Acceleration due to gravity

Considering a body with the mass M as a source of a gravitational field, the strength of that field, or the gravitational acceleration, is given by:

                                 r
                     r       Mr                                    M
                     g = − G 2 . The modulus of g is g = G 2
                                 r
                             r                                     r

Here G is the gravitational constant, G = 6.67428 * 10 − 11 N m 2 / kg 2 , r is the distance between a body of

                                                    r

mass m and the center of the gravitational field, r is the vector radius of that body having the mass m. If the source of the gravitational field has a spherical shape, then r is the sphere’s radius. Taking into account that the Earth is an oblate spheroid, the distance r is not that of a sphere and varies from the equator to the poles.

                               rp
                                              x              m
                                                r
                                                            y
                                          q
                                O                    re

A normal section (on the equatorial plane) is almost an ellipse, so, r can be done by:

                 r = re2 cos2 θ + rp2 sin2 θ

where r e and r p are the equatorial radius and polar radius, respectively and θ is the latitude, or the angle made by r with the equatorial plane. References 1. V.Dorobantu and Simona Pretorian, Physics between fear and respect, Vol. 3, Edited by Politehnica

                                         Timisoara, 2007, ISBN 978-973-625-493-2