Final answer:
The Battin satellite equation, also known as the vis-viva equation, relates the period of a satellite's orbit to its distance from the central body using Kepler's third law of planetary motion and the conservation of energy.
Step-by-step explanation:
The Battin satellite equation, also known as the vis-viva equation, relates the period of a satellite's orbit to its distance from the central body. It is given by the equation:
T² = 4π²a³ / GM
- T is the period of the orbit
- a is the semi-major axis of the orbit
- G is the gravitational constant
- M is the mass of the central body
This equation is derived using Kepler's third law of planetary motion and the conservation of energy.