Where necessary, use | G = 6·7 × 10^{-11}Nm^{2}kg^{-2}^{mass of earth, M = 6·0 × 1024 kgradius of earth, R = 6400km} |

**Question 1**

**Calculate the magnitude of the earth’s gravitational field strength at a point 1500km above the surface of the earth.**

**Question 2**

**Calculate the gravitational potential at a point on the earth’s surface.**

**Question 3**

**The acceleration due to gravity at the surface of the moon is about 1·6ms**

^{-2}. The diameter of the moon is about 3460km. Use these figures to calculate the average density of the moon.

**Question 4**

**A space-ship is moving directly away from the earth. When it is just outside the earth’s atmosphere, it is moving at 5kms**

^{-1}. If the rocket motors are stopped at this point, how far away from the centre of the earth will the space-ship be when it starts to "fall" back towards the earth?

N.B. the height of the earth’s atmosphere is very small compared with the radius of the earth.

**Question 5**

**Assume the earth to be a sphere of uniformly distributed mass. Let g**

_{1}be the gravitational field strength at a point2000km

*above*the earth’s surface and let g

_{2}be the gravitational field strength at a point 2000km

*below*the earth’s surface. Calculate the ratio g

_{1}/g

_{2}.

**Question 6**

**A person can jump (vertically) 2·5m on the earth. How high could the same person jump on a planet which has**

*twice*the average density of the earth and

*three times*the radius of the earth?

**Question 7**

**A planet has**

*half*the radius of the earth and the acceleration due to gravity on the planet is found to be

*twice*the acceleration due to gravity on the earth. If the average density of the earth is , calculate the average density of the other planet (in terms of ).

**Question**

**8**

A planet of mass m

orbiting at a distance r = 3×10

Calculate

a) the value of g at 5×10

b) the distance from the centre of the planet at which g = zero.

_{1}= 6×10^{24}kg has a satellite (moon) of mass m_{2}= 4×10^{23}kgorbiting at a distance r = 3×10

^{5}km.Calculate

a) the value of g at 5×10

^{4}km from the centre of the planetb) the distance from the centre of the planet at which g = zero.