The discussion revolves around understanding the mathematical basis for tidal forces, specifically comparing the influence of the moon and the sun on tides. The original poster expresses a belief that the moon has a greater effect and seeks clarification on the mathematical transition from gravitational force to tidal force, particularly the significance of the 1/r³ relationship.
Several participants are engaged in clarifying the mathematical concepts involved. Some have suggested looking into existing resources, such as the Wikipedia article on Tidal Force, which may provide a derivation relevant to the discussion. The conversation is ongoing, with multiple perspectives being explored.
Participants note the importance of understanding the spatial derivative of gravitational force and how it relates to the phenomenon of tides. There is an acknowledgment of the complexity involved in deriving the tidal force equation, particularly for points on the Earth's surface.
In what way does this statement not contain both the question and the answer?Vitani11 said:I know the moon does. I know it is because tidal forces fall off as 1/r3. But why? Mathematically, I mean.
Did you try a search on Tidal Force? Even the Wikipedia article on Tidal Force shows a short derivation (granted it's for the locations lying along the line joining the centers of the two interacting bodies, but it avoids the vector math required for the more general solution for points located anywhere on the surface of the smaller body).Vitani11 said:I should have been more specific. How do you get from F = GMm/r2 to an equation for tides that has a 1/r3 in it?
Vitani11 said:I should have been more specific. How do you get from F = GMm/r2 to an equation for tides that has a 1/r3 in it?