Question

Derive the Battin satellite equation.

Answer 1

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

1. 
   
2. T is the period of the orbit
3. 
   
4. a is the semi-major axis of the orbit
5. 
   
6. G is the gravitational constant
7. 
   
8. 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.