Paper 4 Gravitational Fields Drills

Q1 Inverse-square data

A simulation gives the gravitational field strength $g$ at distance $r$ from the centre of a planet.

$r/10^6\mathrm{m}$	7.0	8.0	9.0	10.0	12.0
$g/\mathrm{N}\mathrm{k}{\mathrm{g}}^{-1}$	8.17	6.25	4.94	4.00	2.78

Define the transformed quantity

$$q={\left(\frac{10^6\mathrm{m}}{r}\right)}^2.$$

1. Calculate $q$ for every value of $r$. [2]
2. Plot $g$ against $q$ and draw a best-fit straight line. [5]

3. Use the gradient to determine the planet’s mass. [3]
4. Explain why distances must be measured from the planet’s centre. [2]
5. Suggest one reason real measurements near a planet may deviate from the point-mass model. [1]

Q2 Orbit data

Several satellites orbit the same planet in circular orbits. A student wants to test $T^2\propto r^3$.

1. State the graph that should be plotted. [1]
2. State how $GM$ can be found from the gradient. [2]
3. Explain why the orbit radius is not the height above the surface. [2]
4. State one condition required for the circular-orbit model. [1]