Orbits of planets and satellites Flashcards
Kepler’s third law
the square of the orbital period (T) is directly proportional to the cube
of the radius (r)
what happens 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
What is the total energy of an orbiting satellite made up of?
- its kinetic and potential energy, and is
constant. - For example, if the height of a satellite is decreased, its gravitational potential energy will
decrease, however it will travel at a higher speed meaning kinetic energy increases, therefore total
energy is always kept constant.
equation of Total energy of a satellite v
Total energy of a satellite = kinetic energy + potential energy
escape velocity
is the minimum velocity it must travel at, in order to escape
the gravitational field at the surface of a mass. This is the velocity at which the object’s kinetic
energy is equal to the magnitude of its gravitational potential energy.
- Ek = Ep, Ep is GMm/r
- rearrange to get V which is escape velocity
synchronous orbit
- one where the orbital period of the satellite is equal to the rotational
period of the object that it is orbiting,
Geostationary satellites
follow a specific geosynchronous orbit, meaning their orbital period is 24
hours and they always stay above the same point on the Earth, because they orbit directly
above the equator.
Why are geostationary satellites useful
for sending TV and telephone
signals because it is always above the same point on the Earth so you don’t have to alter the
plane of an aerial or transmitter.
how to find orbital radius?
you use this equation : T^2 = 4π^2/GM x r^3
- rearrange for r to get the orbital radius
Low-orbit satellites
- have significantly lower orbits in comparison to geostationary satellites,
therefore they travel much faster meaning their orbital periods are much smaller. - Because of this, these satellites require
less powerful transmitters and can potentially orbit across the entire
Earth’s surface. ( this is why they are useful)
what are low-orbit satellites useful for ?
- monitoring the weather
- making scientific
- observations about places which are unreachable and military applications.
- They can also be
used for communications but because they travel so quickly, many satellites must work together to
allow constant coverage for a certain region.
Kepler third law deriviation
1) set equal the Centripetal force equation to the Gravitational force equation
2) Rearrange the equation to make v^2 the subject.
3)use v = 2πr/T and square the equation to get v^2 = 4π^2 r ^2 / T^2
4) set num 3 equation to num 2 equation
5)Rearrange to make T² the subject
6) As 4π2/GM is a constant, this shows that T^2 ∝ r^3
Compare the PE and KE of a lower orbit to a higher one
A lower orbit (smaller m ) has less potential energy and more kinetic energy than a higher orbit ( bigger r )
