Syllabus Points — Gravitational Fields

13.1 Gravitational field

1. understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass
2. represent a gravitational field by means of field lines

13.2 Gravitational force between point masses

1. understand that, for a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre
2. recall and use Newton's law of gravitation $F = Gm_1m_2/r^2$ for the force between two point masses
3. analyse circular orbits in gravitational fields by relating the gravitational force to the centripetal acceleration it causes
4. understand that a satellite in a geostationary orbit remains at the same point above the Earth's surface, with an orbital period of 24 hours, orbiting from west to east, directly above the Equator

13.3 Gravitational field of a point mass

1. derive, from Newton's law of gravitation and the definition of gravitational field, the equation $g = GM/r^2$ for the gravitational field strength due to a point mass
2. recall and use $g = GM/r^2$
3. understand why $g$ is approximately constant for small changes in height near the Earth's surface

13.4 Gravitational potential

1. define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point
2. use $\phi = -GM/r$ for the gravitational potential in the field due to a point mass
3. understand how the concept of gravitational potential leads to the gravitational potential energy of two point masses and use $E_P = -GMm/r$