Write an expression for the gravitational potential VgV_{\text{g}}Vg at the surface of a planet of mass MMM and radius rrr.
The table below shows some astrophysical data for Mercury and Titan.
| Planet/Moon | Mass / kg\text{kg}kg | Radius / m\text{m}m | Mean distance from Sun / m\text{m}m |
|---|---|---|---|
| Mercury | 3.30×10233.30 \times 10^{23}3.30×1023 | 2.44×1062.44 \times 10^{6}2.44×106 | 5.79×10105.79 \times 10^{10}5.79×1010 |
| Titan | 1.35×10231.35 \times 10^{23}1.35×1023 | 2.58×1062.58 \times 10^{6}2.58×106 | 1.43×10121.43 \times 10^{12}1.43×1012 |
Show that the escape velocity vvv of a gas molecule on the surface of Titan is given by the equation
v=2GMr v = \sqrt{\frac{2GM}{r}} v=r2GMwhere MMM is the mass of Titan and rrr is its radius.
Calculate the escape velocity vvv of gas molecules on the surface of Titan.
Explain why Mercury has almost no atmosphere whilst Titan retains a dense atmosphere. Use data from the table to support your explanation.
31 exam-style questions on OCR A A Level Physics Gravitational fields, covering Point and spherical masses, Newton's law of gravitation, Planetary motion, and Gravitational potential and energy. Each one has a worked solution and a mark scheme showing where the marks go.