Answer to Question #163641 in Field Theory for Vakel

Question

(i.) State Newton's law of gravitation. Give the meaning of any symbol you use.

 

Define the terms gravitational field and gravitational field strength.

 

Use your answers in (i) and (ii) to show that the magnitude of the gravitational field strength at the earth's surface is F GM where M is the mass of the earth, R is the radius of the earth and G is the gravitational constant.

Answer 1

For two bodies having masses m and M with a distance r between their centers of mass, the equation for Newton’s universal law of gravitation is

$$F=\frac{GmM}{r^2}$$

where F is the magnitude of the gravitational force and G is a proportionality factor called the gravitational constant. G is a universal gravitational constant.

Gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body.

The gravitational field strength is the weight per unit mass.

$$F=mg=\frac{GmM}{R^2}\\g=\frac{GM}{R^2}$$