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¦b²ü°¨ªº¥v¸Ö¤¤(¨Ì§Q¨È¯S)¤¤,¬ö¿ýµÛ¯S¬¥¨Ì¾Ôª§(Trojan War)¤@³õÃö©ó§ÆÃ¾©M¯S¬¥¨Ì¡A¨â¤j°}Àçªº¾Ôª§¡A¬°´Á¤Q¦~ªº¾Ôª§¡A³Ì«á¥Ñ¤ì°¨p¿Ñµ²§ô¡A¾Ô«áÁcºaªº¯S¬¥¨Ì«°¤@©]¶¡®ø¥¢©ó¥@¤W¡C¯S¬¥¨Ì¤p¦æ¬P¸s(Trojan Asteroids)ªº©R¦W¥Ñ¨Ó«h¬O¦]¬°¤Ñ¤å¾Ç®a§â¨ä¤¤¦ì©óL4ªº¤p¦æ¬P¥H§ÆÃ¾^¶¯¨Ó©R¦W¡A¨ä¤¤¦ì©óL5ªº¤p¦æ¬P¥H¯S¬¥¨Ì^¶¯¨Ó©R¦W¡A¦³¨Ç¤p¦æ¬P·|¦b¬Û¹ï©ó¤ì¬PªºL4©ML5¶¡¨Ó¦^¹B¦æ¡A¦n¹³¨âx¥æ¾Ô¡C¦A¥[¤W¤§«e¦b°ª¤¤¬ãµo¤H¤~°ö¨|pµe¤¤¡A´¿¸g±µÄ²¹L©Ô®æ®Ô¤éÂI(Lagrange Point)¤Wªº¤p¦æ¬Py¹DÃ©w¹B°Ê¡A·PÄ±«Ü¦³½ì¡A©ó¬O·Q¦A²`¤J±´°Q¦ì©ó©Ô®æ®Ô¤éÂI(L4©ML5)¤Wªº¤p¦æ¬P¸sªº¯S©Ê¤Î¨äy¸ñÅÜ¤Æ±¡§Î¡C

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§Q¥Îºô¸ô¤W¥i¥H§K¶O¨ú±oªº³nÅé¨Ó¬ã¨s¦ì©ó©Ô®æ®Ô¤éÂI¤Wªº¤p¦æ¬P¹B°Ê¯S©Ê¡A§Q¥Îª½±µpºâ¤p¦æ¬Pªºy¸ñÅÜ¤Æ±¡§Î¡A§ä¥X¦bL4¤ÎL5ªþªñªºÃ©wy¹Dªì©lªº¦ì¸m¡C

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¤@¡BµwÅé

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¤G¡B³nÅé

1¡BDebian Linux §@·~¨t²Î

2¡BG77

FORTRAN 77ª©, Â²©öªº¬ì¾Çµ{¦¡

3¡BGnuplot

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¸v¡B¬ã¨s¹Lµ{©Î¤èªk:

¤@¡B±N©Ò»Ý§@·~¨t²Î¡B³nÅé¤Î¬ÛÃö®M¥ó¦w¸Ë§¹²¦¡C

¤G¡Bpºâ¤½¦¡ªº±À¾É:

³] $\Large F$ ¬°¸U¦³¤Þ¤O, $\Large A$ ¦V¤ß¥[³t«×, $\Large M$ ¡B $\Large m$ ¤À§O¬°¨âÁû¤ÑÅéªº½è¶q, $\Large R$ ¬°¨âÁû¤ÑÅé¶¡¶ZÂ÷, $\Large G$ ¬°¸U¦³¤Þ¤O±`¼Æ, $\Large {(X_1,Y_1,Z_1)}$ ¡B $\Large {(X_2,Y_2,Z_2)}$ ¤À§O¬°¥LÌªºªì©l¦ì¸m,pºâ®É¶¡¶¡¹j¬° $\Large\Delta t$ , $\Large A_{X0},A_{Y0},A_{Z0}$ ¬°ªì©lªº¥[³t«×¤À¶q, $\Large V_{X0},V_{Y0},V_{Z0}$ ¬°ªì©lªº³t«×

¥Ñ¤û¹yªº²Ä¤G¹B°Ê©w«ß©M¸U¦³¤Þ¤O©w«ß¥iª¾:

$\Large\longrightarrow F=mA=\frac {GMm} {R^2}$

$\Large\longrightarrow A=\frac {GM} {R^2}$

¨º§ÚÌ¦A§âA©î¸Ñ¬°x¤è¦V¤À¶q,Y¤è¦V¤À¶q,Z¤è¦V¤À¶q:

$\Large\longrightarrow A_X=A_{X0}+A\time\frac {X_1-X_2} {R}$

$\Large\longrightarrow A_Y=A_{Y0}+A\time\frac {Y_1-Y_2} {R}$

$\Large\longrightarrow A_Z=A_{Z0}+A\time\frac {Z_1-Z_2} {R}$

¨º§ÚÌ¤S¥i¥H¥Ñ¥[³t«×ºâ¥X«á¨Óªº³t«×: $\Large\Delta V=A \time \Delta t$ ,©Ò¥H«á¨Óªº³t«× $\Large V=$ ªì©l³t«× $\Large +\Delta V$

$\Large\longrightarrow V_X=V_{X0}+A_X\time{\Delta}t$

$\Large\longrightarrow V_Y=V_{Y0}+A_Y\time{\Delta}t$

$\Large\longrightarrow V_Z=V_{Z0}+A_Z\time{\Delta}t$

§ÚÌ¤S¥i¥H¥Ñ³t«×±À±o«á¨Óªº¦ì¸m:¦ì²¾ $\Large\Delta S=V\time\Delta t$ ,©Ò¥H«á¨Óªº¦ì¸m $\Large S=$ ªì©l¦ì¸m $\Large +\Delta S$

$\Large\longrightarrow X=X_2+V_X\time{\Delta}t$

$\Large\longrightarrow Y=Y_2+V_Y\time{\Delta}t$

$\Large\longrightarrow Z=Z_2+V_Z\time{\Delta}t$

¤T¡B®y¼ÐªºÂà´«:

(¤@)¥²¾

³]¤Ó¶§¡B¤ì¬P¡B¤p¦æ¬Pªºªì©l¦ì¸m¤À§O¬° $\Large(X_{S0},Y_{S0})$ ¡B $\Large(X_{J0},Y_{J0})$ ¡B $\Large(X_{A0},Y_{A0})$ ¡C

«á¨Ópºâªº¦ì¸m¤À§O¬° $\Large(X_{S1},Y_{S1})$ ¡B $\Large(X_{J1},Y_{J1})$ ¡B $\Large(X_{A1},Y_{A1})$ ¡C

¥²¾ $\longrightarrow$ $\Large(0,0)$ $\Large(X_{J1}-X_{S1},Y_{J1}-Y_{S1})$ ¡B $\Large(X_{A1}-X_{S1},Y_{A1}-Y_{S1})$

(¤G)±ÛÂà

§Q¥Î½Æ¼Æ®y¼Ð¨t±ÛÂàªº¤èªk:³]¥²¾«á¤§¤Ó¶§-¤ì¬P³s½u»Pì¨Ó¤§¤Ó¶§-¤ì¬P³s½u§¨ ¥¿ $\Large\theta$ ¨¤,«á¨Ó®y¼Ð±ÛÂàt $\Large\theta$ ¨¤,«h©Ò±o®y¼Ð§Y¬°Âà°Ê®y¼Ð¨t,¦¹®y¼Ð§Y¥H¤Ó¶§¬°ìÂI,¤Ó¶§-¤ì¬P³s½u¬°X¶b¡C

¥²¾¤Î±ÛÂà«á¤§®y¼Ð $\longrightarrow$

Sun:

$\Large X_S = 0$

$\Large Y_S = 0$

Jupiter:

$\Large X_J=\Large(X_{J1}-X_{S1})\time cos(-\theta)-(Y_{J1}-Y_{S1})\time sin(-\theta)$

$\Large Y_J=\Large(X_{J1}-X_{S1})\time sin(-\theta)+(Y_{J1}-Y_{S1})\time cos(-\theta)$

Asteroids:

$\Large X_A=\Large(X_{A1}-X_{S1})\time cos(-\theta)-(Y_{A1}-Y_{S1})\time sin(-\theta)$

$\Large Y_A=\Large(X_{A1}-X_{S1})\time sin(-\theta)+(Y_{A1}-Y_{S1})\time cos(-\theta)$

¨ä¤¤:

$\Large sin(\theta) = \frac {(Y_{J1}-Y_{S1})} {\left| \vec {S_1J_1}\right|}$

$\Large cos(\theta) = \frac {(X_{J1}-X_{S1})} {\left| \vec {S_1J_1}\right|}$

Attach:science2.f

¥î¡B¬ã¨sµ²ªG:

¤@¡B¨¤¦ì¸m¤£¦P®Éªº¤p¦æ¬PÃ©w±¡§Î:

°ÝÃD:¼ÒÀÀ¦bÂà°Ê®y¼Ð¨t¤¤,¤p¦æ¬Pªì©l¦ì¸m©MìÂIªº³s½u(§Y¤Ó¶§-¤p¦æ¬P³s½u)©MX¶b(§Y¤é-¤ì³s½u)ªº§¨¨¤,¹ï¨äy¸ñªº¼vÅT¡C

ªì©l±ø¥ó:

	½è¶q	X	Y	Z	Vx	Vy	Vz
¤Ó¶§	$\Large 1.98911\time10^{30}$	0	0	0	0	0	0
¤ì¬P	$\Large 1.8986\time10^{27}$	5.2AU	0	0	0	$V_J$	0
¤p¦æ¬P	$\Large\longrightarrow 0$	$\Large R_J\time cos(\theta)$	$\Large R_J\time sin(\theta)$	0	$\Large cos(\theta+90^\circ)V_J$	$\Large sin(\theta+90^\circ)V_J$	0

¨ä¤¤: $\Large V_J=\frac {2 \pi R_J} {T_J} =\frac {2\pi \time5.20336301AU} {3.74\time10^8}$ , $\Large\Delta t$ (®É¶¡¶¡¹j)¬°¤@¤Ñ(86400¬í),pºâ®É¶¡¬°¤Q¸U¦~¡C

©T©wÅÜ¦]:¬PÅé½è¶q(¨ä¤¤¤p¦æ¬Pªº½è¶qµø¬°ÁÍªñ©ó¹s)¡B¤Ó¶§©M¤ì¬Pªºªì©l¦ì¸m¡Bªì³t«×¡C

¾Þ±±ÅÜ¦]:¤p¦æ¬P¦ì¸m¡Bªì³t«×¡C

¤U±ªº¹Ï¬°¤p¦æ¬Pªºy¸ñ¥i¥HÃ©wªº¦s¦b©ó¤ì¬Py¹D¤W¡C

¨ä¤¤:¤p¦æ¬Pªì©l¦ì¸m¦b $\Large\60^\circ$ ©M $\Large\{-60}^\circ$ ( $\Large\{300}^\circ$ )®É¡A¤p¦æ¬P©M¤ì¬P¤@°_«O«ù¬Û¦Pªº¶ZÂ÷Â¶¤é¹B°Ê¡A¦¹¨âÂI§Y¬°©Ô®æ®Ô¤éÂI¡C

¤U±ªº¹Ï¬°¤p¦æ¬PµLªkÃ©w¦s¦b©ó¤ì¬Py¹D¤W¡C

¤G¡B¤p¦æ¬P¤½Âà¥b®|ªº§ïÅÜ¹ï¨äy¸ñ¼vÅT

°ÝÃD¡J¦b¬Û¦Pªº§¨¨¤(§Y°ÝÃD¤@¤§¨¤«×)¤¤,¤p¦æ¬Py¹Dªº§ïÅÜ¹ï¨äy¸ñªº¼vÅT¡C

ªì©l±ø¥ó:

	½è¶q	X	Y	Z	Vx	Vy	Vz
¤Ó¶§	$\Large 1.99\time10^{30}$	0	0	0	0	0	0
¤ì¬P	$\Large 1.90\time10^{27}$	5.2AU	0	0	0	$V_J$	0
¤p¦æ¬P	$\Large\longrightarrow 0$	$\Large R_A\time cos(\theta)$	$\Large R_A\time sin(\theta)$	0	$\Large \sqrt {\frac {R_A} {R_J} }cos(\theta+90^\circ)V_J$	$\Large \sqrt {\frac {R_A} {R_J} }sin(\theta+90^\circ)V_J$	0

¨ä¤¤: $\Large V_J=\frac {2 \pi R}T=\frac {2\pi \time5.2AU} {3.74\time10^8}$

¥Ñ§J¤R°Ç²Ä¤T©w«ßª¾: $\Large {\frac {{R_A}^3} {{T_A}^2}} = {\frac {{R_J}^3} {{T_J}^2}}$ ,¤S $\Large V_J= {\frac {2 \pi R_J} {T_J} }$ ¡B $\Large V_A={\frac {2 \pi R_A} {T_A} }$ ,§Y¥i±o $\longrightarrow$ $\Large V_A =\sqrt{\frac {R_J} {R_A} }\time V_J$

$\Large\Delta t$ (®É¶¡¶¡¹j)¬°¤@¤Ñ(86400¬í),pºâ®É¶¡¬°¤Q¸U¦~¡C

¾Þ±±ÅÜ¦]:¤p¦æ¬P¦ì¸m¡Bªì³t«×¡C

¥»¹êÅç¤¤,¥u¦Ò¼{ $\Large 60^\circ$ ¦Ü $\Large 300^\circ$ ªº¦ì¸m¡C¤S¥Ñ¹êÅç¤@¤¤±oª¾ $\Large 150^\circ$ ¦Ü $\Large 210^\circ$ ªº¦ì¸m,¤p¦æ¬PµLªkÃ©wªº¦s¦b©ó¤ì¬Py¹D,©Ò¥H¥»¹êÅç¥ç¤£¦Ò¼{¡C¤S¥Ñpºâµ²ªGµo²{±q $\Large 225^\circ$ ¦Ü $\Large 300^\circ$ ©M±q $\Large 60^\circ$ ¦Ü $\Large 135^\circ$ ¤jP¬Û¦P,¬G¥u¬D¿ï´X±i¥Nªíªº¹Ï¡C

(¤@)¡B¤p¦æ¬P¦b¤ì¬Py¹D¥~°¼:

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±q¹Ï¤¤¥i¥H¤jPµo²{,·í¤p¦æ¬P¶ZÂ÷©Ô®æ®Ô¤éÂI¶Vªñ®É,¤p¦æ¬P¥i¥H¸û»·Â÷¤ì¬Py¹D¡A¦ÓÁÙ¯àÃ©wªº¦s¦b¨äì¨Óy¹D¤W¡A¤Ï¤§¡A·í¤p¦æ¬P¶ZÂ÷©Ô®æ®Ô¤éÂI¶V»·®É¡A¤p¦æ¬P«h¶·¶ZÂ÷¨äì¦³y¹D¸ûªñ¡A¤~¯àÃ©wªº¦ì©ó¨äy¹D¤W¡C

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2.±q¹Ï.13¨ì¹Ï.24¤¤¡A¥i¥HÂk¯Ç¥X¹Ï.27ªºµ²ªG¡A¤p¦æ¬P¦bpºâ¤Q¸U¦~¤º¡A¦ì©ó¹Ï.27¤Î¹Ï.28ªº°Ï¶ô¬O¥i¥HÃ©wªº¡C¦ý¤p¦æ¬Pªì©l¬Û¦ì¨¤¶ZL4?¤ÎL5·U»·®É¡A¨ä¥i°¾²¾ªºy¹D¥b®|´N·U¤p¡C

¬m¡Bµ²½×:

¤@¡B¦b¤Q¸U¦~ªº¼ÒÀÀ¤¤¡A¤p¦æ¬P»PX¶bªº§¨¨¤¥Ñ $\Large 30^\circ$ ¦Ü $\Large 135^\circ$ ©M $\Large 225^\circ$ ¦Ü $\Large 330^\circ$ ®É,¤p¦æ¬P¥i¥HÃ©wªº¦b¨äì¦³y¹D¤W¹B¦æ¡C¨Ã¬Û¹ï©ó¤ì¬P°µ¨Ó¦^ªº¹B¦æ¡A¨ä¤¤ $\Large 60^\circ$ ©M $\Large -60^\circ$ ªº³o¨âÂI«ÜÃ©wªº¤@ª½¦s¦b©ó¨äì¨Ó¦ì¸m¤W¡A¨Ã¥¼¹ï¤ì¬P§@¬Û¹ï¹B°Ê¡A¦¹¨âÓÂI§Y¬°©Ô®æ®Ô¤éÂI©Ò¦b¡C

¤G¡B¦b¤Q¸U¦~ªº¼ÒÀÀ¤¤¡Aªì©l¦ì¸m¦b $\Large 60^\circ$ ¡B $\Large 75^\circ$ ¡B $\Large 90^\circ$ ªº¤p¦æ¬P·QÃ©w¦s¦by¹D¤W,«h°¾Â÷y¹D¤£±o¶W¹L¦Ê¤À¤§¥| $R_J$ (¤ì¬P¤½Âà¥b®|),¦Ó¦b $\Large 105^\circ$ ¡B $\Large 120^\circ$ ¡B $\Large 135^\circ$ ªº¤p¦æ¬P«h¤À§O¤£¥i°¾Â÷¶W¹L¦Ê¤À¤§¤T $R_J$ ¡B¦Ê¤À¤§¤G $R_J$ ¡B¦Ê¤À¤§¤@ $R_J$ ¡A¨ä¾l¦b $\Large 225^\circ$ ¤§«áªº¤p¦æ¬P¤jP¤W©M«e±¤@P¡C¥Ñ¨¤«×©M³Ì¤j°¾²¾¶q¨Ó¬Ý,¥iµo²{¤p¦æ¬P¶Z©Ô®æ®Ô¤éÂIªº»·ªñ¼vÅT¨ä³Ì¤j¥i°¾²¾y¹D¶q,·U»·,«h¶V¤p,¶Vªñ,«h¶V¤j¡C