MathPlotAI Logo MathPlotAI

Tidal Accelerations (Not to Scale)

Tidal Accelerations (Not to Scale)
Loading the math board and drawing, please wait…
2020-01-02 22:19
CircleVectorGeometric ConstructionGraphing
This GeoGebra example visualizes the acceleration vectors caused by the Moon and Earth on different points of Earth's surface, explaining the formation of tidal bulges. It demonstrates how gravitational forces from the Moon and Earth combine vectorially, producing differential accelerations that stretch Earth along the Moon-Earth axis and compress it perpendicularly. The construction uses Circle commands to define the Earth and Moon, and Vector commands to draw acceleration arrows from Earth's center to surface points, with labeled objects such as gm (Moon's gravity), aEM (Earth-Moon acceleration), and multiple points E0–E22 representing surface locations. The model is not to scale but emphasizes directional patterns. This resource is suitable for high school physics or introductory astronomy courses, as well as mathematics classes focusing on vector addition and spatial reasoning.

GeoGebra Commands & Parameters

  1. Circle(E, (re * s)) → E_{c}'
  2. Circle(E, re) → E_{c}
  3. Vector(E9, (x(E9) + x(E9m), y(E9) + y(E9m))) → E9M
  4. Vector(E9, (x(E9) + x(E9e), y(E9) + y(E9e))) → E9E
  5. Vector(E0, (x(E0) + x(E0m), y(E0) + y(E0m))) → E0M
  6. Vector(E0, (x(E0) + x(E0e), y(E0) + y(E0e))) → E0E
  7. Vector(E1, (x(E1) + x(E1m), y(E1) + y(E1m))) → E1M
  8. Vector(E1, (x(E1) + x(E1e), y(E1) + y(E1e))) → E1E
  9. Vector(E2, (x(E2) + x(E2m), y(E2) + y(E2m))) → E2M
  10. Vector(E2, (x(E2) + x(E2e), y(E2) + y(E2e))) → E2E
  11. Vector(E3, (x(E3) + x(E3m), y(E3) + y(E3m))) → E3M
  12. Vector(E3, (x(E3) + x(E3e), y(E3) + y(E3e))) → E3E
  13. Vector(E4, (x(E4) + x(E4m), y(E4) + y(E4m))) → E4M
  14. Vector(E4, (x(E4) + x(E4e), y(E4) + y(E4e))) → E4E
  15. Vector(E5, (x(E5) + x(E5m), y(E5) + y(E5m))) → E5M
  16. Vector(E5, (x(E5) + x(E5e), y(E5) + y(E5e))) → E5E
  17. Vector(E6, (x(E6) + x(E6m), y(E6) + y(E6m))) → E6M
  18. Vector(E6, (x(E6) + x(E6e), y(E6) + y(E6e))) → E6E
  19. Vector(E7, (x(E7) + x(E7m), y(E7) + y(E7m))) → E7M
  20. Vector(E7, (x(E7) + x(E7e), y(E7) + y(E7e))) → E7E
  21. Vector(E8, (x(E8) + x(E8m), y(E8) + y(E8m))) → E8M
  22. Vector(E8, (x(E8) + x(E8e), y(E8) + y(E8e))) → E8E
  23. Vector(E10, (x(E10) + x(E10m), y(E10) + y(E10m))) → E10M
  24. Vector(E10, (x(E10) + x(E10e), y(E10) + y(E10e))) → E10E
  25. Vector(E11, (x(E11) + x(E11m), y(E11) + y(E11m))) → E11M
  26. Vector(E11, (x(E11) + x(E11e), y(E11) + y(E11e))) → E11E
  27. Vector(E12, (x(E12) + x(E12m), y(E12) + y(E12m))) → E12M
  28. Vector(E12, (x(E12) + x(E12e), y(E12) + y(E12e))) → E12E
  29. Vector(E13, (x(E13) + x(E13m), y(E13) + y(E13m))) → E13M
  30. Vector(E13, (x(E13) + x(E13e), y(E13) + y(E13e))) → E13E
  31. Vector(E14, (x(E14) + x(E14m), y(E14) + y(E14m))) → E14M
  32. Vector(E14, (x(E14) + x(E14e), y(E14) + y(E14e))) → E14E
  33. Vector(E15, (x(E15) + x(E15m), y(E15) + y(E15m))) → E15M
  34. Vector(E15, (x(E15) + x(E15e), y(E15) + y(E15e))) → E15E
  35. Vector(E16, (x(E16) + x(E16m), y(E16) + y(E16m))) → E16M
  36. Vector(E16, (x(E16) + x(E16e), y(E16) + y(E16e))) → E16E
  37. Vector(E17, (x(E17) + x(E17m), y(E17) + y(E17m))) → E17M
  38. Vector(E17, (x(E17) + x(E17e), y(E17) + y(E17e))) → E17E
  39. Vector(E18, (x(E18) + x(E18m), y(E18) + y(E18m))) → E18M
  40. Vector(E18, (x(E18) + x(E18e), y(E18) + y(E18e))) → E18E
  41. Vector(E19, (x(E19) + x(E19m), y(E19) + y(E19m))) → E19M
  42. Vector(E19, (x(E19) + x(E19e), y(E19) + y(E19e))) → E19E
  43. Vector(E20, (x(E20) + x(E20m), y(E20) + y(E20m))) → E20M
  44. Vector(E20, (x(E20) + x(E20e), y(E20) + y(E20e))) → E20E
  45. Vector(E21, (x(E21) + x(E21m), y(E21) + y(E21m))) → E21M
  46. Vector(E21, (x(E21) + x(E21e), y(E21) + y(E21e))) → E21E
  47. Vector(E22, (x(E22) + x(E22m), y(E22) + y(E22m))) → E22M
  48. Vector(E22, (x(E22) + x(E22e), y(E22) + y(E22e))) → E22E
  49. Vector(E23, (x(E23) + x(E23m), y(E23) + y(E23m))) → E23M
  50. Vector(E23, (x(E23) + x(E23e), y(E23) + y(E23e))) → E23E
  51. Vector(E24, (x(E24) + x(E24m), y(E24) + y(E24m))) → E24M
  52. Vector(E24, (x(E24) + x(E24e), y(E24) + y(E24e))) → E24E
  53. Vector(E25, (x(E25) + x(E25m), y(E25) + y(E25m))) → E25M
  54. Vector(E25, (x(E25) + x(E25e), y(E25) + y(E25e))) → E25E
  55. Vector(E26, (x(E26) + x(E26m), y(E26) + y(E26m))) → E26M
  56. Vector(E26, (x(E26) + x(E26e), y(E26) + y(E26e))) → E26E
  57. Vector(E27, (x(E27) + x(E27m), y(E27) + y(E27m))) → E27M
  58. Vector(E27, (x(E27) + x(E27e), y(E27) + y(E27e))) → E27E
  59. Vector(E28, (x(E28) + x(E28m), y(E28) + y(E28m))) → E28M
  60. Vector(E28, (x(E28) + x(E28e), y(E28) + y(E28e))) → E28E
  61. Vector(E29, (x(E29) + x(E29m), y(E29) + y(E29m))) → E29M
  62. Vector(E29, (x(E29) + x(E29e), y(E29) + y(E29e))) → E29E
  63. Vector(E30, (x(E30) + x(E30m), y(E30) + y(E30m))) → E30M
  64. Vector(E30, (x(E30) + x(E30e), y(E30) + y(E30e))) → E30E
  65. Vector(E31, (x(E31) + x(E31m), y(E31) + y(E31m))) → E31M
  66. Vector(E31, (x(E31) + x(E31e), y(E31) + y(E31e))) → E31E
  67. Vector(E32, (x(E32) + x(E32m), y(E32) + y(E32m))) → E32M
  68. Vector(E32, (x(E32) + x(E32e), y(E32) + y(E32e))) → E32E
  69. Vector(E33, (x(E33) + x(E33m), y(E33) + y(E33m))) → E33M
  70. Vector(E33, (x(E33) + x(E33e), y(E33) + y(E33e))) → E33E
  71. Vector(E34, (x(E34) + x(E34m), y(E34) + y(E34m))) → E34M
  72. Vector(E34, (x(E34) + x(E34e), y(E34) + y(E34e))) → E34E
  73. Vector(E35, (x(E35) + x(E35m), y(E35) + y(E35m))) → E35M
  74. Vector(E35, (x(E35) + x(E35e), y(E35) + y(E35e))) → E35E
  75. Circle(M, (rm * s)) → E_{m}'
  76. Circle(M, rm) → E_{m}
  77. Vector(E9', (x(E9') + x(E9m'), y(E9') + y(E9m'))) → E9M'
  78. Vector(E9', (x(E9') + x(E9e'), y(E9') + y(E9e'))) → E9E'
  79. Vector(E0', (x(E0') + x(E0m'), y(E0') + y(E0m'))) → E0M'
  80. Vector(E0', (x(E0') + x(E0e'), y(E0') + y(E0e'))) → E0E'
  81. Vector(E1', (x(E1') + x(E1m'), y(E1') + y(E1m'))) → E1M'
  82. Vector(E1', (x(E1') + x(E1e'), y(E1') + y(E1e'))) → E1E'
  83. Vector(E2', (x(E2') + x(E2m'), y(E2') + y(E2m'))) → E2M'
  84. Vector(E2', (x(E2') + x(E2e'), y(E2') + y(E2e'))) → E2E'
  85. Vector(E3', (x(E3') + x(E3m'), y(E3') + y(E3m'))) → E3M'
  86. Vector(E3', (x(E3') + x(E3e'), y(E3') + y(E3e'))) → E3E'
  87. Vector(E4', (x(E4') + x(E4m'), y(E4') + y(E4m'))) → E4M'
  88. Vector(E4', (x(E4') + x(E4e'), y(E4') + y(E4e'))) → E4E'
  89. Vector(E5', (x(E5') + x(E5m'), y(E5') + y(E5m'))) → E5M'
  90. Vector(E5', (x(E5') + x(E5e'), y(E5') + y(E5e'))) → E5E'
  91. Vector(E6', (x(E6') + x(E6m'), y(E6') + y(E6m'))) → E6M'
  92. Vector(E6', (x(E6') + x(E6e'), y(E6') + y(E6e'))) → E6E'
  93. Vector(E7', (x(E7') + x(E7m'), y(E7') + y(E7m'))) → E7M'
  94. Vector(E7', (x(E7') + x(E7e'), y(E7') + y(E7e'))) → E7E'
  95. Vector(E8', (x(E8') + x(E8m'), y(E8') + y(E8m'))) → E8M'
  96. Vector(E8', (x(E8') + x(E8e'), y(E8') + y(E8e'))) → E8E'
  97. Vector(E10', (x(E10') + x(E10m'), y(E10') + y(E10m'))) → E10M'
  98. Vector(E10', (x(E10') + x(E10e'), y(E10') + y(E10e'))) → E10E'
  99. Vector(E11', (x(E11') + x(E11m'), y(E11') + y(E11m'))) → E11M'
  100. Vector(E11', (x(E11') + x(E11e'), y(E11') + y(E11e'))) → E11E'
  101. Vector(E12', (x(E12') + x(E12m'), y(E12') + y(E12m'))) → E12M'
  102. Vector(E12', (x(E12') + x(E12e'), y(E12') + y(E12e'))) → E12E'
  103. Vector(E13', (x(E13') + x(E13m'), y(E13') + y(E13m'))) → E13M'
  104. Vector(E13', (x(E13') + x(E13e'), y(E13') + y(E13e'))) → E13E'
  105. Vector(E14', (x(E14') + x(E14m'), y(E14') + y(E14m'))) → E14M'
  106. Vector(E14', (x(E14') + x(E14e'), y(E14') + y(E14e'))) → E14E'
  107. Vector(E15', (x(E15') + x(E15m'), y(E15') + y(E15m'))) → E15M'
  108. Vector(E15', (x(E15') + x(E15e'), y(E15') + y(E15e'))) → E15E'
  109. Vector(E16', (x(E16') + x(E16m'), y(E16') + y(E16m'))) → E16M'
  110. Vector(E16', (x(E16') + x(E16e'), y(E16') + y(E16e'))) → E16E'
  111. Vector(E17', (x(E17') + x(E17m'), y(E17') + y(E17m'))) → E17M'
  112. Vector(E17', (x(E17') + x(E17e'), y(E17') + y(E17e'))) → E17E'
  113. Vector(E18', (x(E18') + x(E18m'), y(E18') + y(E18m'))) → E18M'
  114. Vector(E18', (x(E18') + x(E18e'), y(E18') + y(E18e'))) → E18E'
  115. Vector(E19', (x(E19') + x(E19m'), y(E19') + y(E19m'))) → E19M'
  116. Vector(E19', (x(E19') + x(E19e'), y(E19') + y(E19e'))) → E19E'
  117. Vector(E20', (x(E20') + x(E20m'), y(E20') + y(E20m'))) → E20M'
  118. Vector(E20', (x(E20') + x(E20e'), y(E20') + y(E20e'))) → E20E'
  119. Vector(E21', (x(E21') + x(E21m'), y(E21') + y(E21m'))) → E21M'
  120. Vector(E21', (x(E21') + x(E21e'), y(E21') + y(E21e'))) → E21E'
  121. Vector(E22', (x(E22') + x(E22m'), y(E22') + y(E22m'))) → E22M'
  122. Vector(E22', (x(E22') + x(E22e'), y(E22') + y(E22e'))) → E22E'
  123. Vector(E23', (x(E23') + x(E23m'), y(E23') + y(E23m'))) → E23M'
  124. Vector(E23', (x(E23') + x(E23e'), y(E23') + y(E23e'))) → E23E'
  125. Vector(E24', (x(E24') + x(E24m'), y(E24') + y(E24m'))) → E24M'
  126. Vector(E24', (x(E24') + x(E24e'), y(E24') + y(E24e'))) → E24E'
  127. Vector(E25', (x(E25') + x(E25m'), y(E25') + y(E25m'))) → E25M'
  128. Vector(E25', (x(E25') + x(E25e'), y(E25') + y(E25e'))) → E25E'
  129. Vector(E26', (x(E26') + x(E26m'), y(E26') + y(E26m'))) → E26M'
  130. Vector(E26', (x(E26') + x(E26e'), y(E26') + y(E26e'))) → E26E'
  131. Vector(E27', (x(E27') + x(E27m'), y(E27') + y(E27m'))) → E27M'
  132. Vector(E27', (x(E27') + x(E27e'), y(E27') + y(E27e'))) → E27E'
  133. Vector(E28', (x(E28') + x(E28m'), y(E28') + y(E28m'))) → E28M'
  134. Vector(E28', (x(E28') + x(E28e'), y(E28') + y(E28e'))) → E28E'
  135. Vector(E29', (x(E29') + x(E29m'), y(E29') + y(E29m'))) → E29M'
  136. Vector(E29', (x(E29') + x(E29e'), y(E29') + y(E29e'))) → E29E'
  137. Vector(E30', (x(E30') + x(E30m'), y(E30') + y(E30m'))) → E30M'
  138. Vector(E30', (x(E30') + x(E30e'), y(E30') + y(E30e'))) → E30E'
  139. Vector(E31', (x(E31') + x(E31m'), y(E31') + y(E31m'))) → E31M'
  140. Vector(E31', (x(E31') + x(E31e'), y(E31') + y(E31e'))) → E31E'
  141. Vector(E32', (x(E32') + x(E32m'), y(E32') + y(E32m'))) → E32M'
  142. Vector(E32', (x(E32') + x(E32e'), y(E32') + y(E32e'))) → E32E'
  143. Vector(E33', (x(E33') + x(E33m'), y(E33') + y(E33m'))) → E33M'
  144. Vector(E33', (x(E33') + x(E33e'), y(E33') + y(E33e'))) → E33E'
  145. Vector(E34', (x(E34') + x(E34m'), y(E34') + y(E34m'))) → E34M'
  146. Vector(E34', (x(E34') + x(E34e'), y(E34') + y(E34e'))) → E34E'
  147. Vector(E35', (x(E35') + x(E35m'), y(E35') + y(E35m'))) → E35M'
  148. Vector(E35', (x(E35') + x(E35e'), y(E35') + y(E35e'))) → E35E'

AI Drawing Prompt Reference

Draw a diagram showing the Earth and Moon. The Earth is a circle, and the Moon is below it. Draw 22 vectors from the center of the Earth to its surface, each representing the acceleration caused by the Moon and Earth's gravity at different points on the Earth's surface. The length and direction of the vectors indicate the magnitude and direction of the acceleration. Use dashed lines to show the gravitational force between the Earth and Moon. Label the centers of the Earth and Moon, and the 22 points on the Earth's surface.
The prompt above was compiled from the original drawing commands and is for reference only.