Tidal Accelerations (To Scale)

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2020-01-02 22:55

① This example demonstrates tidal acceleration vectors at various points on Earth's surface, explaining the formation of tidal bulges and tides with a true-to-scale representation. ② Core mathematical concepts include universal gravitation, centripetal acceleration, vector addition and decomposition, and the distribution of tidal (tractive) forces. ③ Construction highlights: using GeoGebra's Circle command to define Earth and the Moon's orbit, and Vector command to draw acceleration vectors; key objects include scale factor, Earth center E, Moon mass m, gravitational parameter gm, Earth-Moon distance aEM, and auxiliary points (E0m, E9m, E1–E27) for computing and plotting the vector field. ④ Suitable for high school physics or introductory astronomy/mechanics courses, as well as mathematics classes focusing on vector operations and geometric construction, helping students visualize how vector direction and magnitude vary with position.

GeoGebra Commands & Parameters

Circle(E, re) → E_{c}
Vector(E9, (x(E9) + x(E9m), y(E9) + y(E9m))) → E9M
Vector(E9, (x(E9) + x(E9e), y(E9) + y(E9e))) → E9E
Vector(E0, (x(E0) + x(E0m), y(E0) + y(E0m))) → E0M
Vector(E0, (x(E0) + x(E0e), y(E0) + y(E0e))) → E0E
Vector(E1, (x(E1) + x(E1m), y(E1) + y(E1m))) → E1M
Vector(E1, (x(E1) + x(E1e), y(E1) + y(E1e))) → E1E
Vector(E2, (x(E2) + x(E2m), y(E2) + y(E2m))) → E2M
Vector(E2, (x(E2) + x(E2e), y(E2) + y(E2e))) → E2E
Vector(E3, (x(E3) + x(E3m), y(E3) + y(E3m))) → E3M
Vector(E3, (x(E3) + x(E3e), y(E3) + y(E3e))) → E3E
Vector(E4, (x(E4) + x(E4m), y(E4) + y(E4m))) → E4M
Vector(E4, (x(E4) + x(E4e), y(E4) + y(E4e))) → E4E
Vector(E5, (x(E5) + x(E5m), y(E5) + y(E5m))) → E5M
Vector(E5, (x(E5) + x(E5e), y(E5) + y(E5e))) → E5E
Vector(E6, (x(E6) + x(E6m), y(E6) + y(E6m))) → E6M
Vector(E6, (x(E6) + x(E6e), y(E6) + y(E6e))) → E6E
Vector(E7, (x(E7) + x(E7m), y(E7) + y(E7m))) → E7M
Vector(E7, (x(E7) + x(E7e), y(E7) + y(E7e))) → E7E
Vector(E8, (x(E8) + x(E8m), y(E8) + y(E8m))) → E8M
Vector(E8, (x(E8) + x(E8e), y(E8) + y(E8e))) → E8E
Vector(E10, (x(E10) + x(E10m), y(E10) + y(E10m))) → E10M
Vector(E10, (x(E10) + x(E10e), y(E10) + y(E10e))) → E10E
Vector(E11, (x(E11) + x(E11m), y(E11) + y(E11m))) → E11M
Vector(E11, (x(E11) + x(E11e), y(E11) + y(E11e))) → E11E
Vector(E12, (x(E12) + x(E12m), y(E12) + y(E12m))) → E12M
Vector(E12, (x(E12) + x(E12e), y(E12) + y(E12e))) → E12E
Vector(E13, (x(E13) + x(E13m), y(E13) + y(E13m))) → E13M
Vector(E13, (x(E13) + x(E13e), y(E13) + y(E13e))) → E13E
Vector(E14, (x(E14) + x(E14m), y(E14) + y(E14m))) → E14M
Vector(E14, (x(E14) + x(E14e), y(E14) + y(E14e))) → E14E
Vector(E15, (x(E15) + x(E15m), y(E15) + y(E15m))) → E15M
Vector(E15, (x(E15) + x(E15e), y(E15) + y(E15e))) → E15E
Vector(E16, (x(E16) + x(E16m), y(E16) + y(E16m))) → E16M
Vector(E16, (x(E16) + x(E16e), y(E16) + y(E16e))) → E16E
Vector(E17, (x(E17) + x(E17m), y(E17) + y(E17m))) → E17M
Vector(E17, (x(E17) + x(E17e), y(E17) + y(E17e))) → E17E
Vector(E18, (x(E18) + x(E18m), y(E18) + y(E18m))) → E18M
Vector(E18, (x(E18) + x(E18e), y(E18) + y(E18e))) → E18E
Vector(E19, (x(E19) + x(E19m), y(E19) + y(E19m))) → E19M
Vector(E19, (x(E19) + x(E19e), y(E19) + y(E19e))) → E19E
Vector(E20, (x(E20) + x(E20m), y(E20) + y(E20m))) → E20M
Vector(E20, (x(E20) + x(E20e), y(E20) + y(E20e))) → E20E
Vector(E21, (x(E21) + x(E21m), y(E21) + y(E21m))) → E21M
Vector(E21, (x(E21) + x(E21e), y(E21) + y(E21e))) → E21E
Vector(E22, (x(E22) + x(E22m), y(E22) + y(E22m))) → E22M
Vector(E22, (x(E22) + x(E22e), y(E22) + y(E22e))) → E22E
Vector(E23, (x(E23) + x(E23m), y(E23) + y(E23m))) → E23M
Vector(E23, (x(E23) + x(E23e), y(E23) + y(E23e))) → E23E
Vector(E24, (x(E24) + x(E24m), y(E24) + y(E24m))) → E24M
Vector(E24, (x(E24) + x(E24e), y(E24) + y(E24e))) → E24E
Vector(E25, (x(E25) + x(E25m), y(E25) + y(E25m))) → E25M
Vector(E25, (x(E25) + x(E25e), y(E25) + y(E25e))) → E25E
Vector(E26, (x(E26) + x(E26m), y(E26) + y(E26m))) → E26M
Vector(E26, (x(E26) + x(E26e), y(E26) + y(E26e))) → E26E
Vector(E27, (x(E27) + x(E27m), y(E27) + y(E27m))) → E27M
Vector(E27, (x(E27) + x(E27e), y(E27) + y(E27e))) → E27E
Vector(E28, (x(E28) + x(E28m), y(E28) + y(E28m))) → E28M
Vector(E28, (x(E28) + x(E28e), y(E28) + y(E28e))) → E28E
Vector(E29, (x(E29) + x(E29m), y(E29) + y(E29m))) → E29M
Vector(E29, (x(E29) + x(E29e), y(E29) + y(E29e))) → E29E
Vector(E30, (x(E30) + x(E30m), y(E30) + y(E30m))) → E30M
Vector(E30, (x(E30) + x(E30e), y(E30) + y(E30e))) → E30E
Vector(E31, (x(E31) + x(E31m), y(E31) + y(E31m))) → E31M
Vector(E31, (x(E31) + x(E31e), y(E31) + y(E31e))) → E31E
Vector(E32, (x(E32) + x(E32m), y(E32) + y(E32m))) → E32M
Vector(E32, (x(E32) + x(E32e), y(E32) + y(E32e))) → E32E
Vector(E33, (x(E33) + x(E33m), y(E33) + y(E33m))) → E33M
Vector(E33, (x(E33) + x(E33e), y(E33) + y(E33e))) → E33E
Vector(E34, (x(E34) + x(E34m), y(E34) + y(E34m))) → E34M
Vector(E34, (x(E34) + x(E34e), y(E34) + y(E34e))) → E34E
Vector(E35, (x(E35) + x(E35m), y(E35) + y(E35m))) → E35M
Vector(E35, (x(E35) + x(E35e), y(E35) + y(E35e))) → E35E
Circle(M, rm) → E_{m}

AI Drawing Prompt Reference

Draw a to-scale diagram of tidal accelerations. Place Earth as a circle with its center marked, and the Moon at a distance to the right. On Earth's surface, distribute many sample points evenly. From each point, draw two vectors: one pointing toward the Moon (representing lunar gravitational acceleration) and one pointing toward Earth's center (representing Earth's gravitational acceleration). Scale the vector lengths according to real physical proportions to show how tidal forces vary across the surface. The diagram should clearly illustrate the direction and magnitude changes of tractive forces, explaining the formation of tidal bulges.

The prompt above was compiled from the original drawing commands and is for reference only.