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Gravitational Fields · Paper 2 — Free Physics HL Practice Questions

1ChallengeSAQ-LGravitational force and field strength9 marksPaper 2~14 min
A team of planetary scientists analyses data from a probe in a circular polar orbit an altitude of 240 km240\,\text{km} above the surface of Xylos, a planet with no atmosphere. The surface gravitational field strength of Xylos is gs=8.4 N kg−1g_s = 8.4\,\text{N\,kg}^{-1} and its radius is R=3.20×106 mR = 3.20 \times 10^{6}\,\text{m}. The mass of the probe is m=500 kgm = 500\,\text{kg}.
(a)
Calculate the gravitational force acting on the probe while in orbit. [3 marks]
(b)
State why the gravitational field strength at the orbital altitude is less than gsg_s. [1 mark]
(c)
Calculate the factor by which the gravitational field strength is reduced from the surface value to the orbital altitude. [2 marks]
(d)
The probe must measure the gravitational field strength at its orbital altitude with a fractional uncertainty of no more than 0.5%0.5\%. Using the relationship g∝r−2g \propto r^{-2}, evaluate whether knowing the probe's altitude to within ±1 km\pm 1\,\text{km} is sufficient to achieve this precision. [3 marks]
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