Inhaltsverzeichnis

MerkurVenusErdeMarsJupiterSaturnUranusNeptun

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

\[\begin{align} \Delta l &= + 6\overset{''}{.}40\sin(251\overset{\circ}{.}388 + 20\overset{\circ}{.}196\cdot T) + 1\overset{''}{.}87\sin(207\overset{\circ}{.}504 + 150\overset{\circ}{.}264\cdot T) \\ & + 0\overset{''}{.}27\sin(150\overset{\circ}{.}804 + 119\overset{\circ}{.}016\ T) + 0\overset{''}{.}2\sin(128\overset{\circ}{.}916 + 893\overset{\circ}{.}304\cdot T) \\ l_3 &= M_3 + 102\overset{\circ}{.}940308 + (6191\overset{''}{.}2\cdot T + 1\overset{''}{.}1\cdot T^2 + \Delta l + \delta l + \text{dl})/3600'' \\ b_3 &= - (\text{db} + \delta b)/3600'' \\ r_3 &= 1.0001398\text{ AE} - 7.0 \cdot 10^{-7}\text{ AE} \cdot T + 10^{-6}\text{ AE }(\text{dr} + \delta r) \end{align}\tag{5}\]