Define the gravitational field.
At a distance $x$ from the centre of a uniform spherical planet with mass $M$, the gravitational field strength $g$ is $g = \frac{GM}{x^2}$, where $G$ is the gravitational constant and $x$ exceeds the planet’s radius.
Describe the arrangement of the field lines outside the planet that shows the planet’s gravitational field.
Explain why, for small vertical height changes near the surface of the planet, $g$ may be taken as constant.
Assume the Earth is a uniform sphere. For Earth, the product $GM$ is $3.99 \times 10^{14}\,\text{m}^3\,\text{s}^{-2}$.
Determine Earth’s radius $R$, giving your answer to three significant figures.
Calculate the gravitational potential at Earth’s surface, and include a unit in your answer.
Explain why the gravitational potential energy of two point masses is negative for every finite separation.