How to calculate the size and orientation of a tidal bulge

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SUMMARY

The discussion focuses on calculating the size and orientation of tidal bulges created by the moon's gravitational influence on Earth. Key concepts include the gravitational attraction between the Earth and the moon, the effect of Earth's rotation on the position of the tidal bulge, and the need to account for the compression of matter in the bulge area. The conversation emphasizes the importance of developing formulas that can be applied not only to the Earth-moon system but also to other celestial bodies.

PREREQUISITES
  • Understanding of gravitational forces and Newton's law of universal gravitation
  • Familiarity with the concept of tidal forces and their effects on planetary bodies
  • Knowledge of Earth's rotational dynamics and its impact on tidal bulges
  • Basic mathematical skills for applying formulas related to gravity and tidal calculations
NEXT STEPS
  • Research the mathematical models for calculating tidal forces, specifically using Newton's law of gravitation
  • Explore the effects of Earth's rotation on tidal bulge positioning and speed
  • Learn about the compression of materials under gravitational forces, particularly in the context of tidal bulges
  • Investigate tidal calculations for other celestial bodies, such as moons of Jupiter or Saturn
USEFUL FOR

Astronomers, physicists, geophysicists, and anyone interested in understanding tidal mechanics and gravitational interactions between celestial bodies.

em370
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How would one go about calculating the size of a tidal bulge created by the moon? I know how to calculate the gravity between two points and to calculate the attractive force of matter to the center of the Earth in the bulge you would subtract its opposite direction attraction to the matter, but how would you do this with a large amount of matter and be able to calculate the loss in compression in that area? Also, because the Earth spins faster than the moon the bulge would be ahead of the the moon causing it to speed up due to a slight increase in gravity from the direction of the bulge. How would you be able to calculate how far ahead of the moon the bulge would be? I am specifically asking about the Earth and moon but would appreciate it if the formulas could be expanded so that they could be viable for other orbiting bodies.
 
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