Gravitational fields
A force field is an area in which an object experiences a non-contact force. Force fields can be
represented as vectors, which describe the direction of the force that would be exerted on the
object, from this knowledge you can deduce the direction of the field. They can also be
represented as diagrams containing field lines, the distance between field lines represents the
strength of the force exerted by the field in that region.
A gravitational field is a force field in which objects with mass experience a force.
Gravitational field strength
There are two types of gravitational field; a uniform field or radial field. These can be
represented as the following field lines:
The arrows on the field lines show the direction that a force acts on a mass. A uniform field exerts
the same gravitational force on a mass everywhere in the field, as shown by the parallel and
equally spaced field lines. In a radial field the force exerted depends on the position of the
object in the field, e.g in the diagram above, as an object moves further away from the centre, the
magnitude of force would decrease because the distance between field lines increases. The
Earth’s gravitational field is radial, however very close to the surface it is almost completely
uniform.
Gravitational field strength (g)
Gravitational field strength (g) is the force per unit mass exerted by a gravitational field on an
object. This value is constant in a uniform field, but varies in a radial field. The general formula for
calculating the gravitational field strength is: G=F/m
Newton’s law of universal gravitation
Gravity acts on any objects which have mass and is always attractive.
Newton’s law of gravitation shows that the magnitude of the gravitational force between two
masses is directly proportional to the product of the masses, and is inversely proportional to
the square of the distance between them, (where the distance is measured between the two
centres of the masses).
Gravitational field strength in a radial field
An example of a radial gravitational field, is the one formed by a point mass.
The gravitational field strength (g) in a radial field varies and you can derive an equation for the
gravitational field strength at a point in the field using Newton’s law of gravitation and the general
formula for gravitational field strength as shown below:
Gravitational potential
Gravitational potential (V) at a point is the work done per unit mass when moving an object from
infinity to that point. Gravitational potential at infinity is zero, and as an object moves from infinity
to a point, energy is released as the gravitational potential energy is reduced, therefore
gravitational potential is always negative.
gravitational potential difference
The gravitational potential difference is the energy needed to move a unit mass between
two points and therefore can be used to find the work done when moving an object in a
gravitational field.
Similarities comparing electric and gravitational fields
Forces both follow an inverse-square law
Use field lines to be represented and can both
be either uniform or radial
Use equations of a similar form to find the
force exerted and field strength (though use
different values)
Differences comparing electric and gravitational fields
In gravitational fields, the force exerted is
always attractive, while in electric fields the
force can be either repulsive or attractive.
Electric force acts on charge, while
gravitational force acts on mass.
Orbital motion Explanation and step 1
Kepler’s third law is that the square of the orbital period (T) is directly proportional to the cube
of the radius (r): 7’-oc 7-3 . This can be derived through the following process:
- When an object orbits a mass, it experiences a gravitational force towards the centre of the
mass, and as the object is moving in a circle, this gravitational force acts as the centripetal
force. Therefore we can equate the equations of centripetal force and gravitational force:
Step 2
Rearrange the equation to make vsquared the subject
Step 3
Velocity is the rate of change of displacement, therefore you can find v in terms of radius (r) and
orbital period (7):
Because the diameter of a circle is 2xr, and the object will travel this distance in one orbital period.
Step 4
Substitute the equation for 12 in terms of r and 7, into the original equation (from step 2).
Step 5
Rearrange to make T2 the subject.
TIP
You must be able to apply Newton’s laws of motions and gravitation to orbital motion as shown
above. It is important to keep in mind that if an orbit is circular, all the equations you learnt to do
with circular motion will apply.
