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Conservation of Energy (Vis-Viva Equation)

The total mechanical energy (

E

) of an orbiting body is constant. The Vis-Viva equation relates speed (

v

), distance (

r

), and semi-major axis (

a

v^2 = \text{GM} \text{}(\frac{2}{r} - \frac{1}{a})

📜

The statement of the theorem

The total specific mechanical energy

E

of an orbiting body is conserved, defined as:\n

E = \frac{1}{2} v^2 - \frac{\mu}{r} = \text{constant}

\nThis leads to the Vis-Viva equation, which relates the speed

v

, distance

r

, and semi-major axis

a

:\n

v^2 = \mu \left( \frac{2}{r} - \frac{1}{a} \right)

Source: Wikipedia