## Action at a distance and gravitational fields

Physics Narrative for 11-14

#### How gravity alters from one planet to the next and how it varies with distance

Physicists use the idea of a field when dealing with forces, such as gravity, that act at a distance with no contact between the objects involved. The field occupies the space where the gravitational force acts, so at the surface of the Earth we live our lives in a gravitational field.

At any position, the strength of the gravitational field, or the gravitational field strength, is given by the gravitational force per kilogram.

At the surface of the Earth, for example, the strength of the Earth's gravitational field is 9.8 newton / kilogram.

This is so close to 10 newton / kilogram that this approximate value is often used.

Check this value out by hanging a 1 kilogram mass on a spring balance or newton meter. The reading shows about 10 newton.

#### The Moon's gravitational field

The strength of the Moon's gravitational field is only one sixth of the strength of the Earth's gravitational field. This is because the Moon has a much smaller mass.

At the surface of the Moon, the strength of the Moon's gravitational field is 1.7 newton / kilogram(An approximate value of 2 newton / kilogram is often used).

This means that if you go to the Moon, you are still pulled towards the surface by a significant force but you can jump a lot higher.

Alternatively, if you were able to land on a bigger planet such as Jupiter or Saturn, you would experience a much bigger gravitational force.

#### How field strength varies with distance: the inverse square law

You may have noticed that the gravitational field strengths given above are quoted for the surface of the Earth or Moon. The gravitational field strength decreases as the separation from the planet increases.

As you move away from the surface of the planet this dilution

of gravity follows a definite inverse square relationship, where distances are measured from the centre of the Earth (or Moon).

Write the radius of the Earth as R, so that the surface of the Earth is a distance R from the centre.

Then:

- At a distance R from the centre of the Earth gravitational field strength is 10 newton kilogram
^{-1}. - At a distance 2R from the centre of the Earth gravitational field strength is 2.5 newton kilogram
^{-1}. - At a distance 3R from the centre of the Earth gravitational field strength is 1.1 newton kilogram
^{-1}.

The rule is that if you:

Double the distance from the centre of the Earth, the force will be four times weaker.

Triple the distance from the centre of the Earth, the force will be nine times weaker.

In general terms, we can say that:

Gravitational field strength is inversely proportional to the square of the distance from the centre of the Earth. You can also write this as: gravitational field strength is proportional to 1*r*^{ 2}, where *r* is the distance from the centre of the Earth.