7 J01/III/2 (part)

b The moon Charon (discovered in 1978) orbits the planet Pluto. The graph shows the variation of the gravitational potential f with distance d above the surface of Pluto along a line joining the centres of Pluto and Charon.

The gravitational potential is taken as being zero at infinity.

(i)  Suggest why all values of gravitational potential are negative.

(ii)  Use the graph to determine, giving an explanation of your working,

1. the distance from the surface of Pluto at which the acceleration of free fall is zero,

2. the acceleration of free fall on the surface of Charon.

[0.052 m s-2]

c A lump of rock of mass 2.5 kg is ejected from the surface of Charon such that it travels towards Pluto.

(i) Using data from the graph, determine the minimum speed with which the rock hit the surface of Pluto.

[933 m s-1]

(ii) Suggest why, if the rock travels from Pluto to Charon, the minimum speed on reaching Charon is different from that calculated in (i).

Satellite Motion and Circular Motion

8 J93/II/1 modified

A planet P of mass m orbits the Sun S of mass M in a circular orbit of radius r and period T as shown on the diagram below.

(a) On the diagram, draw an arrow representing the linear velocity of P and label this v.

Draw a second arrow representing the direction of the resultant force acting on P. Label this F.

(b) (i) Write down an expression, in terms of m, r and T, for the magnitude of resultant force F.

(iii) Write down an expression, in terms of m, M, r and G, for the magnitude of the gravitational force exerted by the Sun on the planet.

(iii) Hence, show that .

9 N79/I/4 (part)

Explain what is meant by (i) gravitational field strength, (ii) gravitational potential. How do these quantities vary with distance x from a point mass?

It can be shown that, for planets performing circular orbits about a sun, the period of revolution t is related to the radius r of the orbit by the equation t = Arn, where A and n are constants. Values of t and the mean radius r for some of the planets of our solar system are given in the table below.

Planet / t / year / r / 106 km
Mercury / 0.241 / 58
Venus / 0.615 / 108
Mars / 1.88 / 228
Jupiter / 11.9 / 778
Saturn / 29.5 / 1430

a. By drawing a suitable graph, deduce the values of A and n.

[5.4 x 10-13 yr km-1.52, 1.52]

b. Find the mean radius of the Earth’s orbit. [1.54 x 108 km]

10. N99/III/2

a Explain how an object travelling in a circle with constant speed has an acceleration. In what direction is this acceleration?

- 3 - Physics/ATS/2009