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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.
Usually, by convention, it is negative, to keep various equations consistent with elliptical orbits. The semi major axis is directly linked to the specific orbital energy ( ϵ {\displaystyle \epsilon \,} ) or characteristic energy C 3 {\displaystyle C_{3}} of the orbit, and to the velocity the body attains at as the distance tends to infinity ...
The characteristic energy with respect to Sun was negative, and MAVEN – instead of heading to infinity – entered an elliptical orbit around the Sun. But the maximal velocity on the new orbit could be approximated to 33.5 km/s by assuming that it reached practical "infinity" at 3.5 km/s and that such Earth-bound "infinity" also moves with ...
The central body in an orbital system can be ... the negative of the specific orbital energy, where the latter is defined as the total energy of the system ...
Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.
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
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital . This theorem is named after Tjalling Koopmans, who published this result in 1934. [1]
where E is the total orbital energy, L is the angular momentum, m rdc is the reduced mass, and the coefficient of the inverse-square law central force such as in the theory of gravity or electrostatics in classical physics: = (is negative for an attractive force, positive for a repulsive one; related to the Kepler problem)