Io, one of Jupiter’s natural satellites, moves in an orbit of radius with a time…

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Io, one of Jupiter’s natural satellites, moves in an orbit of radius

4.22\times10^{8}\,\text{m}

with a time period of

1.77\,\text{days}

. (i) Using these data, calculate the numerical value of the constant

k

that relates

T^{2}

and

r^{3}

for bodies revolving around Jupiter. (ii) A space probe is to be placed in a circular orbit around Jupiter such that its orbital period is

2.00\times10^{5}\,\text{s}

. Determine the required orbital radius for the probe. (iii) The equatorial radius of Jupiter is

7.15\times10^{7}\,\text{m}

. How many Jupiter radii does the orbit calculated in part (ii) correspond to?