Newton's law of gravitation Cambridge International AS & A Level Physics revision
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In plain words
Newton saw that the force that pulls an apple to the ground is the same one that holds the Moon in its orbit. Any two masses attract each other, with a force that depends on both masses and drops away quickly with distance: twice as far apart, a quarter of the pull.
5 things to know
- Newton's law of gravitation: F = Gm₁m₂ ÷ r², where G = 6.67 × 10⁻¹¹ N m² kg⁻² and r is the distance between the centres of the two masses.
- For any point outside a uniform sphere, the sphere behaves as if all its mass were at its centre.
- Dividing by the small mass gives the field strength due to a mass M: g = GM ÷ r².
- Both are inverse square laws: at twice the distance, the force and the field strength are a quarter as big.
- Near the Earth's surface g is almost constant, because even a climb of several kilometres is tiny beside the Earth's radius of 6400 km, so r hardly changes.
Worked example
Find the gravitational field strength at the surface of the Earth. (Mass of the Earth = 5.97 × 10²⁴ kg; radius = 6.37 × 10⁶ m.)
- g = GM ÷ r² = 6.67 × 10⁻¹¹ × 5.97 × 10²⁴ ÷ (6.37 × 10⁶)².
- = 3.98 × 10¹⁴ ÷ 4.06 × 10¹³.
- = 9.81 N/kg.
Tips and tricks
- r is measured from the centre of the planet: add the height above the surface to the radius.
- Remember to square r. It is the commonest slip.
It lands in your notebook with its questions as flashcards.
Newton's law of gravitation: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
The distance between two masses is doubled. What happens to the gravitational force between them?
The force is proportional to 1 ÷ r².
One of two masses is doubled. What happens to the gravitational force between them?
The force is proportional to each mass.
What are the units of G?
From G = Fr² ÷ m₁m₂.
In g = GM ÷ r² for a planet, where is r measured from?
A sphere acts as if its mass were all at its centre.
At what distance from the centre of the Earth is g one ninth of its value at the surface?Stretch
g is proportional to 1 ÷ r², and 1 ÷ 3² is one ninth.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Newton's law of gravitation
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Find the gravitational force between two 5.0 kg masses whose centres are 0.20 m apart.[3]
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4.2 × 10⁻⁸ N. 6.67 × 10⁻¹¹ × 5.0 × 5.0 ÷ 0.20².
At the Earth's surface g is 9.81 N/kg. Find g at a height above the surface equal to the Earth's radius.[2]
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2.45 N/kg. The distance from the centre has doubled, so g is a quarter.
The Moon has a mass of 7.35 × 10²² kg and a radius of 1.74 × 10⁶ m. Find the gravitational field strength at its surface.[3]
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1.62 N/kg.
Answers: Newton's law of gravitation
- 1. 4.2 × 10⁻⁸ N. 6.67 × 10⁻¹¹ × 5.0 × 5.0 ÷ 0.20².
- 2. 2.45 N/kg. The distance from the centre has doubled, so g is a quarter.
- 3. 1.62 N/kg.