Solid earth Tide The potential at point P U=GM*/ We can expand 1/ as n+I n (cosy) 1√/R2-2 Arcos y+r2 R n=0 For n=0: Uo is gm*/R and is constant for the whole Earth For n=1; U1=GM/R2[r cosy]. Taking the gradient of U1; force is independent of position in Earth. This term drives the orbital motion of the earth 04/17/02 12.540Lec1804/17/02 12.540 Lec 18 10 Solid Earth Tide • The potential at point P U=GM*/ l • We can expand 1/ l as: • For n=0; U 0 is GM*/R and is constant for the whole Earth • For n=1; U1=GM*/R 2[r cos ψ]. Taking the gradient of U1; force is independent of position in Earth. This term drives the orbital motion of the Earth 1 l = 1 R 2 − 2Rrcosψ + r 2 = r n R n +1 n = 0 ∞ ∑ Pn (cosψ)