|[[tabellen:merkur_de200|Merkur]]|[[tabellen:venus_de200|Venus]]|[[tabellen:erde_de200|Erde]]|[[tabellen:mars_de200|Mars]]|[[tabellen:jupiter_de200|Jupiter]]|[[tabellen:saturn_de200|Saturn]]|[[tabellen:uranus_de200|Uranus]]|[[tabellen:neptun_de200|Neptun]]| ====== Merkur ====== {{ :merkur_vsop87.png?nolink&100|}} ===== mittlere Anomalien ===== {{tablelayout?rowsHeaderSource=Auto&colwidth="70px,430px"&float=center}} ^ Tabelle 1 || | $M_1 =$ | $174\overset{\circ}{.}794652 + 149400\overset{\circ}{.}0 \cdot T + 72\overset{\circ}{.}515304 \cdot T$ | | $M_2 =$ | $50\overset{\circ}{.}191992 + 58320\overset{\circ}{.}0 \cdot T + 197\overset{\circ}{.}655984 \cdot T$ | | $M_3 =$ | $357\overset{\circ}{.}762996 + 35640\overset{\circ}{.}0 \cdot T + 359\overset{\circ}{.}213004 \cdot T$ | | $M_5 =$ | $20\overset{\circ}{.}103012 + 2880\overset{\circ}{.}0 \cdot T + 154\overset{\circ}{.}743012 \cdot T$ | | $M_6 =$ | $317\overset{\circ}{.}639988 + 1080\overset{\circ}{.}0 \cdot T + 141\overset{\circ}{.}959988 \cdot T$ | ===== Tabellen ===== \[\begin{align} dl &= \sum_{n=1}^{17} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{17} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{17} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\tag{1}\] {{tablelayout?rowsHeaderSource=Auto&colwidth="-"&float=center}} ^ Tabelle 2: Keplerterme |||||||||| ^ $n$ ^ $a_n['']$ ^ $b_n['']$ ^ $c_n['']$ ^ $d_n['']$ ^ $e_n['']$ ^ $f_n['']$ ^ $p_n$ ^ $s_n$ ^ $t_n$ ^ | $01$ | $259.74 $ | $84547.39 $ | $11683.22$ | $21203.79$ | $-78342.34$ | $0.01$ | $1$ | $0$ | $0$ | | $02$ | $2.30 $ | $5.04 $ | $138.55 $ | $-71.01 $ | $-7.52 $ | $0.02$ | $1$ | $0$ | $1$ | | $03$ | $0.01 $ | $-0.01 $ | $-0.19 $ | $-0.54 $ | $0.01 $ | $0.01$ | $1$ | $0$ | $2$ | | $04$ | $-549.71$ | $10394.44$ | $2390.29$ | $4306.79$ | $-7955.45 $ | $0.00$ | $2$ | $0$ | $0$ | | $05$ | $-4.77 $ | $8.91 $ | $28.49 $ | $-14.18 $ | $-1.53 $ | $0.00$ | $2$ | $0$ | $1$ | | $06$ | $0.00 $ | $0.00 $ | $-0.04 $ | $-0.11 $ | $0.00 $ | $0.00$ | $2$ | $0$ | $2$ | | $07$ | $-234.04$ | $1748.74 $ | $535.41 $ | $984.33 $ | $-1212.86 $ | $0.00$ | $3$ | $0$ | $0$ | | $08$ | $-2.03 $ | $3.48 $ | $6.56 $ | $-2.91 $ | $-0.35 $ | $0.00$ | $3$ | $0$ | $1$ | | $09$ | $-77.64 $ | $332.63 $ | $124.40 $ | $237.03 $ | $-219.23 $ | $0.00$ | $4$ | $0$ | $0$ | | $10$ | $-0.70 $ | $1.10 $ | $1.59 $ | $-0.59 $ | $-0.08 $ | $0.00$ | $4$ | $0$ | $1$ | | $11$ | $-23.59 $ | $67.28 $ | $29.44 $ | $58.77 $ | $-43.54 $ | $0.00$ | $5$ | $0$ | $0$ | | $12$ | $-0.23 $ | $0.32 $ | $0.39 $ | $-0.11 $ | $-0.02 $ | $0.00$ | $5$ | $0$ | $1$ | | $13$ | $-6.86 $ | $14.06 $ | $7.03 $ | $14.84 $ | $-9.18 $ | $0.00$ | $6$ | $0$ | $0$ | | $14$ | $-0.07 $ | $0.09 $ | $0.10 $ | $-0.02 $ | $-0.01 $ | $0.00$ | $6$ | $0$ | $1$ | | $15$ | $-1.94 $ | $2.98 $ | $1.69 $ | $3.80 $ | $-2.02 $ | $0.00$ | $7$ | $0$ | $0$ | | $16$ | $-0.54 $ | $0.63 $ | $0.41 $ | $0.98 $ | $-0.46 $ | $0.00$ | $8$ | $0$ | $0$ | | $17$ | $-0.15 $ | $0.13 $ | $0.10 $ | $0.25 $ | $-0.11 $ | $0.00$ | $9$ | $0$ | $0$ | \[\begin{align} dl &= \sum_{n=18}^{54} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=18}^{54} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=18}^{54} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\tag{2}\] {{tablelayout?rowsHeaderSource=Auto&colwidth="-"&float=center}} ^ Tabelle 3: Störterme der Planeten |||||||||| ^ Störungen durch die Venus |||||||||| ^ $n$ ^ $a_n['']$ ^ $b_n['']$ ^ $c_n['']$ ^ $d_n['']$ ^ $e_n['']$ ^ $f_n['']$ ^ $p_n$ ^ $s_n$ ^ $t_n$ ^ | $18$ | $-0.17$ | $-0.06$ | $-0.06$ | $-0.07$ | $-0.05$ | $0.14 $ | $-1$ | $-2$ | $0$ | | $19$ | $0.24 $ | $-0.16$ | $0.04 $ | $-0.01$ | $-0.11$ | $-0.16$ | $0 $ | $-1$ | $0$ | | $20$ | $-0.68$ | $-0.25$ | $-0.16$ | $-0.18$ | $-0.26$ | $0.73 $ | $0 $ | $-2$ | $0$ | | $21$ | $0.37 $ | $0.08 $ | $0.13 $ | $-0.12$ | $0.06 $ | $-0.28$ | $0 $ | $-5$ | $0$ | | $22$ | $0.58 $ | $-0.41$ | $0.01 $ | $-0.01$ | $0.26 $ | $0.36 $ | $1 $ | $-1$ | $0$ | | $23$ | $-3.51$ | $-1.23$ | $-0.05$ | $-0.06$ | $0.23 $ | $-0.63$ | $1 $ | $-2$ | $0$ | | $24$ | $0.08 $ | $0.53 $ | $0.02 $ | $-0.09$ | $-0.11$ | $0.04 $ | $1 $ | $-3$ | $0$ | | $25$ | $1.44 $ | $0.31 $ | $0.34 $ | $0.29 $ | $0.30 $ | $-1.39$ | $1 $ | $-5$ | $0$ | | $26$ | $0.15 $ | $-0.11$ | $0.02 $ | $-0.04$ | $0.09 $ | $0.12 $ | $2 $ | $-1$ | $0$ | | $27$ | $-1.99$ | $-0.68$ | $-0.20$ | $0.03 $ | $0.65 $ | $-1.91$ | $2 $ | $-2$ | $0$ | | $28$ | $-0.34$ | $-1.28$ | $0.03 $ | $0.03 $ | $0.97 $ | $-0.26$ | $2 $ | $-3$ | $0$ | | $29$ | $-0.33$ | $0.35 $ | $-0.01$ | $0.00 $ | $-0.13$ | $-0.13$ | $2 $ | $-4$ | $0$ | | $30$ | $7.19 $ | $1.56 $ | $0.06 $ | $0.05 $ | $-0.05$ | $0.12 $ | $2 $ | $-5$ | $0$ | | $31$ | $-0.52$ | $-0.18$ | $-0.16$ | $0.03 $ | $0.13 $ | $-0.39$ | $3 $ | $-2$ | $0$ | | $32$ | $-0.11$ | $-0.42$ | $-0.05$ | $-0.05$ | $0.36 $ | $-0.10$ | $3 $ | $-3$ | $0$ | | $33$ | $-0.19$ | $0.22 $ | $-0.01$ | $0.02 $ | $-0.23$ | $-0.20$ | $3 $ | $-4$ | $0$ | | $34$ | $2.77 $ | $0.49 $ | $0.40 $ | $-0.12$ | $-0.45$ | $2.56 $ | $3 $ | $-5$ | $0$ | | $35$ | $0.67 $ | $0.12 $ | $0.24 $ | $-0.08$ | $-0.09$ | $0.47 $ | $4 $ | $-5$ | $0$ | | $36$ | $0.18 $ | $0.03 $ | $0.09 $ | $-0.03$ | $-0.02$ | $0.12 $ | $5 $ | $-5$ | $0$ | ^ Störungen durch die Erde |||||||||| ^ $n$ ^ $a_n['']$ ^ $b_n['']$ ^ $c_n['']$ ^ $d_n['']$ ^ $e_n['']$ ^ $f_n['']$ ^ $p_n$ ^ $s_n$ ^ $t_n$ ^ | $37$ | $-0.11$ | $-0.07$ | $-0.02$ | $-0.04$ | $-0.08$ | $0.11 $ | $0$ | $-4$ | $0$ | | $38$ | $0.10 $ | $-0.20$ | $0.00 $ | $0.00 $ | $0.15 $ | $0.07 $ | $1$ | $-1$ | $0$ | | $39$ | $-0.35$ | $0.28 $ | $-0.01$ | $0.00 $ | $-0.13$ | $-0.17$ | $1$ | $-2$ | $0$ | | $40$ | $-0.67$ | $-0.45$ | $-0.01$ | $-0.01$ | $0.00 $ | $0.01 $ | $1$ | $-4$ | $0$ | | $41$ | $-0.20$ | $0.16 $ | $-0.01$ | $0.02 $ | $-0.16$ | $-0.20$ | $2$ | $-2$ | $0$ | | $42$ | $0.13 $ | $-0.02$ | $0.01 $ | $0.00 $ | $0.02 $ | $0.14 $ | $2$ | $-3$ | $0$ | | $43$ | $-0.33$ | $-0.18$ | $-0.04$ | $0.00 $ | $0.17 $ | $-0.31$ | $2$ | $-4$ | $0$ | ^ Störungen durch den Jupiter |||||||||| ^ $n$ ^ $a_n['']$ ^ $b_n['']$ ^ $c_n['']$ ^ $d_n['']$ ^ $e_n['']$ ^ $f_n['']$ ^ $p_n$ ^ $s_n$ ^ $t_n$ ^ | $44$ | $-0.08$ | $0.16 $ | $-0.04$ | $0.01 $ | $-0.15$ | $0.08 $ | $-1$ | $-1$ | $0$ | | $45$ | $0.10 $ | $-0.06$ | $0.07 $ | $-0.01$ | $-0.07$ | $-0.12$ | $-1$ | $-2$ | $0$ | | $46$ | $-0.31$ | $0.48 $ | $-0.03$ | $-0.02$ | $-0.02$ | $0.13 $ | $0 $ | $-1$ | $0$ | | $47$ | $0.42 $ | $-0.26$ | $0.20 $ | $-0.03$ | $-0.38$ | $-0.50$ | $0 $ | $-2$ | $0$ | | $48$ | $-0.70$ | $0.01 $ | $0.00 $ | $-0.03$ | $-0.02$ | $0.63 $ | $1 $ | $-1$ | $0$ | | $49$ | $2.61 $ | $-1.97$ | $0.01 $ | $0.01 $ | $1.74 $ | $2.32 $ | $1 $ | $-2$ | $0$ | | $50$ | $0.32 $ | $-0.15$ | $0.00 $ | $0.00 $ | $0.13 $ | $0.28 $ | $1 $ | $-3$ | $0$ | | $51$ | $-0.18$ | $0.01 $ | $-0.03$ | $0.03 $ | $0.00 $ | $-0.13$ | $2 $ | $-1$ | $0$ | | $52$ | $0.75 $ | $-0.56$ | $0.08 $ | $-0.17$ | $0.45 $ | $0.60 $ | $2 $ | $-2$ | $0$ | | $53$ | $0.20 $ | $-0.15$ | $0.04 $ | $-0.08$ | $0.10 $ | $0.14 $ | $3 $ | $-2$ | $0$ | ^ Störungen durch den Saturn |||||||||| ^ $n$ ^ $a_n['']$ ^ $b_n['']$ ^ $c_n['']$ ^ $d_n['']$ ^ $e_n['']$ ^ $f_n['']$ ^ $p_n$ ^ $s_n$ ^ $t_n$ ^ | $54$ | $-0.19$ | $0.33$ | $0.00$ | $0.00$ | $0.00$ | $0.00$ | $1$ | $-2$ | $0$ | ===== Heliozentrische Koordinaten ===== \[\begin{align} l_1 &= M_1 + 77\overset{\circ}{.}449644 + (2\overset{''}{.}8 + 5604\overset{''}{.}9\cdot T + 1\overset{''}{.}1\cdot T^2 + \text{dl})/3600'' \\ b_1 &= (- 2522\overset{''}{.}15 - 30\overset{''}{.}18\cdot T + 0\overset{''}{.}04\cdot T^2 + \text{db})/3600'' \\ r_1 &= 0.3952829\text{ AE} + 1.6 \cdot 10^{-6}\text{ AE} \cdot T + 10^{-6}\text{ AE dr}$ \end{align}\tag{3}\]