Q1. Keppler's laws describe the motion of planets. Which statement is NOT one of Keppler's three laws?

• A. The orbit of a planet is an ellipse with the Sun at one of two foci.
• B. A line segment joining planet to Sun sweeps out equal areas per unit time.
• C. The orbital period of a planet is dependent on the Mass of the Sun and the length semi-major axis.
• D. The orbital period squared is proportional to the length of the semi major axis cubed.

Q2-3. The diagram shows 2 asteroids. Both asteroids are attracted to each other by the force of gravity. Asteroid X is much larger and more massive than asteroid Y.

2. Which one of the following best describes the relative sizes of the forces of gravity F_X and F_Y acting on the asteroids?

• A. F_X is zero, F_Y is non-zero.
• B. F_X > F_Y (and both are non-zero).
• C. F_X < F_Y (and both are non-zero).
• D. F_X = F_Y (and both are non-zero).

3. If the mass of both asteroids is doubled, how does this affect F_Y?

• A. The force is the same.
• B. The force is 2 x larger.
• C. The force is 4 x larger.
• D. The force is 8 x larger.

4. The gravitational field strength, 'g' at a point is defined as ..

• A. the force acting per unit mass.
• B. the force acting per unit time.
• C. the change in velocity per unit mass.
• D. the change in velocity per unit volume.

5-7. A small satellite of mass m is in orbit around a large planet of mass M at a distance of r from the centre of the planet.

The gravitational constant is 'G'.

The orbit can be assumed to be circular.

5. The value of the gravitational field strength 'g' acting on the satellite is calculated. What is these statements is true?

• A. The value of g is independent of the value of r.
• B. The value of g is independent of the value of M.
• C. The value of g is independent of the value of G.
• D. The value of g is independent of the value of m.

6. The gravitational field strength provides a centripetal acceleration keeping the satellite in orbit. Which of these formulas can be used to calculate the value of the orbital velocity v?

• A. ${GM \over r^2} = {mv^2 \over r}$
• B. ${GM \over r^2} = {mv \over r^2}$
• C. ${GM \over r^2} = {v^2 \over r}$
• D. ${GMm \over r^2} = {mv \over r^2}$

7. The satellite moves closer to the planet to take images of the surface. How will this affect g and v, the velocity of the satellite in orbit?

8. The gravitational field strength on the surface of Mars of radius R_m is g_m. What will be the gravitational field strength at a height of 2R_m above the surface?

• A. ${g_m \over 2}$
• B. ${g_m \over 3}$
• C. ${g_m \over 4}$
• D. ${g_m \over 9}$

9. The diagram shows gravitational field lines around the Earth.

These lines show..

• A. the size of the force acting on a small test mass.
• B. the direction of the force acting on a small test mass.
• C. the path followed by all objects acted on by gravity around the Earth.
• D. the direction of action of the gravitational constant.

10. The diagram shows a planet and a moon of similar density. At approximately which point will the gravitational field strength between the planet and moon be zero?