a region where any other mass will experience a force
the gravitational field strength , g , at a point us defined as the
force that acts on a unit mass placed at that point
g = F/m
units Nkg^{-1}
vector quantity
a gravitational field can be represented by
sketching field lines around a mass
the field lines show the direction of force that acts on another mass
near the earths surface the field lines are approx
parallel to each other and perpendicular to the surface of the earth , the field is said to be uniform - the gravitational field strength is the same magnitude and direction throughout the field
on a larger scale the field lines around a spherical mass
spread out radially
force of gravity on a small mass near a much larger spherical mass is always directed to
the centre of the larger mass
the magnitude of g in a radial field .... with increased distance from the massive body
decreases
over small distances which are much less than the earths radius the change in gravitational field strength is
insignificant so the field is considered to be uniform
for a radial field such as that due to a spherical mass , M , the force that acts on a small mass , m , placed at distance , r, is given by Newtons law as
F = GMm/r^{2}
g = F/m therefor g also =
g = GMm/mr^{2}
so
g = GM/r^{r}
inside the earth as r becomes smaller the mass becomes smaller so g