Topic 4.1: Gravitational Fields Questions

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

State, in terms of energy, the condition for an object to escape from a planet without further propulsion.

The work done to bring two bodies together from infinite separation to a distance r apart is the

The International Space Station orbits about 420 km above Earth's surface. Earth's radius is 6400 km and g at the surface is 9.8 N kg⁻¹.

Show that g at the height of the station is about 8.6 N kg⁻¹.

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

State the direction of the satellite's acceleration.

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

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.

Satellite X orbits a planet at radius r and satellite Y orbits the same planet at radius 2r.

Which is correct?

State Newton's universal law of gravitation.

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

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.

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.

A spacecraft coasts high above a planet. In one sentence, give the meaning of the escape speed at the spacecraft's position.

Four moons are described by (mass, radius): (M, R), (3M, 2R), (2M, 3R), (M, 2R).

Which moon has the largest escape speed?

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.

A comet's path round the Sun is the ellipse shown. Its speed is greatest at point P.

Mark, with an X, where the Sun could be.

Mission control boosts a satellite into a higher circular orbit around the same planet.

What happens to its speed and to its orbital period?

Two rocks of different mass are released from rest at the same height above an airless planet.

How do their accelerations compare at release and just before impact?

Earth (6.0 × 10²⁴ kg) holds the Moon 3.8 × 10⁵ km from its centre.

Calculate the strength of Earth's pull per kilogram where the Moon is (the gravitational field strength there).

Mars has radius 3400 km and surface gravitational field strength 3.7 N kg⁻¹. A probe orbits 300 km above its surface.

Show that g at the probe is about 3.1 N kg⁻¹.