Level 6: Newton's law of gravity

Gravity and orbits · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

This level puts the whole of gravity into one equation, \(F = GMm/r^2\), and gets everything else out of it: the 3.71 m/s² of Mars from its mass and size, the speed and period of any circular orbit, Kepler's third law, the special orbit where a satellite hangs over one spot of Mars, and finally how to weigh a planet by watching its moon.

Lesson	You will be able to
The law of gravity	Use \(F = GMm/r^2\) for planets, moons and people, and say how \(G\) was measured
g from a planet's size and mass	Derive \(g = GM/R^2\), get 3.71 m/s² for Mars, and compare planets by ratios
Orbital speed	Derive \(v = \sqrt{GM/r}\) and find the speed and period of an orbit round Mars or Earth
Kepler's third law	Derive \(T^2 = 4\pi^2 r^3 / GM\) and use it for planets and moons
Areostationary orbit	Find the orbit that keeps pace with the spin of Mars, and say what it is for
Weighing planets	Find the mass of Mars from Phobos's orbit, and the mass of the Sun from Earth's

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