## Calculating gravitational forces

Physics Narrative for 11-14

#### Find out how to calculate gravitational forces

Suppose you want to calculate the size of the gravitational force acting between you and your colleague as you approach each other (one metre apart) in the corridor. We can do this quite simply by using Newton's equation: force_{gravity} = *G* × *M* × *m*separation^{2} .

Suppose: your mass, *m*, is 60 kilogram; the mass of your colleague, *M*, is 70 kg; your centre-to-centre separation, *r*, is 1 m; and *G* is 6.67 × 10^{-11} newton square metre kilogram^{-2}.

Inserting these values into the equation to get 6.67 × 10^{-11} newton square metre kilogram^{-2} × 60 kilogram × 70 kilogram1 metre^{2}. You can work out this force and you'll get 2.8 × 10^{-7} newton.

In other words you exert a gravitational pulling force of 0.28 millionths of a newton on your colleague! The force exists but it is too small to notice in practice.

From the numbers it is clear that because the value of G is so small, the magnitude of the gravitational force will be very small, unless one or other of the objects has a very large mass.

You can use Newton's equation to check out the empirical observation that a 1 kilogram mass experiences a gravitational pull of about 10 N at the surface of the Earth. This is calculating the gravitational pull at the Earth's surface

force_{gravity} = *G* × *M* × *m*separation^{2}

Where: mass, *m*, is 1 kilogram; mass of the Earth, *M*, is 6.0 × 10^{24} kilogram; the radius of the Earth (separation of masses), *r*, is 6.4 × 10^{6} m; and *G* is 6.67 × 10^{-11} newton square metre^{kilogram-2}}.

Inserting these values into the equation, and work this out to get a force of 9.8 newton .

As expected, the pull of the Earth on a 1 kilogram mass at its surface is about 10 N .