The table gives data for Jupiter and three of its moons

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

The table gives data for Jupiter and three of its moons, including the radius

r

of each object.

Object	Mass/kg	$r$ / m	Orbital radius around Jupiter/m
Jupiter	$1.9 \times 10^{27}$	$7.1 \times 10^7$
Io	$8.9 \times 10^{22}$	$1.8 \times 10^6$	$4.9 \times 10^8$
Ganymede	$1.5 \times 10^{23}$	$2.6 \times 10^6$	$1.06 \times 10^9$
Callisto	$1.1 \times 10^{23}$	$2.4 \times 10^6$	$1.88 \times 10^9$

A spacecraft is to be sent from Io to infinity. (a) Calculate, for the surface of Io, the gravitational field strength

g_{\text{Io}}

due to the mass of Io. State an appropriate unit for your answer. [2] (b.i) Show that the

\frac{\text{gravitational potential due to Jupiter at the orbit of Io}}{\text{gravitational potential due to Io at the surface of Io}}

is about 80. [2] (b.ii) Outline, using (b)(i), why it is not correct to use the equation

\sqrt{\frac{2G \times \text{mass of Io}}{\text{radius of Io}}}

to calculate the speed required for the spacecraft to reach infinity from the surface of Io. [1] (c) An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. [2]

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