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Gravity and motion — Question 162

Original QCE Vault practice · 7 marks

Q162 · Practice questionComplex unfamiliar7 marks

QUESTION 162 (7 marks)

Four small moons have circular orbits about the same planet. The graph shows T2T^2 against r3r^3, where rr is measured from the planet's centre. Treat the fitted line through the origin as exact for this question. Use G=6.67×10−11 N m2 kg−2G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}.
T squared in units of 10 to the 7 s squared versus r cubed in units of 10 to the 21 m cubed. A straight line through the origin passes through (1,2.5), (2,5), (3,7.5) and (4,10).
a)
Determine the gradient of the graph in SI units.
[2 marks]
b)
Determine the mass of the planet.
[3 marks]
c)
Predict the period of a moon at radius 1.50×107 m1.50\times10^7\,\mathrm m.
[2 marks]
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