All Flashcards
What are the key differences between circular and elliptical orbits in terms of energy?
Circular: Total, kinetic, potential energy, and angular momentum are constant. Elliptical: Total energy and angular momentum are constant, but kinetic and potential energy vary.
Compare kinetic energy at periapsis and apoapsis in an elliptical orbit.
Periapsis: Kinetic energy is at its maximum. Apoapsis: Kinetic energy is at its minimum.
Compare potential energy at periapsis and apoapsis in an elliptical orbit.
Periapsis: Gravitational potential energy is most negative. Apoapsis: Gravitational potential energy is least negative.
Compare the total mechanical energy required for a satellite to be in a circular orbit versus the energy required to achieve escape velocity.
Circular Orbit: Total energy is negative. Escape Velocity: Total energy is zero.
Compare the motion of the central object and the satellite.
Central Object: Treated as stationary due to its significantly larger mass. Satellite: Orbits around the central object.
Define gravitational potential energy.
The energy an object possesses due to its position in a gravitational field; it's negative, with zero defined at infinity.
What is escape velocity?
The minimum speed an object needs to escape the gravitational pull of a central object.
Define total mechanical energy in the context of orbits.
The sum of kinetic and gravitational potential energy of a satellite in orbit.
What is periapsis?
The point in an orbit closest to the central object.
What is apoapsis?
The point in an orbit farthest from the central object.
What are the steps to derive the escape velocity formula?
- Start with the total mechanical energy equation: . 2. Set the total energy to zero for escape: . 3. Solve for : .