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The law of gravitation

Newton's law of gravitation says that two masses attract each other with a force proportional to the product of the masses and inversely proportional to the square of the distance between the centres. Double the distance gives a quarter of the force. At the Earth's surface the law gives the acceleration of gravity when one mass is the Earth's and the distance is the Earth's radius. The constant G is the same for all masses, from apples to planets.

F = G\frac{m_1 m_2}{r^2}

gravitational force

g = \frac{GM}{R^2}

surface acceleration of gravity

Symbols

$G$	gravitational constant, 6.67·10⁻¹¹	Nm²/kg²
$M$	Earth's mass, 5.97·10²⁴	kg
$R$	Earth's radius, 6.37·10⁶	m

Example

With the Earth's mass and radius:

$g = \dfrac{6.67 \cdot 10^{-11} \cdot 5.97 \cdot 10^{24}}{(6.37 \cdot 10^{6})^2} \approx 9.81$ m/s².

The distance in the law is measured between the centres, not between the surfaces.

Practise circular motion and gravitation for free →

← Centripetal force · Orbital speed of a satellite →

Part of Physics 2: Circular motion and gravitation.