IB Physics SL D.1.4 Gravitational field strength

Practise calculating and interpreting gravitational field strength around planets and stars, including surface values, zero-field points and directions from diagrams.

Exam points

calculate g from g = GM/r^2 at a surface or orbital radius, with careful substitution of radius and units
compare field strength at different distances or for different planets using mass and radius ratios
determine the direction or resultant value of acceleration from field lines or from two masses acting together

[Maximum number: 4]

(a)

Deduce that the gravitational field strength g at the surface of a spherical planet of uniform density is given by

g=\frac{G M}{R^{2}}

where M is the mass of the planet, R is its radius and G is the gravitational constant. You can assume that spherical objects of uniform density act as point masses.

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(b)

The gravitational field strength at the surface of Mars $g_{\mathrm{M}}$ is related to the gravitational field strength at the surface of the Earth $g_{\mathrm{E}}$ by

g_{\mathrm{M}}=0.38 \times g_{\mathrm{E}}

The radius of Mars $R_{\mathrm{M}}$ is related to the radius of the Earth $R_{\mathrm{E}}$ by

R_{\mathrm{M}}=0.53 \times R_{\mathrm{E}}

Determine the mass of Mars $M_{\mathrm{M}}$ in terms of the mass of the Earth $M_{\mathrm{E}}$ .

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D.1.4—Gravitational field strength question 1

Question (a)

Question (b)