changes of gravitational and kinetic energy

motion in a uniform gravitational field

the gravitational field and potential of a point mass

modelling the mass of a spherical object as a point mass at its centre

angular velocity in rad s^–1

motion in a horizontal circle and in a circular gravitational orbit.

Make appropriate use of:

(i) the terms: force, kinetic and potential energy, gravitational field, gravitational potential, equipotential surface

by sketching and interpreting:

(ii) graphs showing gravitational potential as area under a graph of gravitational field versus distance, graphs showing changes in gravitational potential energy as area under a graph of gravitational force versus distance between two distance values

(iii) graphs showing force as related to the tangent of a graph of gravitational potential energy versus distance, graphs showing field strength as related to the tangent of a graph of gravitational potential versus distance

(iv) diagrams of gravitational fields and the corresponding equipotential surfaces.

uniform gravitational field, gravitational potential energy change = $mgh$

Learners will also be expected to recall this equation

energy exchange, work done, $∆E = F∆s$; no work done when the force is perpendicular to the displacement, resulting in no work being done whilst moving along equipotentials

$a = \dfrac{v^2}{r}$,
$F = \dfrac{mv^2}{r} = mrω^2$

the radial components:
$F_{grav} = -\dfrac{GmM}{r^2}$,
$g = \dfrac{F_{grav}}{m} = -\dfrac{GM}{r^2}$

gravitational potential energy
$E_{grav} = -\dfrac{GMm}{r}$

gravitational potential
$V_{grav} = \dfrac{E_{grav}}{m} = -\dfrac{GM}{r}$