13.1 Universal Gravitation

1a2 marks

Planets create large gravitational fields.

State what is meant by a gravitational field.

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1 mark

The Earth has a larger gravitational field strength than the moon.

State what is meant by gravitational field strength.

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4 marks

Saturn has a gravitational field strength of 10.5 N kg^–1 on its surface and a radius of 58 000 km.

(i)

State the acceleration due to gravity of an object on Saturn.

[1]

(ii)

Calculate the mass of Saturn.

[3]

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2 marks

Fig 1.1 represents Saturn as an isolated uniform sphere.

Sketch the lines to represent the gravitational field outside the sphere.

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2 marks

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

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4 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

$ρ = \frac{3 π n^{3}}{G T^{2}}$

where G is the gravitational constant.

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3 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

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CIE A Level Physics

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