Orbits of Planets & Satellites
Physics: AQA A Level, topic 7.2.4
Orbital Period and Radius
When an object orbits a more massive body it has a set period and radius which depend on each other.
Orbital period
- The time taken for an object to do one full orbit is called the period.
- Even if the orbit is elliptical the period will remain constant.
Orbital radius
- The orbital radius is the average distance between the centre of the body and the centre of the object.
- For the circle, the radius is always the same.
- For an elliptical orbit, the radius changes.
Relationship
- Orbital period and radius have the following relationship:
- The period squared is proportional to the radius cubed.
- The constant of proportionality can be found by finding the gradient of a graph of period squared against radius cubed.
- This is Kepler's third law.
Energies of Orbiting Objects
Sometimes, considering the total energy of a system, such as a satellite orbiting a planet, can be much easier than thinking about the resultant force and acceleration of an object.
Circular orbits
- In a circular orbit around a planet, the satellite is always on the same equipotential and so the total energy of an orbiting satellite is constant.
- The planet does no work on the satellites, so there is no loss in potential and no loss in gravitational potential energy (GPE).
- The radius of the orbit does not change.
- The satellite does not change kinetic energy (KE) and so has a constant speed.
Non-circular orbits
- This approach also works for non-circular orbits such as ellipses and parabolas.
- This is because we can show that the total energy of an orbiting satellite is always equal to half of the gravitational potential energy of the satellite.
- This is because gravitational field strength follows an inverse-square law.
Test yourself on Orbits of Planets & Satellites
What is the relationship between orbital period and orbital radius of an object?
Which statements about orbits are correct?
What happens to the period of a planet's orbit when the radius doubles?
Which of these statements is true for circular orbits?
For which type of orbit do satellites travel along an equipotential?