4 Worksheet

gravitational constant G = 6.67 × 10–11 N m2 kg–2

Intermediate level
1 Define gravitational field strength at a point in space. [1]
2 Show that the gravitational constant G has the unit N m2 kg–2. [2]
3 The gravitational field strength on the surface of the Moon is 1.6 N kg–1.
What is the weight of an astronaut of mass 80 kg standing on the surface of the Moon? [2]
4 Calculate the magnitude of the gravitational force between the objects described below.
You may assume that the objects are ‘point masses’.
a two protons separated by a distance of 5.0 × 10–14 m
(mass of a proton = 1.7 × 10–27 kg) [3]

b two binary stars, each of mass 5.0 × 1028 kg, with

a separation of 8.0 × 1012m [2]

c two 1500 kg elephants separated by a distance of 2.0 m [2]

5 The diagram shows the Moon and an artificial satellite orbiting round the Earth.
The radius of the Earth is R.

a Write an equation for the gravitational field strength g at a distance r from the centre of
an isolated object of mass M. [1]
b By what factor would the gravitational field decrease if the distance from the centre of
the mass were doubled? [2]
c The satellite orbits at a distance of 5R from the Earth’s centre and the Moon is at a
distance of 59R. Calculate the ratio:
gravitational field strength at position of satellite
[3]
gravitational field strength at position of Moon

COAS Physics 2 Teacher Resources Original material © Cambridge University Press 2009 1
 4 Worksheet

Higher level
6 The planet Neptune has a mass of 1.0 × 1026 kg and a radius of 2.2 × 107 m.
Calculate the surface gravitational field strength of Neptune. [3]
7 Calculate the radius of Pluto, given its mass is 5.0 × 1023 kg and its surface
gravitational field strength has been estimated to be 4.0 N kg–1. [3]
8 A space probe of mass 1800 kg is travelling from Earth to the planet Mars.
The space probe is midway between the planets. Use the data given to calculate:
a the gravitational force on the space probe due to the Earth [3]
b the gravitational force on the space probe due to Mars [2]
c the acceleration of the probe due to the gravitational force acting on it. [3]

Data
separation between Earth and Mars = 7.8 × 1010 m
mass of Earth = 6.0 × 1024 kg mass of Mars = 6.4 × 1023 kg

9 An artificial satellite orbits the Earth at a height of 400 km above its surface.
The satellite has a mass 5000 kg, the radius of the Earth is 6400 km and the mass of the
Earth is 6.0 × 1024 kg. For this satellite, calculate:
a the gravitational force experienced [3]
b its centripetal acceleration [2]
c its orbital speed. [3]

10 a State Kepler’s third law of planetary motion. [1]

b The Moon orbits the Earth at a distance of 3.84 × 105 km from the centre of the Earth.
The orbital period of the Moon is 27.3 days. Use this information to calculate:
i the distance from the Earth’s centre of a geostationary satellite [3]
ii the mass of the Earth. [3]

Extension
11 The planets in our Solar System orbit the Sun in almost circular orbits.
a Show that the orbital speed v of a planet at a distance r from the centre of the Sun is
given by:
GM
v= [4]
r
b The mean distance between the Sun and the Earth is 1.5 × 1011 m and the mass of the Sun
is 2.0 × 1030 kg.
Calculate the orbital speed of the Earth as it travels round the Sun. [2]
12 There is point between the Earth and the Moon where the net gravitational field strength
is zero. At this point the Earth’s gravitational field strength is equal in magnitude but
opposite in direction to the gravitational field strength of the Moon.
Given that:
mass of Earth
= 81
mass of Moon
calculate how far this point is from the centre of the Moon in terms of R, where R is
the separation between the centres of the Earth and the Moon. [4]
Total: Score: %
57

COAS Physics 2 Teacher Resources Original material © Cambridge University Press 2009 2