Understanding Tidal Forces and Their Proportionalities

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SUMMARY

Tidal forces are inversely proportional to the cube of the distance due to the nature of gravitational potential, which is proportional to 1/r. The second derivative of this potential results in a force that varies as 1/r³. This explains why the Moon, despite its smaller size, exerts a stronger tidal force on Earth compared to the Sun. The discussion references specific equations and resources, including a tidal force tensor explanation found at http://www.geocities.com/physics_world/mech/tidal_force_tensor.htm and additional insights at http://stommel.tamu.edu/~baum/reid/book1/book/node36.html.

PREREQUISITES
  • Understanding of gravitational potential and its mathematical representation
  • Familiarity with the concept of tidal forces in physics
  • Basic knowledge of calculus, particularly derivatives
  • Awareness of the differences between local and global gravitational effects
NEXT STEPS
  • Research the mathematical derivation of tidal forces from gravitational potential
  • Study the implications of tidal forces in astrophysics and planetary science
  • Explore the differences between tidal forces and gravitational forces
  • Examine case studies of tidal effects on various celestial bodies
USEFUL FOR

Astronomers, physicists, students studying gravitational dynamics, and anyone interested in the effects of celestial bodies on tides.

mprm86
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Why are tidal forces inversely proportional to the cube of the distance, and not to the square, as normal gravity force?
Where can I find more ifo about this?
Thanks in advance.
 
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mprm86 said:
Why are tidal forces inversely proportional to the cube of the distance, and not to the square, as normal gravity force?
Where can I find more ifo about this?
Thanks in advance.
Who said that? The tidal force within a small region of a local Cartesian system in free-fall has forces which are linear in the force. Those forces along the radial axis point away from the origin while those perpendicular to the radial point towards the origin. It is the origin of the coordinates which varies as the inverse cube. See Eq. (4) in http://www.geocities.com/physics_world/mech/tidal_force_tensor.htm

The gravitational potential is proportional to 1/r so the second derivative is proportional to 1/r3.

Pete
 
See an explanation http://stommel.tamu.edu/~baum/reid/book1/book/node36.html
Since they vary with the cube of the distance, tidal forces are very weak. That is why the small Moon exerts on the Earth a much stronger tidal force than the gigantic Sun. If they were linear, as pmb_phy says, the Sun would prevail.
 
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