Orbit data for several moons of a distant planet are used to construct a graph of…

PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Orbit data for several moons of a distant planet are used to construct a graph of orbital period squared

T^{2}

(in s

^{2}

) on the vertical axis versus orbital radius cubed

R^{3}

(in m

^{3}

) on the horizontal axis. The best-fit line has a slope of

1.7 \times 10^{-13}\,\text{s}^{2}\!\cdot\!\text{m}^{-3}

. Using

G = 6.67 \times 10^{-11}\,\text{N}\,\text{m}^{2}\,\text{kg}^{-2}

, which of the following is the best estimate of the planet’s mass? (a)

1.0 \times 10^{23}\,\text{kg}

(b)

6.0 \times 10^{24}\,\text{kg}

(c)

3.5 \times 10^{24}\,\text{kg}

(d)

3.5 \times 10^{25}\,\text{kg}