Tidal Potential

Let us consider the balance of forces acting upon a unit mass at a point A on the Earth’s surface. This mass moves in a gravitational field caused by the attracting forces of the Earth, G(A), of the Moon, the Sun and, generally speaking, of all the other perturbing bodies in the Solar System. Let us designate the attracting forces of these bodies as ∑ _i ⊺ _i (A); in what follows, ⊺ is a vectorial quantity. Let us introduce an inertial system of coordinates with its center at a point 0. Then Newtoon’s second law for the absolute motion of a unit mass at the point A can be written as 1.1.1$$ \frac{{d_a^2}}{{d{t^2}}}{\mathbf{O}}A{\text{ = }}{\mathbf{P}}\left( A \right) + G(A){\text{ + }}\sum\limits_i {^Ti(A){\text{ + }}{\mathbf{F}}(A).} $$ where P(A) denotes pressure and F(A is the friction force; the subscript a in the operator d _a 2/ dt2 indicates membership of the inertial coordinate system; time t will be defined below.