Vis Viva Equation — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Vis-viva Equation This equation relates the orbital speed of an object to its distance from the central body and the semi-major axis, applicable to any two-body gravitational system (elliptical, parabolic, or hyperbolic orbits). Apply the principle of conservation of mechanical energy (E = K + U). Define the total energy E using the kinetic energy (K = 1 2 mv 2) and gravitational potential energy (U = - GMm r ). Relate the total energy E to the semi-major axis 'a' using the orbital energy equation (E = - GMm 2a ). Equate the two expressions for E and solve for the orbital speed squared, v 2. r > 0 a > 0 Confusing the semi-major axis (a) with the radius at the point of measurement (r). Assuming the equation only applies to circular orbits (in which case, r = a). Forgetting that the mass 'm' of the orbiting body cancels out during the derivation.