**Gravitational Field Strength (g)**

The Earth, in common with many other planets, is very nearly a perfect sphere Although we think that the bumps on its surface (such as Mount Everest!) should make it a 'bumpy sphere, the size of it makes it a relatively smooth ball - in fact smoother than a billiards ball.

The gravitational field is **radial** - the **field lines** pulling directly towards the centre. The closer in we get, the stronger the pull. This is shown by the **field lines being closer together**.

The concentration of gravitational field lines is an indication of the gravitational field strength at any point, which is formally defined as:

The gravitational force per unit mass at that point.

So we can write that statement as an equation:

Let

g = gravitational force field strength at a point

F = force

m = mass

Then

# g = F/m

The unit will be newtons per kilogram (N/kg)

From** F = ma** you know that a = F/m, so gravitational field strength is the same thing as acceleration. In the 'olden days' (when I studied physics - we put the unit of g as that of acceleration and referred to 'g' as acclereation due to gravity...)

A gravitational field strength of 9.81 N/kg therefore causes an acceleration of 9.81 m/s^{2}. This is the average gravitational field strength at the surface of the Earth - a distance of the radius of the Earth from the point the field lines come from.

A **common mistake **to make in questions is to forget that the radius of the Earth needs to be included in calculations.

**Example:** A satellite is 4000 km above the Earth's surface. What is the acceleration due to gravity at this point? (Mass of Earth = 6.0 × 10^{24} kg - Radius of the Earth = 6.37 x 10^{6} m)

r = (4.0 + 6.37) x 10^{6}m = 10.37 x 10^{6}m

# g = -GM/r^{2}

= (6.67 x 10^{-11} x 6.0 × 10^{24})/ (10.37 x 10^{6})^{2}

= 3.72 ms^{-2}

**Gravitational Field strength is a vector because it has a direction.**

### Parallel lines of the Gravitational Field near the Earth' Surface

If we look at a small section of the Earth's surface it appears to be flat. For many years people thought the Earth WAS flat!

If we consider the field lines over a section of the Earth's surface we find that they are virtually parallel, rising perpendicular to the surface up into the 'sky'. The field is then a **uniform field**. It is still the same field but we are just looking at a tiny portion of it.

This is similar as to how we think of the rays of the sun as being parallel when they reach the Earth's atmosphere. Click here

**Click here** to find out about gravitational potential