<P> When a system approximates a two - body system, instantaneous orbital speed at a given point of the orbit can be computed from its distance to the central body and the object's specific orbital energy . (Specific orbital energy is constant and independent of position .) </P> <P> In the following, it is assumed that the system is a two - body system and the orbiting object has a negligible mass compared to the larger (central) object . In real - world orbital mechanics, it is the system's barycenter, not the larger object, which is at the focus . Specific orbital energy = K.E. + P.E. (kinetic energy + potential energy). Since kinetic energy is always non-negative (greater than or equal to zero, ≥ 0) and potential energy is always non-positive (less than or equal to zero, ≤ 0), the sign of this may be positive, zero, or negative and the sign tells us something about the type of orbit: </P> <Ul> <Li> If the specific orbital energy is positive the orbit is open, following a hyperbola with the larger body the focus of the hyperbola . Objects in open orbits do not return; once past periapsis their distance from the focus increases without bound . See radial hyperbolic trajectory </Li> <Li> If the specific orbital energy is zero, (K.E = - P.E.): the orbit is thus a parabola with focus at the other body . See radial parabolic trajectory . Parabolic orbits are also open . </Li> <Li> If the energy is negative, K.E. + P.E. <0: The orbit is closed . The motion is on an ellipse with one focus at the other body . See radial elliptic trajectory, free - fall time . Planets have closed orbits around the Sun . </Li> </Ul> <Li> If the specific orbital energy is positive the orbit is open, following a hyperbola with the larger body the focus of the hyperbola . Objects in open orbits do not return; once past periapsis their distance from the focus increases without bound . See radial hyperbolic trajectory </Li>

Obtain the formula for the orbital speed of a satellite of the earth