Orbits of planets and satellites (A-level only) Flashcards – AQA A-level Physics (7408)

What force supplies the centripetal force for a planet or satellite in a circular orbit?

Gravity.

What equation equates gravitational and centripetal forces for a body of mass $m$ orbiting a spherical body of mass $M$ at radius $r$ and speed $v$?

$\frac{GMm}{r^2}=\frac{mv^2}{r}$

What is the circular orbital speed at radius $r$ around a spherical body of mass $M$?

$v=\sqrt{\frac{GM}{r}}$

What is the orbital period of a circular orbit in terms of its radius $r$ and speed $v$?

$T=\frac{2\pi r}{v}$

What is the circular orbital period $T$ at radius $r$ around a spherical body of mass $M$? Give the formula for $T$ and its equivalent squared form.

$T=2\pi\sqrt{\frac{r^3}{GM}}$ $T^2=\frac{4\pi^2r^3}{GM}$

For circular orbits around the same central mass, how is the squared period related to orbital radius?

$T^2\propto r^3$. Larger orbits have longer periods.

For circular orbits around the same central mass, how does orbital speed change as radius increases?

It decreases.

What is the gravitational potential energy of a satellite of mass $m$ at distance $r$ from the centre of a body of mass $M$, taking potential energy as zero at infinity?

$U=-\frac{GMm}{r}$

What is the kinetic energy of a satellite of mass $m$ in a circular orbit of radius $r$ around a body of mass $M$?

$K=\frac{GMm}{2r}$

What is the total mechanical energy of a satellite of mass $m$ in a circular orbit of radius $r$ around a body of mass $M$?

$E=-\frac{GMm}{2r}$

What does a satellite’s negative total mechanical energy indicate?

It is in a gravitationally bound orbit.

What change in total energy is required to move a satellite to a larger circular orbit?

Its total energy must increase.

How do gravitational potential energy and orbital kinetic energy change when a satellite moves to a larger circular orbit?

Potential energy becomes less negative, while kinetic energy decreases.

What is escape velocity?

The minimum launch speed needed to reach infinite distance from a gravitating body with zero speed remaining, without further propulsion.

For escape from distance $r$ from the centre of a spherical body of mass $M$, what is the minimum initial energy condition? Take gravitational potential energy as zero at infinity and the escaping object's mass as $m$.

Initial kinetic plus gravitational potential energy must be zero:

$\frac{1}{2}mv_{\mathrm{esc}}^2-\frac{GMm}{r}=0$

What is the escape velocity at distance $r$ from the centre of a spherical body of mass $M$?

$v_{\mathrm{esc}}=\sqrt{\frac{2GM}{r}}$

How does escape velocity depend on the escaping object's mass?

It is independent of the object's mass.

What assumption about energy losses underlies the ideal escape-velocity formula?

There are no energy losses.

What observation advantage does a low Earth orbit satellite's proximity to Earth provide?

It can provide detailed observations.

How does a low Earth orbit satellite's proximity to Earth affect signal travel time?

It gives a relatively short signal travel time.

Why can continuous coverage of one location require multiple low Earth orbit satellites?

Each satellite moves across the sky relative to the ground.

What are two uses of low Earth orbit satellites?

Earth observation and communications.

Where does a geostationary satellite remain relative to Earth?

Above the same equatorial location.

What regional coverage can a geostationary satellite provide?

Continuous coverage of a large region.

What are two uses of geostationary satellites?

Communications and weather observation.

How does a geostationary satellite's greater distance affect signal travel time?

It makes signal travel times longer.

What geographical limitation affects geostationary satellite coverage?

Coverage is limited at high latitudes.