Newton's Law of Gravitation and Gravitational Field Strength
Any two masses attract with a force that falls off as the square of their separation. Dividing that force by the test mass leaves a field strength that belongs to the source alone.
What a learner can do afterwards
- Uses F = GMm over r squared with r measured centre to centre
- Shows that surface g follows from GM over R squared, and predicts g at a stated height
- Sketches the radial field of a single mass and says what the spacing of the lines shows
1 · Read
Every mass attracts every other mass along the line joining their centres. The force grows with each mass and shrinks with the square of the distance r between centres. In symbols, F equals G M m over r squared, where G is the gravitational constant.
The same pull holds an apple on its tree and the Moon in its orbit. Each body pulls the other equally hard in opposite directions, even when one mass is far larger.
Field strength g is the force per unit mass, in newtons per kilogram. Divide F by the test mass m and g equals G M over r squared, which depends on the source mass alone. At the surface r is the planet's radius R. A radial field sketch uses inward lines, spaced wider where the field is weaker.
Measure r from centre to centre. Since g equals G M over r squared, g at distance r is the surface value times (R over r) squared. At 3 Earth radii from the centre, g = 9.8 / 3 squared = 9.8 / 9, about 1.09 N/kg. The same rule means doubling any separation quarters the force.
Masses pull along their joining line with a force that falls as one over r squared.
Rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.