Quick questions on Newton's law of universal gravitation explained: HSC Physics Module 5

Force is inversely proportional to the square of the distance. Doubling $r$ reduces the force to one quarter. Halving $r$ quadruples the force. This rapid fall-off explains why Earth's gravity dominates near the surface but becomes negligible far from the planet.

The gravitational field strength $g$ at a point is the gravitational force per unit mass on a test mass placed there:

For an object of mass $m$ in free fall in a gravitational field $g$, the acceleration is $a = g$ (regardless of $m$, because $F = mg$ and $a = F/m$). All objects fall with the same acceleration in a given gravitational field, in the absence of air resistance.

State Newton's law of universal gravitation in words and as an equation, defining every symbol. [2 marks]

Calculate the gravitational field strength on the surface of Mars given $M = 6.42 \times 10^{23} \text{ kg}$ and $r = 3.39 \times 10^6 \text{ m}$. [2 marks]

A satellite of mass $500 \text{ kg}$ is placed at an altitude of $400 \text{ km}$ above Earth. (a) Calculate the gravitational force on it. (b) Compare this with its weight at Earth's surface.