Understanding Tidal Forces and Their Proportionalities

In summary, tidal forces are inversely proportional to the cube of the distance because they vary with the gravitational potential, which is proportional to 1/r. This means that tidal forces are very weak, which explains why the small Moon has a stronger tidal force on the Earth than the much larger Sun. More information on this topic can be found at the link provided by Pete, which explains the concept further.
  • #1
mprm86
52
0
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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  • #2
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
 
  • #3
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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FAQ: Understanding Tidal Forces and Their Proportionalities

What are tidal forces?

Tidal forces are the gravitational forces exerted by one astronomical body on another. These forces are responsible for the rise and fall of tides on Earth.

How do tidal forces affect the oceans?

Tidal forces cause the Earth's oceans to bulge towards the moon and the sun. This creates high tides on the sides of the Earth facing these bodies, and low tides on the opposite sides.

What is the relationship between the distance of a body and its tidal force?

The tidal force exerted by a body on another body decreases as the distance between them increases. This is known as the inverse-square law, which states that the force is inversely proportional to the square of the distance between the bodies.

Do all bodies experience tidal forces?

Yes, all bodies in the universe experience tidal forces to some degree. However, the magnitude of these forces depends on the mass and distance of the bodies involved.

Can tidal forces have other effects besides tides?

Yes, tidal forces can also cause tidal heating, which is the generation of heat due to the stretching and compression of a body caused by tidal forces. This can have significant impacts on the geological activity and evolution of a body.

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