The **gravitational field strength**
(written as g or E_{G}) or **gravitational field intensity** at a
point in a field is defined as the force per unit mass at that point (constant for a uniform field
such as that near the surface of the Earth).

Therefore: E_{G} = F/m =
g

Figure 1 shows lines of equal gravitational field strength (g) around the Earth
(dotted). The lines are all equally separated in terms of field strength but the radial distance
between them increases as you move further from the planet. This means that there is little
change in g with distance near to the Earth's surface.

The **gravitational potential (V _{G})** at a point in a field is
defined as the work done in bringing unit mass to that point from
infinity.

V

where m is the mass of the body producing the field and r is the distance from its centre. The negative sign denotes that V

The change in gravitational potential (ΔV

Therefore: ΔV_{G} = ΔE/m

The
diagram (Figure 2(a) shows lines of equipotential around the Earth (dotted). Notice that the
equipotentials get further apart although the potential difference between successive lines is
the same. The field lines (full lines) are at right angles to the
equipotentials.

The gravitational potential
gradient is defined as the rate of change of gravitational potential with distance in the field.
This is equal to the gravitational field intensity (g = E_{G}) at that
point.

Therefore: g = E_{G} = -ΔV_{G}/Δr

You should be
able to see that the gravitational field strength is the same as the gravitational potential
gradient.

Put simply it is the rate at which the field changes as the distance from the mass
producing the field changes.

At points far from the Earth the field lines are changing their separation as the gravitational field strength (g) changes (Figure 2(b). However near the surface of the Earth the value of the gravitational field strength (g) is sensibly constant with height as long as this change of height is not too great. (See Figure 2(c))