A natural satellite orbits Planet Y in a nearly circular path at an altitude of above…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A natural satellite orbits Planet Y in a nearly circular path at an altitude of

300\,\text{km}

above the planet’s surface. Tracking stations measure the satellite’s orbital period to be

5.1\times10^{3}\,\text{s}

. Planet Y is approximately spherical with radius

2.5\times10^{6}\,\text{m}

. Ignore atmospheric drag. (a) Derive an algebraic expression for the orbital speed

v

of a satellite in a circular orbit of radius

r

around a planet of mass

M

in terms of

r

and the orbital period

T

. (b) Using your result from part (a) and the measured orbital data, determine the mass of Planet Y. (c) Suppose an earlier fly-by mission estimated Planet Y’s mass to be

4.5\times10^{24}\,\text{kg}

. Calculate the percent difference between that estimate and the value you found in part (b). Suggest one plausible source of discrepancy between the two determinations.

Related theory

Browse the problem library