Gravitational force between point masses

Section: Gravitational Fields  |  Syllabus: Cambridge A Level Physics (9702)

Newton's Cannonball Experiment

Newton used a thought experiment to explain orbits. If a cannonball is fired from a high mountain fast enough, the curvature of the Earth prevents it from ever hitting the ground. It stays in orbit indefinitely.

Figure 13.2: Newton's Cannonball

Show a mountain on Earth firing projectiles. Path A and B fall to Earth. Path C/D are fired fast enough to circle the globe, showing that an orbit is essentially a "continual fall" that never hits the surface.

Newton was the first to realize that the same laws of physics apply to both an apple falling from a tree and the Moon orbiting the Earth.

Newton's Law of Gravitation

Any two point masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

F = (Gm_1m_2/r^2)

Where G is the gravitational constant (6.67 × 10^-11 N m^2 kg^-2).

Definition: Point Mass

A sphere of uniform density can be treated as if all its mass is concentrated at its centre. Thus, astronomical bodies (planets/moons) are treated as point masses for calculations.

Worked Example: GPS Satellite Force

Question: Calculate the force between Earth (5.97 × 10^24 kg) and a 1600 kg satellite at a height of 20,200 km. Earth radius = 6.37 × 10^6 m.

Solution

1. Identify total radius r: r = (6.37 × 10^6) + (20,200 × 10^3) = 2.657 × 10^7 m.

2. Calculate F: F = 6.67 × 10^-11 × 5.97 × 10^24 × 1600(2.657 × 10^7)^2 = 902 N.

Interactive revision notes, videos and practice questions load below.

Related: Past Papers Topical Questions AS Physics A2 Chemistry Grade Boundaries Command Words