A LevelPhysicsCIETopic Questions13. Gravitational Fields13.2 Gravitational Force Between Point Masses

Syllabus Edition

First teaching 2023

First exams 2025

|

Gravitational Force Between Point Masses (CIE A Level Physics)

Topic Questions

DownloadView
Easy
Medium
Hard
Easy
Medium
Hard
1a
Sme Calculator2 marks

State Newton's law of gravitation.

How did you do?

1b
Sme Calculator2 marks

Newton's law of gravitation assumes the masses are point masses. 

The planets in our Solar System and the Sun are not point masses. 

Explain why the law still applies to the planets in our Solar System.

How did you do?

1c
Sme Calculator1 mark

Explain why g is approximately constant for small changes in height near the Earth’s surface.

How did you do?

1d
Sme Calculator3 marks

The gravitational force between the Earth and the Sun is 3.52 × 1022 N.  

Calculate the radius of the Earth's orbit around the Sun. 

   Mass of Earth = 6.0 × 1024 kg

   Mass of Sun = 2.0 × 1030 kg

How did you do?

Did this page help you?

2a
Sme Calculator3 marks

Explain what is meant by a geostationary orbit.

How did you do?

2b
Sme Calculator2 marks

A satellite of mass m is in a circular orbit around a planet of mass M with linear speed v. 

Show that M is given by the expression:

            M space equals space fraction numerator v squared r space over denominator G end fraction

How did you do?

2c
Sme Calculator2 marks

Show that the mass M can also be written in terms of the time period of the satellite T as

            M space equals space fraction numerator 4 pi squared r cubed space over denominator T squared G end fraction

How did you do?

2d
Sme Calculator4 marks

Calculate the radius of a geostationary orbit around Earth. 

Mass of Earth = 6.0 × 1024 kg

How did you do?

Did this page help you?

1a
Sme Calculator2 marks

Scientists want to put a satellite in orbit around planet Venus.

Justify how Newton's law of gravitation can be applied to a satellite orbiting Venus, when neither the satellite, nor the planet are point masses.

How did you do?

1b
Sme Calculator6 marks

The satellite's orbital time, T, and its orbital radius, R, are linked by the equation:

T2 = kR3

Venus has a mass of 4.9 × 1024 kg.

Determine the value of the constant k, and give the units in SI base units.

How did you do?

1c
Sme Calculator2 marks

One day on Venus is equal to 116 Earth days and 18 Earth hours. 

Determine the orbital speed of the satellite in m s−1.

How did you do?

1d
Sme Calculator2 marks

The gravitational potential energy between the satellite and Venus is −2.08 × 108 J. 

Calculate the magnitude of the gravitational force keeping the satellite in orbit. Explain your answer. 

How did you do?

Did this page help you?

2a
Sme Calculator3 marks

A kilogram mass rests on the surface of the Earth as shown in Fig. 1.1. A spherical rock S, whose centre of mass is underneath the Earth's surface at a distance d of 3.5 km, has a radius of 2 km. The density of the rock is 2500 kg m–3. 

sl-sq-6-2-hard-q5a

Fig. 1.1

Determine the size of the force exerted on the kilogram mass by the rock S, justifying any approximations.  

How did you do?

2b
Sme Calculator4 marks

The spherical region of rock, S, is now replaced with a different type of rock and there is a hollow, H, made in the sphere such that its diameter is equal to the radius of S, as shown in Fig. 1.2.

The mass of sphere S with the new rock and the hollow is equal to the mass of sphere S in part (a) and is represented by M. 

The centre of the 1 kg mass m still sits at a distance 3.5 km from the centre of S. 

13-2-h-2b-cie-ial-physics-sq

Fig. 1.2

One student assumes that the force F between the mass m and sphere S is equal, despite the presence of the hollow H.

Explain why the student is incorrect in their assumption. 

How did you do?

2c
Sme Calculator3 marks

The new F between S and m with hollow H is 49 over 64 times the previous F without hollow H.

Calculate the distance between the new centre of mass of S and the geometric centre of the new shape of S. 

How did you do?

Did this page help you?

1a
Sme Calculator2 marks

Explain how the force(s) on a satellite can result in the satellite being in a circular orbit around a planet.

How did you do?

1b
Sme Calculator4 marks

The Earth and the Moon may be considered to be uniform spheres that are isolated in space. The Earth has mass M, radius R and mean density ρ. 

The Moon, mass m, is in a circular orbit about the Earth with radius nR, as illustrated in Fig. 1.1.

 

q1b-paper-4-specimen-2022-cie-ial-physics

Fig. 1.1

The Moon makes one complete orbit of the Earth in time T.

Show that the mean density ρ of the Earth is given by the expression

rho equals fraction numerator 3 pi n cubed over denominator G T squared end fraction

where G is the gravitational constant.

How did you do?

1c
Sme Calculator3 marks

The radius R of the Earth is 6.38 × 106 m and the distance between the centre of the Earth and the centre of the Moon is 3.84 × 108 m.

The period T of the orbit of the Moon about the Earth is 27.3 days.

Use the expression in (b) to calculate ρ.



ρ = ................................... kg m–3 

How did you do?

Did this page help you?

2a
Sme Calculator5 marks

Explain 

(i)
What is meant by a geostationary orbit.
[3]
(ii)
Why it is preferable to have a satellite in this orbit for TV and telephone signals
[2]

How did you do?

2b
Sme Calculator4 marks

A satellite of mass m is in orbit around a planet. 

The mass M of the planet may be considered to be concentrated at its centre.

Show that the time period T of the orbit of the satellite is given by the expression

T squared space equals space open parentheses fraction numerator 4 pi squared R cubed over denominator G M end fraction close parentheses

 

where R is the radius of the orbit of the satellite and G is the gravitational constant. 

Explain your working.

How did you do?

2c
Sme Calculator2 marks

The radius of a geostationary orbit around Earth is 4.2 × 107 m.

 Calculate the mass of the Earth.

How did you do?

2d
Sme Calculator3 marks

The radius of the Earth is 6400 km.

Determine the ratio

fraction numerator gravitational space field space strength space of space satellite space on space the space Earth apostrophe straight s space surface over denominator gravitational space field space strength space of space the space satellite space at space the space geostationary space orbit end fraction

How did you do?

Did this page help you?

3a
Sme Calculator3 marks

One of Jupiter's moons, Europa, has an orbital period of 85 hours and an orbital radius of 670 900 km.

Explain why Europa moves with uniform circular motion.

How did you do?

3b
Sme Calculator2 marks

Show that the orbital speed of Europa is 14 km s–1.

How did you do?

3c
Sme Calculator3 marks

Determine the mass of Jupiter.

How did you do?

3d
Sme Calculator3 marks

Ganymede is the largest of Jupiter’s Moons. It has an orbital period of 7.15 days and an orbital speed of 10.880 km s–1.

Calculate the ratio

fraction numerator o r b i t a l space r a d i u s space o f thin space E u r o p a over denominator o r b i t a l space r a d i u s space o f space G a n y m e d e end fraction

How did you do?

Did this page help you?