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A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version.
The specific orbital energy associated with this orbit is −29.6 MJ/kg: the potential energy is −59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg. Compared with the potential energy at the surface, which is −62.6 MJ/kg., the extra potential energy is 3.4 MJ/kg, and the total extra energy is 33.0 MJ/kg.
If the orbit is elliptical or hyperbolic, then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Disregarding loss or gain however ...
By the conservation of mechanical energy, the energy of the orbit is simply the sum of kinetic and gravitational potential energies, in an unperturbed two-body orbit.By substituting the vis-viva equation into the kinetic energy component, the orbital energy of a circular orbit is given by:
The period of the resultant orbit will be longer than that of the original circular orbit. The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecrafts are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster.
An elliptical orbit is depicted in the top-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy decreases as the orbiting body's speed decreases and distance increases according to Kepler's ...
The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful ...
In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies.It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.