset{\circ}{.}502564 \cdot T$ |
| $M_8 =$ | $259\overset{\circ}{.}805988 + 0\overset{\circ}{.}0 \cdot T + 218\overset{\circ}{.}467008 \cdot T$ |
Tabellen
\[\begin{align} dl &= \sum_{n=1}^{10} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{10} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{10} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\]
| Tabelle 2: Keplerterme | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $01$ | $-78.1$ | $19518.1$ | $2759.5$ | $-311.9$ | $-90718.2$ | $-334.7$ | $1 $ | $0 $ | $0 $ |
| $02$ | $-81.6$ | $107.7 $ | $-2.8 $ | $-43.7 $ | $-497.4 $ | $-379.5$ | $1 $ | $0 $ | $1 $ |
| $03$ | $-6.6 $ | $-3.1 $ | $-0.4 $ | $-0.5 $ | $14.4 $ | $-30.6 $ | $1 $ | $0 $ | $2 $ |
| $04$ | $0.0 $ | $-0.5 $ | $0.0 $ | $0.0 $ | $2.4 $ | $0.0 $ | $1 $ | $0 $ | $3 $ |
| $05$ | $-2.4 $ | $586.1 $ | $130.6 $ | $-14.3 $ | $-2145.2 $ | $-15.3 $ | $2 $ | $0 $ | $0 $ |
| $06$ | $-4.5 $ | $6.6 $ | $0.7 $ | $-1.6 $ | $-24.2 $ | $-17.8 $ | $2 $ | $0 $ | $1 $ |
| $07$ | $-0.4 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.1 $ | $-1.4 $ | $2 $ | $0 $ | $2 $ |
| $08$ | $0.0 $ | $24.5 $ | $7.0 $ | $-0.7 $ | $-76.2 $ | $-0.6 $ | $3 $ | $0 $ | $0 $ |
| $09$ | $-0.2 $ | $0.4 $ | $0.1 $ | $-0.1 $ | $-1.4 $ | $-0.8 $ | $3 $ | $0 $ | $1 $ |
| $10$ | $0.0 $ | $1.1 $ | $0.4 $ | $0.0 $ | $-3.0 $ | $0.1 $ | $4 $ | $0 $ | $0 $ |
\[\begin{align} dl &= \sum_{n=11}^{61} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \\ db &= \sum_{n=11}^{61} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \\ dr &= \sum_{n=11}^{61} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t)) \end{align}\tag{2}\]
| Tabelle 3: Störterme der Planeten | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Störungen durch den Jupiter | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $11$ | $0.0 $ | $0.0 $ | $-0.1 $ | $0.0 $ | $-0.1 $ | $1.7 $ | $-1$ | $-1$ | $0 $ |
| $12$ | $0.5 $ | $-1.2 $ | $-0.9 $ | $0.1 $ | $18.9 $ | $9.1 $ | $0 $ | $-1$ | $0 $ |
| $13$ | $-21.2$ | $48.7 $ | $0.0 $ | $0.0 $ | $-455.5 $ | $198.8 $ | $1 $ | $-1$ | $0 $ |
| $14$ | $-0.5 $ | $1.2 $ | $0.0 $ | $0.0 $ | $-10.9 $ | $-4.8 $ | $1 $ | $-2$ | $0 $ |
| $15$ | $-1.3 $ | $3.2 $ | $0.3 $ | $0.1 $ | $-23.2 $ | $-11.1 $ | $2 $ | $-1$ | $0 $ |
| $16$ | $-0.2 $ | $0.2 $ | $0.0 $ | $0.0 $ | $1.1 $ | $1.5 $ | $2 $ | $-2$ | $0 $ |
| $17$ | $0.0 $ | $0.2 $ | $0.0 $ | $0.0 $ | $-1.8 $ | $0.4 $ | $3 $ | $-1$ | $0 $ |
| Störungen durch den Saturn | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $18$ | $1.4 $ | $-0.5 $ | $-0.4 $ | $-0.8 $ | $-6.4 $ | $9.0 $ | $0 $ | $-1$ | $0 $ |
| $19$ | $-18.6$ | $-12.6 $ | $1.0 $ | $0.3 $ | $36.7 $ | $-336.8$ | $1 $ | $-1$ | $0 $ |
| $20$ | $-0.7 $ | $-0.3 $ | $0.1 $ | $0.0 $ | $0.5 $ | $-7.5 $ | $1 $ | $-2$ | $0 $ |
| $21$ | $20.0 $ | $-141.6 $ | $3.1 $ | $-0.8 $ | $-587.1 $ | $-107.0$ | $2 $ | $-1$ | $0 $ |
| $22$ | $1.0 $ | $1.4 $ | $0.0 $ | $0.0 $ | $5.8 $ | $-4.0 $ | $2 $ | $-1$ | $1 $ |
| $23$ | $1.6 $ | $-3.8 $ | $0.0 $ | $0.0 $ | $-35.6 $ | $-16.0 $ | $2 $ | $-2$ | $0 $ |
| $24$ | $75.3 $ | $-100.9 $ | $-0.8 $ | $0.1 $ | $128.9 $ | $77.5 $ | $3 $ | $-1$ | $0 $ |
| $25$ | $0.2 $ | $1.8 $ | $0.0 $ | $0.0 $ | $-1.9 $ | $0.3 $ | $3 $ | $-1$ | $1 $ |
| $26$ | $2.3 $ | $-1.3 $ | $0.0 $ | $0.1 $ | $-9.5 $ | $-17.9 $ | $3 $ | $-2$ | $0 $ |
| $27$ | $-0.7 $ | $-0.5 $ | $0.0 $ | $0.0 $ | $-4.9 $ | $6.8 $ | $3 $ | $-3$ | $0 $ |
| $28$ | $3.4 $ | $-5.0 $ | $-0.8 $ | $-0.5 $ | $21.6 $ | $14.3 $ | $4 $ | $-1$ | $0 $ |
| $29$ | $1.9 $ | $0.1 $ | $0.0 $ | $0.0 $ | $1.2 $ | $-12.1 $ | $4 $ | $-2$ | $0 $ |
| $30$ | $-0.1 $ | $-0.4 $ | $0.0 $ | $0.0 $ | $-3.9 $ | $1.2 $ | $4 $ | $-3$ | $0 $ |
| $31$ | $-0.2 $ | $0.1 $ | $0.0 $ | $0.0 $ | $1.6 $ | $1.8 $ | $4 $ | $-4$ | $0 $ |
| $32$ | $0.2 $ | $-0.3 $ | $-0.1 $ | $0.0 $ | $1.0 $ | $0.6 $ | $5 $ | $-1$ | $0 $ |
| $33$ | $-2.2 $ | $-2.2 $ | $0.0 $ | $0.0 $ | $-7.7 $ | $8.5 $ | $5 $ | $-2$ | $0 $ |
| $34$ | $0.1 $ | $-0.2 $ | $0.0 $ | $0.0 $ | $-1.4 $ | $-0.4 $ | $5 $ | $-3$ | $0 $ |
| $35$ | $-0.1 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.1 $ | $1.2 $ | $5 $ | $-4$ | $0 $ |
| $36$ | $-0.2 $ | $-0.6 $ | $0.0 $ | $0.0 $ | $1.4 $ | $-0.7 $ | $6 $ | $-2$ | $0 $ |
| Störungen durch den Neptun | |||||||||
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $37$ | $-0.2 $ | $0.2 $ | $-0.1 $ | $0.0 $ | $0.7 $ | $0.7 $ | $-1$ | $-1$ | $0 $ |
| $38$ | $-2.8 $ | $2.5 $ | $-0.4 $ | $-0.1 $ | $8.7 $ | $10.5 $ | $0 $ | $-1$ | $0 $ |
| $39$ | $-28.4$ | $20.3 $ | $0.0 $ | $0.0 $ | $-51.4 $ | $-72.0 $ | $1 $ | $-1$ | $0 $ |
| $40$ | $-0.6 $ | $-0.1 $ | $0.2 $ | $0.4 $ | $4.2 $ | $-14.6 $ | $1 $ | $-2$ | $0 $ |
| $41$ | $0.2 $ | $0.5 $ | $-0.1 $ | $0.1 $ | $3.4 $ | $-1.6 $ | $1 $ | $-3$ | $0 $ |
| $42$ | $-1.8 $ | $1.3 $ | $0.0 $ | $0.3 $ | $-5.5 $ | $-7.7 $ | $2 $ | $-1$ | $0 $ |
| $43$ | $29.4 $ | $10.2 $ | $0.0 $ | $0.0 $ | $-29.0 $ | $83.2 $ | $2 $ | $-2$ | $0 $ |
| $44$ | $8.8 $ | $17.8 $ | $-0.1 $ | $-0.3 $ | $-41.9 $ | $21.5 $ | $2 $ | $-3$ | $0 $ |
| $45$ | $0.0 $ | $0.1 $ | $0.1 $ | $0.0 $ | $-2.1 $ | $-0.9 $ | $2 $ | $-4$ | $0 $ |
| $46$ | $1.5 $ | $0.5 $ | $0.1 $ | $-0.2 $ | $-1.7 $ | $5.1 $ | $3 $ | $-2$ | $0 $ |
| $47$ | $4.4 $ | $14.6 $ | $0.1 $ | $-0.1 $ | $-84.3 $ | $-25.2 $ | $3 $ | $-3$ | $0 $ |
| $48$ | $2.4 $ | $-4.5 $ | $0.0 $ | $0.0 $ | $12.0 $ | $6.2 $ | $3 $ | $-4$ | $0 $ |
| $49$ | $2.9 $ | $-0.9 $ | $0.0 $ | $0.0 $ | $2.1 $ | $6.2 $ | $3 $ | $-5$ | $0 $ |
| $50$ | $0.3 $ | $1.0 $ | $0.1 $ | $-0.1 $ | $-4.0 $ | $1.1 $ | $4 $ | $-3$ | $0 $ |
| $51$ | $2.1 $ | $-2.7 $ | $0.0 $ | $0.0 $ | $17.9 $ | $14.0 $ | $4 $ | $-4$ | $0 $ |
| $52$ | $3.0 $ | $-0.4 $ | $-0.1 $ | $-0.1 $ | $2.3 $ | $17.6 $ | $4 $ | $-5$ | $0 $ |
| $53$ | $-0.6 $ | $-0.5 $ | $0.0 $ | $0.0 $ | $1.1 $ | $-1.6 $ | $4 $ | $-6$ | $0 $ |
| $54$ | $0.2 $ | $-0.2 $ | $0.0 $ | $0.0 $ | $1.0 $ | $0.8 $ | $5 $ | $-4$ | $0 $ |
| $55$ | $-0.9 $ | $-0.1 $ | $0.0 $ | $0.0 $ | $0.6 $ | $-7.1 $ | $5 $ | $-5$ | $0 $ |
| $56$ | $-0.5 $ | $-0.6 $ | $0.0 $ | $0.0 $ | $3.8 $ | $-3.6 $ | $5 $ | $-6$ | $0 $ |
| $57$ | $0.0 $ | $-0.5 $ | $0.0 $ | $0.0 $ | $3.0 $ | $0.1 $ | $5 $ | $-7$ | $0 $ |
| $58$ | $0.2 $ | $0.3 $ | $0.0 $ | $0.0 $ | $-2.7 $ | $1.6 $ | $6 $ | $-6$ | $0 $ |
| $59$ | $-0.1 $ | $0.2 $ | $0.0 $ | $0.0 $ | $-2.0 $ | $-0.4 $ | $6 $ | $-7$ | $0 $ |
| $60$ | $0.1 $ | $-0.2 $ | $0.0 $ | $0.0 $ | $1.3 $ | $0.5 $ | $7 $ | $-7$ | $0 $ |
| $61$ | $0.1 $ | $0.0 $ | $0.0 $ | $0.0 $ | $0.4 $ | $0.9 $ | $7 $ | $-8$ | $0 $ |
\[\begin{align} dl &= \sum_{n=62}^{70} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=62}^{70} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=62}^{70} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{3}\]
| Tabelle 3: Störungen durch den Jupiter und den Saturn | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| n | $a_n['']$ | $b_n['']$ | $c_n['']$ | $d_n['']$ | $e_n['']$ | $f_n['']$ | $p_n$ | $s_n$ | $t_n$ |
| $62$ | $-0.7 $ | $0.4 $ | $0.0 $ | $0.0 $ | $-1.5 $ | $-2.5 $ | $-2$ | $2 $ | $-4$ |
| $63$ | $-0.1 $ | $-0.1 $ | $0.0 $ | $0.0 $ | $-2.2 $ | $1.0 $ | $-1$ | $2 $ | $-4$ |
| $64$ | $0.1 $ | $-0.4 $ | $0.0 $ | $0.0 $ | $1.4 $ | $0.2 $ | $1 $ | $0 $ | $-5$ |
| $65$ | $0.4 $ | $0.5 $ | $0.0 $ | $0.0 $ | $-0.8 $ | $-0.8 $ | $1 $ | $0 $ | $-6$ |
| $66$ | $5.7 $ | $6.3 $ | $0.0 $ | $0.0 $ | $28.5 $ | $-25.5 $ | $2 $ | $0 $ | $-6$ |
| $67$ | $+0.1\cdot T$ | $-0.2\cdot T$ | $+0.0\cdot T$ | $+0.0\cdot T$ | $-1.1\cdot T$ | $-0.6\cdot T$ | $2$ | $0$ | $-6$ |
| $68$ | $-1.4 $ | $29.2$ | $0.0$ | $0.0$ | $-11.4$ | $1.1$ | $3$ | $0$ | $-6$ |
| $69$ | $+0.8\cdot T$ | $-0.4\cdot T$ | $+0.0\cdot T$ | $+0.0\cdot T$ | $+0.2\cdot T$ | $+0.3\cdot T$ | $3$ | $0$ | $-6$ |
| $70$ | $0.0$ | $1.3$ | $0.0$ | $0.0$ | $-6.0$ | $-0.1$ | $4$ | $0$ | $-6$ |
Heliozentrische Koordinaten
\[\begin{align} l_7 &= M_7 + 170\overset{\circ}{.}454348 + (5082\overset{''}{.}3\cdot T + 34\overset{''}{.}2\cdot T^2 + \text{dl})/3600'' \\ b_7 &= (- 130\overset{''}{.}61 - 0\overset{''}{.}54\cdot T + 0\overset{''}{.}04\cdot T^2 + \text{db})/3600'' \\ r_7 &= 19.211991\text{ AE} - 3.33 \cdot 10^{-4}\text{ AE} \cdot T - 5.0 \cdot 10^{-6}\text{ AE} \cdot T^2 + 10^{-5}\text{ AE dr} \end{align}\tag{4}\]