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? 

A planet has triple the mass of Earth and a third of its radius. What is the gravitational field strength on the surface of the planet?

The diagram below shows three uniform masses in a straight line.

The resultant gravitational force on the 1 kg mass is zero if the distance x is:

The gravitational force between two identical uniform spheres of mass M is F when the distance between them d.

If the radius of each sphere is x, what is the correct expression for mass, M?

A satellite of mass m is placed in a geostationary orbit. If the Earth’s angular velocity is ω rad s^–1, what is the circumference of the satellite’s orbit?

A spherical planet of uniform density has two times the mass of the Earth and three times the average radius. The magnitude of the gravitational field strength at the surface of the Earth is g. What is the gravitational field strength at the surface of the planet?

The inverse square law means that halving the radius of a planet results in quadrupling the gravitational field strength at its surface.

The centres of two planets are separated by a distance R. The gravitational force between the two planets is F. What will the force between the planets be when their separation increases to 4R?

A mass at point P gives rise to a gravitational field strength g at point X as shown.

An identical mass is placed at point Q as shown.

What is the resultant gravitational field strength at X in this new situation?

A spacecraft travels away from Earth in a straight line with its motors shut down. At one instant, the speed of the spacecraft is 5.7 km s^-1. After a time of 1000 s, the speed is 5.2 km s^-1. The gravitational field strength acting on the spacecraft during this time interval is:

Which of the following statements about uniform gravitational fields is incorrect?