6.2 Newton’s Law of Gravitation

Let r₀ represent the radius of Earth.

Which of the following shows the variation of the magnitude of the Earth's gravitational field strength g with radial distance r from its centre of mass, r = 0?

You may assume that mass is uniformly distributed beneath the Earth's surface. 

At a point above a moon's surface and a distance from its centre, the gravitational field strength is 5 N kg^–1. At the moon's surface itself, the field strength is 9 N kg^–1. 

Which of the following gives the value for the radius of the planet? 

A binary system consisting of a star of mass M and 5M orbit each other at a distance r between their centre of mass. The resultant gravitational field strength is zero along the line between their centres at a distance  from the centre of the star of mass M. What is the value of the ratio ? 

You may wish to use the quadratic formula: 

For solutions to the equation:

Which single condition enables Newton's universal law of gravitation to be used to predict the force between two masses m₁ and m₂? 

A planet of mass m and radius r rotates so rapidly that material at its equator only just remains on its surface. What is the period of its rotation? 

Two planetary systems, very far apart from each other, have suns with masses S₁ and S₂. They each have exoplanets P₁ and P₂ of mass m₁ and m₂ respectively, which are observed to have circular orbits of equal radii. If P₁ completes an orbit in the time taken by P₂, which of the following may be deduced? 

Two spherical bodies have the same radius, but one has thrice the mass of the other. At which point, A-D on the diagram below, could the resultant gravitational field of the two masses have the greatest magnitude? 

A mass m is placed at the centre of a thin, hollow, spherical shell of mass M and radius r. 

What is the magnitude of the resultant gravitational force on m and M? 

	Magnitude of resultant gravitational force on m	Magnitude of resultant gravitational force on M
A.	0
B.
C.	0	0
D.		0

Two stationary bodies of mass m₁ and m₂ are a distance d apart. A third body, situated on the line joining m₁ and m₂, experiences no resultant gravitational force. Which of the following is a possible distance between the third body and m₁?