积极 AI Logo 积极 AI

日心与地心视角下的太阳系行星位置计算

日心与地心视角下的太阳系行星位置计算
几何画板及绘图内容加载中，请稍等……
2015-05-31 21:35
三角函数解析几何几何作图滑块动画
①本范例演示了从1600年至今，水星、金星、地球、火星、木星和土星在日心与地心视角下的位置计算与可视化；②涉及的核心数学概念包括椭圆、三角函数、乘法、均值、单位圆、内切圆等；③作图要点提炼自GeoGebra命令：Rotate（旋转）、Vector（向量）、Translate（平移）、Circle（圆）、Ellipse（椭圆）、Line（直线）、Intersect（交点）、Midpoint（中点）、Point（点）、Angle（角度）、Root（根）、Distance（距离）、Ray（射线）、Segment（线段）、OrthogonalLine（垂线）、Textfield（文本框）、Sphere（球体）、Plane（平面）、IntersectPath（路径交点）、Tangent（切线）；④适合高中及以上学生及天文爱好者学习天体力学与数学模型。

GeoGebra 命令及参数

  1. Rotate(C, α + (((0.0167 * 180) * ° / 3.141) * sin(α)) + ((0.5 * (((0.0167 * 180) * ° / 3.141))^(2)) * sin((2 * α))), D) → C'
  2. Vector(C', D) → u
  3. Translate(C', u) → C''_1
  4. Circle(A, 0.283464) → r
  5. Ellipse(A, B, C) → c
  6. Line(A, I_4) → n
  7. Intersect(r, n) → J_2, K_2
  8. Midpoint(K_2, A) → L_2
  9. Circle(L_2, 1.524) → s
  10. Intersect(s, n) → M_2, N_2
  11. Ellipse(K_2, A, M_2) → t_2
  12. Intersect(t_2, n) → O_2, P_2
  13. Point(c) → M
  14. Rotate(M, ((2 * π) * t / 365.25), C''_1) → M'_1
  15. Angle(M, C''_1, M'_1) → ϕ
  16. Root(ϕ - x + (0.0167 * sin(x)), 0, 7) → S_3
  17. Distance(C''_1, S_3) → EE
  18. Angle(C, D, C') → β
  19. Point(c) → E
  20. Line(A, L_5) → a
  21. Circle(A, 0.16) → d
  22. Intersect(d, a) → F, G
  23. Midpoint(A, F) → H
  24. Circle(H, 0.387) → e
  25. Intersect(e, a) → I, J
  26. Ellipse(F, A, J) → f
  27. Rotate(J, γ + (((0.206 * 180) * ° / 3.141) * sin(γ)) + ((0.5 * (((0.206 * 180) * ° / 3.141))^(2)) * sin((2 * γ))), H) → J'
  28. Angle(J, H, J') → δ
  29. Ray(H, J') → b
  30. Intersect(f, b) → K,
  31. Segment(C', K) → g
  32. Translate(C', u) → C''
  33. Translate(K, u) → K'
  34. Segment(C'', K') → g'
  35. Segment(D, A) → h
  36. Translate(D, u) → D'
  37. Translate(A, u) → A'
  38. Segment(D', A') → h'
  39. Ray(A, C') → i
  40. Circle(A, 0.723) → k
  41. Rotate(C, ε + (((0.0068 * 180) * ° / 3.141) * sin(ε)) + ((0.5 * (((0.0068 * 180) * ° / 3.141))^(2)) * sin((2 * ε))), A) → C'_1
  42. Angle(C, A, C'_1) → ζ
  43. Ray(A, C'_1) → j
  44. Point(c) → N
  45. Point(c) → O
  46. Point(c) → P
  47. Circle(C'', A') → p
  48. Point(p) → Q
  49. Point(p) → R
  50. Point(p) → S
  51. Point(p) → T
  52. Point(p) → U
  53. Point(c) → V
  54. Point(c) → W
  55. Point(p) → Z
  56. Point(c) → A_1
  57. Point(p) → B_1
  58. Point(c) → C_1
  59. Point(p) → D_1
  60. Point(c) → E_1
  61. Point(p) → F_1
  62. Point(c) → G_1
  63. Point(p) → H_1
  64. Point(c) → I_1
  65. Point(p) → J_1
  66. Point(c) → K_1
  67. Point(p) → L_1
  68. Circle(C'', 1.2) → q
  69. Ray(C'', A') → m
  70. Intersect(q, m) → M_1,
  71. Point(q) → N_1
  72. Point(q) → O_1
  73. Intersect(p, xAxis, 1) → P_1
  74. Intersect(p, xAxis, 2) → Q_1
  75. Point(q) → R_1
  76. Point(q) → S_1
  77. Point(q) → T_1
  78. Point(q) → U_1
  79. Point(q) → V_1
  80. Point(q) → W_1
  81. Point(q) → Z_1
  82. Point(q) → A_2
  83. Point(q) → B_2
  84. Point(q) → C_2
  85. Point(q) → D_2
  86. Point(q) → E_2
  87. Point(q) → F_2
  88. Point(q) → G_2
  89. Point(q) → H_2
  90. Rotate(O_2, η + (((0.093 * 180) * ° / 3.141) * sin(η)) + ((0.5 * (((0.093 * 180) * ° / 3.141))^(2)) * sin((2 * η))), L_2) → Q_2
  91. Angle(O_2, L_2, Q_2) → θ_1
  92. Segment(C', Q_2) → a_1
  93. Translate(C', u) → C''_2
  94. Translate(Q_2, u) → R_2
  95. Line(A', C'') → c_1
  96. Intersect(q, c_1) → S_2, T_2
  97. Rotate(T_2, θ, C'') → U_2
  98. Angle(T_2, C'', U_2) → ι
  99. Line(C'', U_2) → d_1
  100. OrthogonalLine(C'', d_1) → e_1
  101. Segment(C'', A') → f_1
  102. Point(c) → V_2
  103. Circle(A, 0.5) → h_1
  104. Line(A, V'_2) → g_1
  105. Intersect(h_1, g_1) → W_2, Z_2
  106. Midpoint(A, Z_2) → A_3
  107. Circle(A_3, 5.2) → k_1
  108. Intersect(k_1, g_1) → B_3, C_3
  109. Ellipse(Z_2, A, C_3) → p_1
  110. Rotate(B_3, ξ + (((0.0484 * 180) * ° / 3.141) * sin(ξ)) + ((0.5 * (((0.0484 * 180) * ° / 3.141))^(2)) * sin((2 * ξ))), A) → D_3
  111. Angle(B_3, A, D_3) → ν
  112. Ray(A_3, D_3) → j_1
  113. Intersect(p_1, j_1) → E_3,
  114. Segment(C', E_3) → l_1
  115. Translate(C', u) → C''_3
  116. Translate(E_3, u) → F_3
  117. Circle(A, 1.033) → q_1
  118. Intersect(q_1, xAxis, 2) → J_3
  119. Rotate(J_3, 170° + (((n_1 - 2015) * 180) * ° / ((3.141 * 25780))), A) → K_3
  120. Line(A, K'_3) → r_1
  121. Angle(J_3, A, K_3) → ρ
  122. Intersect(q_1, r_1) → L_3, M_3
  123. Midpoint(A, L_3) → N_3
  124. Circle(N_3, 9.5367) → s_1
  125. Intersect(s_1, r_1) → O_3, P_3
  126. Ellipse(A, L_3, O_3) → t_1
  127. Distance(A, P_3) → abstandAP3
  128. Distance(A, O_3) → abstandAO3
  129. Rotate(P_3, σ + (((0.0539 * 180) * ° / 3.141) * sin(σ)) + ((0.5 * (((0.0539 * 180) * ° / 3.141))^(2)) * sin((2 * σ))), N_3) → Q_3
  130. Angle(P_3, N_3, Q_3) → τ
  131. Segment(Q_3, C') → a_2
  132. Translate(Q_3, u) → R_3
  133. Translate(C', u) → C''_4
  134. Textfield(n_1) → Textfeld1
  135. Rotate(M, ((2 * π) * t), C''_1) → M'
  136. Textfield(t) → Textfeld2
  137. Rotate(M, (2 * atan((sqrt((1 + 0.0167) / (1 - 0.0167)) * tan((0.5 * EE))))), A) → M'_2
  138. Angle(M, A, M'_2) → χ
  139. Ray(A, M'_2) → f_2
  140. Intersect(c, f_2) → T_3,
  141. Rotate(O_2, ((2 * π) * t / ((365.25 * 1.88085))) + β_1, L_2) → W_3
  142. Angle(O_2, L_2, W_3) → ψ
  143. Root(ψ - x + (0.09341 * sin(x)), 0, 7) → Z_3
  144. Distance(C''_1, Z_3) → EMa
  145. Rotate(O_2, (2 * atan((sqrt((1 + 0.09341) / (1 - 0.09341)) * tan((0.5 * EMa))))) + β_1, A) → B_4
  146. Rotate(O_2, (2 * atan((sqrt((1 + 0.09341) / (1 - 0.09341)) * tan((0.5 * EMa))))), A) → A_4
  147. Angle(O_2, A, A_4) → ω
  148. Ray(A, A_4) → g_2
  149. Intersect(t_2, g_2) → C_4,
  150. Rotate(W_2, ((2 * π) * t / ((365.25 * 11.862615))) + ε_1, A_3) → E_4
  151. Angle(W_2, A_3, E_4) → ζ_1
  152. Root(ζ_1 - x + (0.04892 * sin(x)), 0, 7) → F_4
  153. Distance(C''_1, F_4) → EJ
  154. Rotate(W_2, (2 * atan((sqrt((1 + 0.04892) / (1 - 0.04892)) * tan((0.5 * EJ))))), A) → G_4
  155. Angle(W_2, A, G_4) → η_1
  156. Ray(A, G_4) → i_2
  157. Intersect(p_1, i_2) → H_4,
  158. Rotate(P_3, ((2 * π) * t / ((365.25 * 29.47498))) + σ_1, N_3) → J_4
  159. Angle(K'_3, N_3, J_4) → σ_2
  160. Root(σ_2 - x + (0.05772 * sin(x)), 0, 7) → K_4
  161. Distance(C''_1, K_4) → ES
  162. Rotate(P_3, (2 * atan((sqrt((1 + 0.05772) / (1 - 0.05772)) * tan((0.5 * ES))))), A) → L_4
  163. Ray(A, L_4) → j_2
  164. Intersect(t_1, j_2) → M_4,
  165. Angle(K'_3, A, L_4) → σ_3
  166. Rotate(C, 30° + (360° * t / ((365.2425 * 25784))), A) → C'_2
  167. Angle(C, A, C'_2) → ι_1
  168. Line(A, C'_2) → k_2
  169. Circle(A, 0.009822897447999999) → p_2
  170. Intersect(p_2, k_2) → N_4, O_4
  171. Midpoint(A, N_4) → P_4
  172. Circle(P_4, 0.7233356) → q_2
  173. Intersect(q_2, k_2) → Q_4, R_4
  174. Ellipse(N_4, A, R_4) → r_2
  175. Rotate(R_4, ((2 * π) * t / ((365.25 * 0.61519726))) + κ_1, P_4) → S_4
  176. Angle(R_4, P_4, S_4) → λ_1
  177. Root(λ_1 - x + (0.00679 * sin(x)), 0, 7) → T_4
  178. Distance(C''_1, T_4) → EV
  179. Rotate(R_4, (2 * atan((sqrt((1 + 0.00679) / (1 - 0.00679)) * tan((0.5 * EV))))), A) → U_4
  180. Angle(R_4, A, U_4) → μ_1
  181. Ray(A, U_4) → l_2
  182. Intersect(q_2, l_2) → V_4,
  183. Vector(T_3, A) → w_1
  184. Translate(T_3, w_1) → W_4
  185. Translate(A, w_1) → A'_1
  186. Translate(T_3, w_1) → A_5
  187. Ray(W_4, A'_1) → s_2
  188. Segment(T_3, V_4) → a_3
  189. Translate(V_4, w_1) → C_5
  190. Segment(W_4, C_5) → b_3
  191. Angle(b_3, s_2) → μ
  192. Segment(T_3, C_4) → c_3
  193. Translate(C_4, w_1) → D_5
  194. Segment(W_4, D_5) → d_3
  195. Ray(D_5, W_4) → e_3
  196. Angle(e_3, s_2) → λ
  197. Point(p) → I_2
  198. Intersect(f, a) → L, D_4
  199. Rotate(L, ((2 * π) * t / ((365.25 * 0.2408467))) + α_1, H) → L'
  200. Angle(L, H, L') → κ
  201. Root(κ - x + (0.20564 * sin(x)), 0, 7) → Z_4
  202. Distance(C''_1, Z_4) → EMe
  203. Rotate(L_5, (2 * atan((sqrt((1 + 0.20564) / (1 - 0.20564)) * tan((0.5 * EMe))))), A) → L'_1
  204. Ray(A, L'_1) → l
  205. Intersect(f, l) → B_5,
  206. Angle(L_5, A, L'_1) → γ_1
  207. Segment(T_3, B_5) → b_1
  208. Translate(B_5, w_1) → E_5
  209. Segment(W_4, E_5) → e_2
  210. Angle(e_2, s_2) → δ_1
  211. Segment(F_5, G_5) → h_2
  212. Segment(T_3, H_4) → m_2
  213. Translate(H_4, w_1) → H_5
  214. Ray(H_5, W_4) → n_2
  215. Point(n_2) → J_5
  216. Angle(n_2, s_2) → ν_1
  217. Point(n_2) → I_5
  218. Circle(W_4, I_5) → f_3
  219. Intersect(f_3, n_2) → K_5, M_5
  220. Circle(W_4, 1.3) → g_3
  221. Intersect(g_3, n_2) → N_5, P_5
  222. Segment(A_1, M_4) → m_1
  223. Translate(M_4, w_1) → G_3
  224. Ray(G_3, W_4) → d_2
  225. Angle(s_2, d_2) → ο
  226. Intersect(g_3, d_2) → H_3, I_3
  227. Point(d_2) → R_5
  228. Segment(H_5, W_4) → b_2
  229. Intersect(g_3, b_2) → U_3,
  230. Point(b_2) → V_3
  231. Vector(U_3, V_3) → v_1
  232. Segment(W_4, G_3) → c_2
  233. Intersect(g_3, c_2) → Q_5,
  234. Point(c_2) → S_5
  235. Vector(Q_5, S_5) → u_1
  236. Rotate(C, 233*°, A) → C'_3
  237. Rotate(C, 333*°, A) → C'_4
  238. Angle(C, A, C'_4) → υ
  239. Line(A, C'_4) → h_3
  240. Rotate(q_2, 3.4*°, h_3) → k_3
  241. Rotate(V_4, 3.4*°, h_3) → T_5
  242. Angle(C, A, C'_5) → ξ_1
  243. Line(A, C'_5) → i_3
  244. Rotate(p_1, 1.3*°, i_3) → p_3
  245. Rotate(H_4, 1.3*°, i_3) → U_5
  246. Rotate(C, 306*°, A) → C'_6
  247. Angle(C, A, C'_6) → ο_1
  248. Line(A, C'_6) → j_3
  249. Rotate(f, 7*°, j_3) → f'
  250. Rotate(B_5, 7*°, j_3) → V_5
  251. Rotate(C, 309*°, A) → C'_7
  252. Angle(C, A, C'_7) → ρ_1
  253. Line(A, C'_7) → l_3
  254. Rotate(t_2, 1.85*°, l_3) → q_3
  255. Rotate(C_4, 1.85*°, l_3) → W_5
  256. Rotate(C, 12*°, A) → C'_8
  257. Angle(C, A, C'_8) → τ_1
  258. Line(A, C'_8) → m_3
  259. Rotate(t_1, 2.49*°, m_3) → r_3
  260. Rotate(M_4, 2.49*°, m_3) → Z_5
  261. Vector(T_3, A) → u_2
  262. Translate(A, u_2) → A'_2
  263. Translate(V_5, u_2) → A_6
  264. Translate(T_5, u_2) → B_6
  265. Translate(W_5, u_2) → C_6
  266. Translate(xOyPlane, Vector[(0, 0, 0)]) → xyEbene'
  267. Translate(U_5, u_2) → D_6
  268. Translate(Z_5, u_2) → E_6
  269. Sphere(W_4, 1) → w_2
  270. Ray(W_4, B_6) → n_3
  271. Intersect(n_3, w_2) → F_6, G_6
  272. Ray(W_4, A_6) → s_3
  273. Intersect(s_3, w_2) → H_6, I_6
  274. Ray(W_4, C_6) → t_3
  275. Intersect(t_3, w_2) → J_6, K_6
  276. Ray(W_4, D_6) → a_4
  277. Intersect(a_4, w_2) → L_6, M_6
  278. Ray(W_4, E_6) → b_4
  279. Intersect(b_4, w_2) → N_6, O_6
  280. Segment(W_4, B_6) → c_4
  281. Segment(W_4, A_6) → d_4
  282. Segment(W_4, A_6) → e_4
  283. Segment(W_4, C_6) → f_4
  284. Segment(W_4, B_6) → g_4
  285. Segment(W_4, D_6) → h_4
  286. Segment(W_4, E_6) → i_4
  287. Rotate(C_7, 78*°, A) → P_6
  288. Angle(C_7, A, P_6) → υ_1
  289. Line(A, P_6) → j_4
  290. Intersect(c, j_4) → Q_6, R_6
  291. Plane(Q_6, j_4) → k_4
  292. Plane(Q_6, R_6, C_7) → l_4
  293. Rotate(l_4, -23.4*°, j_4) → m_4
  294. IntersectPath(m_4, w_2) → p_4
  295. Tangent(T_3, q_2) → n_4, q_4
  296. Translate(n_4, u_2) → r_4
  297. Translate(q_4, u_2) → s_4
  298. Tangent(T_3, f) → t_4, a_5
  299. Translate(a_5, u_2) → b_5
  300. Translate(t_4, u_2) → c_5

AI 绘图提示语参考

绘制太阳系模型，展示从1600年开始的六颗行星在日心说和地心说下的位置计算与可视化。使用椭圆、三角函数、乘法、平均数、单位圆和内切圆等数学概念，通过旋转、向量、平移、画圆、画椭圆等操作，构建行星轨道和位置关系，适合高中生和天文爱好者学习天体力学和数学建模。
以上提示语为根据原始绘图命令整理而来，仅供参考。