ABSTRACT
The first term in the expansion does not yield a force and can be ignored. The second term corresponds to a constant force, Gm/d2, directed towards N, which acts on the earth as a whole and is balanced by the centrifugal force due to the rotation of the earth-moon system. The third term describes the variation of the moon’s potential around the earth. The surface profile of the water is an equipotential surface due to the combined effects of the moon and the earth. The potential of unit mass of water due to the earth’s gravitation
is gh, where, h is the height of the water above its equilibrium level and g = GM/r2 is the acceleration due to gravity at the earth’s surface, where, M is the mass of the earth. Hence, the height of the tide h(θ) is given by:
gh Gmr
d ( ) cosθ θ− −
=
2 1 2
or
h h( ) cosmaxθ θ= −
3 2
1 2
2 ... (13.1)
where,
h mr Mdmax
= 4
3 ... (13.2)
is the maximum height of the tide, which occurs at points B and D (θ = 0 and θ = π). Putting m/M = 0.0123, d = 3,84,400 km, and r = 6378 km we obtain hmax ≈ 0.36 m, which is roughly in line with the observed mean tidal height.
