The energy diagram above shows the energy of a satellite in a circular orbit.
A satellite orbiting a massive object is a bound system. Total energy in a bound system is negative, reflecting the fact that the satellite cannot escape.
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Suppose satellite is in orbit at r
1
and we want to increase the orbit to r
2
- Need to add energy to the satellite
- Satellite moves more slowly in the larger orbit r2, has less kinetic energy
- Total energy increases as r increases
- Satellite had to fire thruster to move to a higher orbit
Escape velocity is the threshold velocity needed for a projectile launched from a massive body to just reach infinity before falling back down. An object launched with a speed faster than escape speed will get away from the planet (become unbound).
Practice problems
1. Find the escape speed for a particle leaving a planet of mass M and radius r.
2. Find the altitude of a geostationary satellite.
3. A binary star system consists of two stars with masses 2.5x1030 kg and 5.0x1030 kg separated by a distance of 3.0x1012 m.
A. Find the center of mass of the system. Use the position of the larger mass star as the origin.
B. Find the orbital period of the system.