Quick questions on Gravitational fields: Newton's law, field strength and orbits - Edexcel A-Level Physics

Like Coulomb's law this is an inverse-square law, but gravity has only one sign (always attractive) and is extremely weak: $G$ is tiny, so gravitational forces matter only when at least one mass is astronomical. Treat spherical bodies as point masses at their centres.

Around a point or spherical mass the field is radial, $g = \frac{GM}{r^2}$, pointing inwards. Close to a planet's surface, over distances small compared with the radius, the field is effectively uniform, which is why we treat $g$ as constant at about $9.8$ N per kg near the ground. The radial $g$ against $r$ graph falls as an inverse square outside the body.

Potential is a scalar that falls off as $\frac{1}{r}$. Equipotential surfaces are concentric spheres around a mass, and no work is done moving along one. The (positive) energy needed to escape to infinity from a surface defines escape velocity, $v_{\text{esc}} = \sqrt{\frac{2GM}{r}}$.

State Newton's law of gravitation in words. [1 mark]

A planet has mass $3.0 \times 10^{24}$ kg and radius $4.0 \times 10^{6}$ m. Find its surface gravitational field strength. [2 marks]

Explain why gravitational potential is always negative. [2 marks]