What is vis-viva equation?

The vis-viva equation is a physical formula that describes the kinetic energy of an object in orbit around another object, such as a planet or a star. It is often used in spaceflight calculations to determine the velocity and energy of spacecraft in orbit.

The vis-viva equation states that the kinetic energy, E, of an object in orbit is proportional to the square of its velocity, v:

E = 1/2 mv^2 - GmM/r

where m is the mass of the object, M is the mass of the central body, r is the distance between the two objects, and G is the gravitational constant.

The vis-viva equation was first derived by the Italian mathematician Giovanni Battista Guglielmini in 1788. It is a fundamental result of Newtonian mechanics and is applicable in many areas of astrophysics and planetary science.