Gravity and Orbits

The Earth moves around the Sun in a circular orbit with a radius of 1.5 × 10⁸ km. What is the Earth’s approximate speed?

• 1.5 × 10³ ms^–1

• 5.0 × 10³ ms^–1

• 1.0 × 10⁴ ms^–1

• 3.0 × 10⁴ ms^–1

A planet of mass M and radius R rotates so rapidly that loose material at the equator only just remains on the surface. What is the period of rotation of the planet?

(G is the universal gravitational constant.)

• $2\pi\sqrt{\frac{R}{GM}}$

• $2\pi\sqrt{\frac{R^2}{GM}}$

• $2\pi\sqrt{\frac{GM}{R^3}}$

• $2\pi\sqrt{\frac{R^3}{GM}}$

The gravitational force between two uniform spheres is 3.1 × 10^–9 N when the distance between their centres is 150 mm. If the mass of one sphere is 2.5 kg, what is the mass of the other?

• 0.043 kg

• 0.42 kg

• 2.8 kg

• 4.1 kg

Masses of M and 2M exert a gravitational force F on each other when the distance between their centres is r. What is the gravitational force between masses of 2M and 4M when the distance between their centres is 4r?

• 0.25F
• 0.50F
• 0.75F
• 1.00F

Satellite X orbits the Earth with radius R. Satellite Y orbits at radius 4R. Which statement is incorrect?

• The speed of Y is greater than the speed of X

• The time period of Y is greater than the time period of X.

• The potential energy of Y is greater than the potential energy of X.

• The gravitational force acting on Y is less than the gravitational force acting on X.

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

A planet has a radius half the Earth’s radius and a mass a quarter of the Earth’s mass. What is the approximate gravitational field strength on the surface of the planet?

• 1.6 N kg^–1

• 5.0 N kg^–1

• 10 N kg^–1

• 20 N kg^–1

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?

• W/4
• W/2
• W
• 2W

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