4.1.1 Introduction

Any two bodies attract each other with a force that is proportional to the product of their masses, and inversely proportional to the square of the distance between them (Newton’s law):

(4‑1)

where

F is the gravitational force

G = (6,6726 ± 0,0009)×10^-11m³kg^-1s^-2 is the
universal gravitational constant

m₁, m₂ are the two point masses

r is the distance between the masses

The simplest case of gravitational attraction occurs between bodies that can be considered as point masses. These are bodies at a relative distance r that is sufficiently large in comparison to the sizes of the bodies to ignore the shape of the bodies. For two spherical bodies with a homogeneous mass distribution Newton’s law is correct also at all locations above their surface (“2-body problem”).

Also third body perturbations and tidal effects are important for an accurate analysis of the gravitational interaction_.