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--- tabellen:erde_de200 [2024/05/08 18:53] – quern
+++ tabellen:erde_de200 [2024/12/20 01:57] (aktuell) – Externe Bearbeitung 127.0.0.1
@@ Zeile 3: / Zeile 3: @@
 ====== Erde-Mond Baryzentrum EMB ======
-{{ :erde_vsop87.png?nolink&200|}}
+{{ :erde_vsop87.png?nolink&100|}}
 ===== mittlere Anomalien =====
 {{tablelayout?rowsHeaderSource=Auto&colwidth="70px,430px"&float=center}}
+^  Tabelle 1  ||
 | $M_2 =$ | $49\overset{\circ}{.}943016 + 58320\overset{\circ}{.}0 \cdot T + 197\overset{\circ}{.}493012 \cdot T$ |
 | $M_3 =$ | $357\overset{\circ}{.}525576 + 35640\overset{\circ}{.}0 \cdot T + 359\overset{\circ}{.}049744 \cdot T$ |
@@ Zeile 16: / Zeile 17: @@
 ===== Erde Mond Baryzentrum =====
-Es folgt die Berechnung des EMB
+Es folgt die Berechnung des EMB:
-| $\delta l =$ | $+ 6\overset{''}{.}454\sin(D) - 0\overset{''}{.}424\sin(D - A) + 0\overset{''}{.}177\sin(D + A)$ |
+\[\begin{align}
-| | $+ 0\overset{''}{.}172\sin(D - M_3) - 0\overset{''}{.}06\sin(D + M_3)$ |
+\delta l &= + 6\overset{''}{.}454\sin(D) - 0\overset{''}{.}424\sin(D - A) + 0\overset{''}{.}177\sin(D + A) \\
-| $\delta b =$ | $+ 0\overset{''}{.}576 \sin(U)$ |
+&+ 0\overset{''}{.}172\sin(D - M_3) - 0\overset{''}{.}06\sin(D + M_3) \\
-| $\delta r =$ | $+ 30.76\text{ AE } \cos(D) - 3.06\text{ AE } \cos(D - A) + 0.85\text{ AE } \cos(D + A)$ |
+\delta b &= + 0\overset{''}{.}576 \sin(U) \\
-| | $+ 0.57\text{ AE } \cos(D - M_3) - 0.58\text{ AE } \cos(D + M_3)$ |
+\delta r &= + 30.76\text{ AE } \cos(D) - 3.06\text{ AE } \cos(D - A) + 0.85\text{ AE } \cos(D + A) \\
+&+ 0.57\text{ AE } \cos(D - M_3) - 0.58\text{ AE } \cos(D + M_3)
+\end{align}\tag{1}\]
 mit den Hilfswerten $A, D$ und $U$:
-| $A =$ | $134\overset{\circ}{.}964 + 477198\overset{\circ}{.}864\cdot T$ |
+\[\begin{align}
-| $D =$ | $297\overset{\circ}{.}864 + 445267\overset{\circ}{.}116\cdot T$ |
+A &= 134\overset{\circ}{.}964 + 477198\overset{\circ}{.}864\cdot T \\
-| $U =$ | $93\overset{\circ}{.}276 + 483202\overset{\circ}{.}008\cdot T$ |
+D &= 297\overset{\circ}{.}864 + 445267\overset{\circ}{.}116\cdot T \\
+U &= 93\overset{\circ}{.}276 + 483202\overset{\circ}{.}008\cdot T
+\end{align}\tag{2}\]
 ===== Tabellen =====
-{{tablelayout?rowsHeaderSource=1&colwidth="690px"&float=center}}
+\[\begin{align}
-| \[\begin{align} dl &= \sum_{n=1}^{6} T^{t_n} (a_n \cos(p_n \ M_p + s_n \ M_s) + b_n \sin(p_n \ M_p + s_n \ M_s)) \\ db &= \sum_{n=1}^{6} T^{t_n} (c_n \cos(p_n \ M_p + s_n \ M_s) + d_n \sin(p_n \ M_p + s_n \ M_s)) \\ dr &= \sum_{n=1}^{6} T^{t_n} (e_n \cos(p_n \ M_p + s_n \ M_s) + f_n \sin(p_n \ M_p + s_n \ M_s)) \end{align}\] |
+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}\]
 {{tablelayout?rowsHeaderSource=Auto&colwidth="-"&float=center}}
-^  Tabelle 1: Keplerterme  ||||||||||
+^  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 $   |  $0$    |
@@ Zeile 43: / Zeile 51: @@
 |  $06$   |  $0.00 $  |  $1.04   $  |  $0.00$   |  $0.00$   |  $-1.75    $  |  $0.00 $   |  $3$    |  $0 $   |  $0$    |
-{{tablelayout?rowsHeaderSource=1&colwidth="690px"&float=center}}
+\[\begin{align}
-| \[\begin{align} dl &= \sum_{n=7}^{52} a_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + b_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ db &= \sum_{n=7}^{52} c_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + d_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \\ dr &= \sum_{n=7}^{52} e_n \cos(p_n \ M_p + s_n \ M_s + t_n \ M_t) + f_n \sin(p_n \ M_p + s_n \ M_s + t_n \ M_t) \end{align}\] |
+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}\]
 {{tablelayout?rowsHeaderSource=Auto&colwidth="-"&float=center}}
-^  Tabelle 2: Störterme der Planeten  ||||||||||
+^  Tabelle 3: Störterme der Planeten  ||||||||||
 ^  Störungen durch die Venus  ||||||||||
 ^  n  ^  $a_n['']$  ^  $b_n['']$  ^  $c_n['']$  ^  $d_n['']$  ^  $e_n['']$  ^  $f_n['']$  ^  $p_n$  ^  $s_n$  ^  $t_n$  ^
@@ Zeile 105: / Zeile 116: @@
 ===== Heliozentrische Koordinaten =====
-| $\Delta l =$ | $+ 6\overset{''}{.}40\sin(251\overset{\circ}{.}388 + 20\overset{\circ}{.}196\cdot T) + 1\overset{''}{.}87\sin(207\overset{\circ}{.}504 + 150\overset{\circ}{.}264\cdot T)$ |
+\[\begin{align}
-| | $+ 0\overset{''}{.}27\sin(150\overset{\circ}{.}804 + 119\overset{\circ}{.}016\ T) + 0\overset{''}{.}2\sin(128\overset{\circ}{.}916 + 893\overset{\circ}{.}304\cdot T)$ |
+\Delta l &= + 6\overset{''}{.}40\sin(251\overset{\circ}{.}388 + 20\overset{\circ}{.}196\cdot T) + 1\overset{''}{.}87\sin(207\overset{\circ}{.}504 + 150\overset{\circ}{.}264\cdot T) \\
-| $l_3 =$ | $M_3 + 102\overset{\circ}{.}940308 + (6191\overset{''}{.}2\cdot T + 1\overset{''}{.}1\cdot T^2 + \Delta l + \delta l + \text{dl})/3600''$ |
+& + 0\overset{''}{.}27\sin(150\overset{\circ}{.}804 + 119\overset{\circ}{.}016\ T) + 0\overset{''}{.}2\sin(128\overset{\circ}{.}916 + 893\overset{\circ}{.}304\cdot T) \\
-| $b_3 =$ | $- (\text{db} + \delta b)/3600''$ |
+l_3 &= M_3 + 102\overset{\circ}{.}940308 + (6191\overset{''}{.}2\cdot T + 1\overset{''}{.}1\cdot T^2 + \Delta l + \delta l + \text{dl})/3600'' \\
-| $r_3 =$ | $1.0001398\text{ AE} - 7.0 \cdot 10^{-7}\text{ AE} \cdot T + 10^{-6}\text{ AE }(\text{dr} + \delta r)$ |
+b_3 &= - (\text{db} + \delta b)/3600'' \\
+r_3 &= 1.0001398\text{ AE} - 7.0 \cdot 10^{-7}\text{ AE} \cdot T + 10^{-6}\text{ AE }(\text{dr} + \delta r)
+\end{align}\tag{5}\]