Search results
Results from the WOW.Com Content Network
In the center of mass frame the kinetic energy is the lowest and the total energy becomes = ˙ + The coordinates x 1 and x 2 can be expressed as = = and in a similar way the energy E is related to the energies E 1 and E 2 that separately contain the kinetic energy of each body: = = ˙ + = = ˙ + = +
The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by =
For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem to find: the time-average of the specific potential energy is equal to −2ε the time-average of r −1 is a −1; the time-average of the specific kinetic energy is equal to ε
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. The average speed is 7.7 km/s, the net delta-v to reach this orbit is 8.1 km/s (the actual delta-v is typically 1.5–2.0 km/s more for atmospheric drag and gravity drag ).
the kinetic energy of the system is equal to the absolute value of the total energy; the potential energy of the system is equal to twice the total energy; The escape velocity from any distance is √ 2 times the speed in a circular orbit at that distance: the kinetic energy is twice as much, hence the total energy is zero. [citation needed]
The central body and orbiting body are also often referred to as the primary and a particle respectively. In the specific cases of an elliptical or circular orbit, the vis-viva equation may be readily derived from conservation of energy and momentum. Specific total energy is constant throughout the orbit.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
Here, the total turn is analogous to turning number, but for open curves (an angle covered by velocity vector). The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity.