General Relativity/Tidal forces

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Radially from an object of mass m, the tidal acceleration is {-2Gm \over r^3}*deltaX and perpendicular to the radial line, the acceleration is {Gm \over r^3}*deltaX (Where G is the gravitational constant and deltaX is the seperation distance of two test particles.

To calculate those, you must remember that the acceleration due to gravity is {Gm \over r^2}. When you consider two test particles separated by a distance of deltaX, the results vary depending on if they are along a common radius from the center of the earth or perpendicular to it. (Any other cases can be decomposed into a combination of those two cases). Where the two test particles are radial, the two effective radii are r and (r+deltaX). If you look at the relative acceleration between the two particles, you get {Gm \over (r+deltaX)^2} - {Gm \over r^2} = { {Gmr^2-Gm(r+deltaX)^2} \over r^2(r+deltaX)^2} = {-2Gmr*deltaX + deltaX^2 \over r^2(r+deltaX)^2} = (approx) {-2Gmr \over r^4} = {-2Gm \over r^3}deltaX

More to follow...

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