View source for General Relativity/Tidal forces

Radially from an object of mass m, the tidal acceleration is <math>{-2Gm \over r^3}*\Delta X</math> and perpendicular to the radial line, the acceleration is <math>{Gm \over r^3}*\Delta X</math> (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 <math>{Gm \over r^2}</math>.  When you consider two test particles separated by a distance of <math>\Delta X</math>, 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+\Delta X).  If you look at the relative acceleration between the two particles, you get <math>{Gm \over (r+\Delta X)^2} - {Gm \over r^2} = { {Gmr^2-Gm(r+\Delta X)^2} \over r^2(r+\Delta X)^2} = {-2Gmr \Delta X + Gm \Delta X^2 \over r^2(r+\Delta X)^2} \sim {-2Gmr \Delta X \over r^4} = {-2Gm \over r^3}\Delta X </math>

More to follow...

[[Category:Physics]]
[[Category:General relativity]]