The Moon may be considered to be a uniform sphere of diameter 3.4 × 103 km and mass 7.4 × 1022 kg. The Moon has no atmosphere.

Question 6

(a) (i) A gravitational field may be represented by lines of gravitational force.

State what is meant by a line of gravitational force. [1]

(ii) By reference to lines of gravitational force near to the surface of the Earth, explain why the gravitational field strength g close to the Earth’s surface is approximately constant. [3]

(b) The Moon may be considered to be a uniform sphere of diameter 3.4 × 10³ km and mass 7.4 × 10²² kg. The Moon has no atmosphere.

During a collision of the Moon with a meteorite, a rock is thrown vertically up from the surface of the Moon with a speed of 2.8 km s^-1.

Assuming that the Moon is isolated in space, determine whether the rock will travel out into distant space or return to the Moon’s surface. [4]

 [Total: 8]

Reference: Past Exam Paper – June 2018 Paper 42 Q1

Solution:

(a) (i) A line of gravitational force represent the direction of the force on a (small test) mass placed in the field.

(ii) At the surface the lines of force are radial. Since the Earth has a large radius, a height above the surface is small (compared to the radius). So, the (radial) lines can be approximated as parallel lines close to the surface. Parallel lines imply that the field strength is constant.

(b)

{The threshold for escape is when the kinetic energy of the rock exceeds the potential energy required to reach infinity.

We need to compare the threshold value and the actual value to conclude whether the rock escape into space or not.}

{In this method we find the escape speed required by the rock to escape into space. If the speed of the rock (= 2.8×10³ m s^-1) is greater than the escape speed, then the rock would travel out into distant space.}

(change in) KE of rock = (change in) PE

½ mv² = GMm / R

{We need to convert values into SI units.

mv² = 2GMm / R }

(m)v² = (m)(2 × 6.67×10^-11 × 7.4×10²²) / (1.7×10³×10³)

v = 2.4 × 10³ m s^-1       

Since the speed of the rock is greater than the escape speed, the rock will travel out into distance space.