The Orbital Mechanics Vis Viva Equation, also known as the Vis Viva equation or the energy equation, is a mathematical formula that describes the relationship between the kinetic and potential energy of an object in orbit.
The equation is used to calculate the velocity, or speed, of an object in orbit around a central body, such as a planet or moon. It is also used to determine the energy of an object in orbit, which can be used to predict its trajectory and orbital path.
The variables in the equation are the semi-major axis of the orbit (a), the gravitational constant (G), and the mass of the central body (M). The equation also includes the mass of the orbiting object (m) and its distance from the central body (r).
The equation is derived from the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted. By applying this law to the gravitational potential energy and kinetic energy of an object in orbit, the equation is derived.
Yes, the equation can be used for objects in elliptical, circular, and parabolic orbits. It is also applicable to objects in hyperbolic orbits, as long as the relative velocities are small compared to the speed of light.