Topic 4.1: Gravitational Fields Questions

State Newton's universal law of gravitation.

Define gravitational field strength at a point, and state its SI unit.

State what is meant by the **escape speed** of a planet.

State Kepler's second law of planetary motion, and state where in its orbit a planet moves with the greatest speed.

A satellite travels at constant speed in a circular orbit around a planet.

State the direction of the satellite's acceleration.

For a planet orbiting the Sun, the orbital period T and orbital radius r are found to obey a relationship of the form Tⁿ ∝ rᵐ, where n and m are whole numbers.

Identify the values of n and m, and hence state the numerical value of the ratio n : m.

Describe, in terms of a **gravitational potential well**, what must happen for a spacecraft resting on a planet's surface to escape the planet completely.

Outline Kepler's first law of planetary motion, and describe one way in which the actual orbits of the planets in the Solar System differ from perfect circles.

A planet of mass 2.0 × 10³⁰ kg has a small moon in a circular orbit of radius 1.1 × 10¹¹ m.

Calculate the orbital speed of the moon.

Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

A planet has mass M = 6.4 × 10²³ kg and radius r = 3.4 × 10⁶ m.

Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

Calculate the **gravitational potential** at its surface.

Two planets, A and B, orbit the same star.

Planet B's orbital radius is 16 times that of planet A.

Determine the factor by which planet B's orbital period is longer than planet A's.

The gravitational field strength at a planet's surface is g, and the planet has radius r.

Using g = GM/r² and the escape-speed formula, **show that** the escape speed from the surface can be written as v_esc = √(2gr).

The gravitational field strength at a point P, a distance r from the centre of a moon, is 7.2 N kg⁻¹.

Determine the difference between the field strength at P and the field strength at a point three times as far from the centre.

Explain how astronomers can determine the mass of the Sun by observing the motion of a planet that orbits it.

Earth orbits the Sun in a near-circular path of radius 1.5 × 10¹¹ m with a period of one year (3.15 × 10⁷ s).

Estimate the mass of the Sun.

Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

A satellite of mass 750 kg orbits at a distance r = 8.0 × 10⁶ m from the centre of a planet of mass M = 6.4 × 10²³ kg.

Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

Calculate the gravitational potential energy of the satellite, and explain why your answer is negative.

Two satellites, P and Q, orbit the same planet in circular orbits.

The orbital radius of Q is nine times that of P.

Deduce the ratio of the orbital speed of P to the orbital speed of Q.

Planet Tarn has 3.0 times the mass of Earth and 1.5 times Earth's diameter.

The gravitational field strength at Earth's surface is 9.8 N kg⁻¹.

Determine the gravitational field strength at Tarn's surface.

A comet follows a highly elliptical orbit around the Sun.

Explain, with reference to Kepler's second law, how and why the comet's speed changes between the point closest to the Sun and the point farthest from the Sun.

A space probe is in a circular orbit of radius 9.4 × 10⁶ m around a planet of mass 4.9 × 10²⁴ kg.

Calculate the probe's orbital speed and the time for one complete orbit (its period).

Take G = 6.67 × 10⁻¹¹ N m² kg⁻².