All Flashcards
What is the effect of increasing a satellite's distance from the central object on its gravitational potential energy?
The gravitational potential energy becomes less negative (increases).
What happens to a satellite's motion when its total mechanical energy is zero?
The satellite achieves escape velocity and breaks free from the central object's gravity, moving away until its speed is zero at an infinite distance.
What is the effect of a satellite getting closer to the central object?
The gravitational potential energy becomes more negative.
What is the effect of increasing the radius of a circular orbit on the satellite's orbital speed?
The satellite's orbital speed decreases.
What is the effect of a satellite reaching escape velocity?
The satellite breaks free from the central object's gravity and continues moving away until its speed is zero at an infinite distance.
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 : .
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.