P.3.7.2.1 Newton's Law

The distance between the Sun and the Earth is 1.5 × 10¹¹ m

What is the gravitational force exerted on the Sun by the Earth?

• 3.5 × 10²² N

• 1.7 × 10²⁶ N

• 5.3 × 10³³ N

• 8.9 × 10⁵⁰ N

Charon is a moon of Pluto that has a mass equal to 1/9 that of Pluto.

Charon is a moon of Pluto that has a mass equal to d that of Pluto.

X is the point at which the resultant gravitational field due to Pluto and Charon is zero.

What is the distance of X from the centre of Pluto?

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The distance between the centres of the Earth and the Moon is 3.8 × 10⁸ m. The mass of the Earth is 6.0 × 10²⁴ kg and the mass of the Moon is 7.4 × 10²² kg.

A spacecraft of mass 10 × 10³ kg is moving along a line joining their centres.

At what distance from the centre of the Earth would the spacecraft experience no resultant force due to the Earth and the Moon?

• 3.8 × 10⁷ m

• 4.8 × 10⁷ m

• 3.4 × 10⁸ m

• 3.8 × 10⁸ m

Which of the following statements about Newton’s law of gravitation is correct?

Newton’s gravitational law explains

• the origin of gravitational forces.

• why a falling satellite burns up when it enters the Earth’s atmosphere.

• why projectiles maintain a uniform horizontal speed.

• how various factors affect the gravitational force between two particles.

Two planets X and Y are in concentric circular orbits about a star S. The radius of the orbit of X is R and the radius of orbit of Y is 2R .

The gravitational force between X and Y is F when angle SXY is 90°, as shown in the diagram.

What is the gravitational force between X and Y when they are nearest to each other?

• 2 F

• 3 F

• 4 F

• 5 F

The gravitational constant, G, is a constant of proportionality in Newton’s law of gravitation. The permittivity of free space, ε₀, is a constant of proportionality in Coulomb’s law.

When comparing the electrostatic force acting on a pair of charged particles to the gravitational force between them, the product ε₀G can appear in the calculation.

Which is a unit for ε₀G?

• C² kg^–2

• C² m^–2

• F kg² N^–1 m^–2

• it has no unit

A spacecraft of mass m is at the mid-point between the centres of a planet of mass M₁ and its moon of mass M₂. If the distance between the spacecraft and the centre of the planet is d, what is the magnitude of the resultant gravitational force on the spacecraft?

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When a space shuttle is in a low orbit around the Earth it experiences gravitational forces F_E due to the Earth, F_M due to the Moon and F_S due to the Sun. Which one of the following correctly shows how the magnitudes of these forces are related to each other?

mass of Sun = 1.99 × 10³⁰ kg

mass of Moon = 7.35 × 10²² kg

mean distance from Earth to Sun = 1.50 × 10¹¹ m

mean distance from Earth to Moon = 3.84 × 10⁸ m

• F_E > F_S > F_M

• F_S > F_E > F_M

• F_E > F_M > F_S

• F_M > F_E > F_S

Which one of the following gives a correct unit for

• N m⁻²

• N kg⁻¹

• N m

• N

An object on the surface of a planet of radius R and mass M has weight W.

What would be the weight of the same object when on the surface of a planet of radius 2R and mass 2M?

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• W

• 2W