Define gravitational potential at a point.
Starting from the equation for the gravitational potential due to a point mass, show that the gravitational potential energy of a point mass
at a distance
from another point mass
is given by
where is the gravitational constant.
The figure below shows the path of a comet of mass as it passes around a star of mass
.
At point X, the comet is from the centre of the star and is moving at a speed of
. At point Y, the comet passes its point of closest approach to the star. At this point, the comet is a distance of
from the centre of the star. Both the comet and the star can be considered as point masses at their centres.
Calculate the magnitude of the change in the gravitational potential energy of the comet as it moves from position X to position Y.
State, with a reason, whether the change in gravitational potential energy in (b)(i) is an increase or a decrease.