Orbital Speed
- As an orbiting object is moving in circular motion, where gravitational force is the centripetal force, and gravitational field strength is the centripetal acceleration, it must maintain a certain speed to continue in circular motion.
- This is the orbital speed.
- This equation is obtained by rearranging the formula for centripetal acceleration:
- Where the centripetal acceleration is g = GM/r².
- The centripetal force acting on a satellite is given by:
Escape Speed
- The above image shows the path of objects thrown at different speeds from a mountain top.
- Object A is thrown at a slow speed, and thus falls back to Earth.
- Object B is thrown at orbital speed, and starts orbiting the Earth.
- Object C is thrown at escape speed, and escapes the Earth's orbit.
- The kinetic energy needed for an object to escape a planet's orbit is equal to the gravitational potential energy between a location and infinity.
- By equating the two values, we can find escape speed:
Total Orbital Energy
- An orbiting object clearly has both potential energy, as it has gravitational potential energy, and kinetic energy, as it is moving.
- The work done to first get an object into orbit is equal to the gravitational potential energy at that point.
- The kinetic energy is based on the orbital speed of the body.
- The total energy is the sum of the two energies.
Graphs of Energy for Orbits
- Kinetic energy, gravitational potential energy and total energy all form hyperbolic energy to orbital radius graphs.
Viscous Drag Force on an Orbiting Body
- Satellites experience a small amount of viscous drag force due to air resistance, acting in the opposite direction to the satellite's motion.
- The drag force reduces the speed of the satellite over time.
- If the speed decreases slightly, the satellite will fall into a slightly lower altitude orbit.
- As it does so, its gravitational potential energy decreases, but its kinetic energy increases.
- Thus the drag force makes the satellite decrease in altitude and increase in speed.
- Eventually, the satellite will crash towards the Earth.
- However, this can be prevented by using thrusters attached to the satellite to give it slight boosts to correct its orbit.
Sources
https://animalia-life.club/qa/pictures/centripetal-acceleration-graph