ABSTRACT
The gravitational force plays the most prominent role in astrophysics. It is responsible for holding the solar system, the galaxies, and the galaxy clusters together. The gravitational force is well described by the Newton’s inverse square law. Consider two point particles of mass M and m. Here we treat heavenly bodies, such as Sun, Earth, etc., as particles. Let ~r denote the position vector of m with respect to M , as shown in Figure 5.1. The force on m due to M is given by
~F = −GMmrˆ r2
, (5.1)
where rˆ is the unit vector along ~r. The negative sign indicates that the force is attractive, that is, toward M . This law is applicable as long as the particles move at speeds much smaller than the speed of light. For most astrophysical applications, Newton’s law is sufficiently accurate. The gravitational force is a central force. This means that its magnitude is a function only of the distance r, and the direction is along the displacement vector ~r.
