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In astrodynamics, the ''vis-viva'' equation, also referred to as orbital-energy-invariance law, 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. ''Vis viva'' (Latin for "live force") is a term from the history of mechanics, and it survives in this sole context. It represents the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the ''vis viva'' accumulated or lost in the system while the work is being done. ==Equation== For any Keplerian orbit (elliptic, parabolic, hyperbolic, or radial), the ''vis-viva'' equation〔Tom Logsdon, (Orbital Mechanics: theory and applications ), John Wiley & Sons, 1998〕 is as follows: : where: * ''v'' is the relative speed of the two bodies * ''r'' is the distance between the two bodies * ''a'' is the semi-major axis (''a'' > 0 for ellipses, ''a'' = ∞ or 1/''a'' = 0 for parabolas, and ''a'' < 0 for hyperbolas) * ''G'' is the gravitational constant * ''M'' is the mass of the central body The product of GM can also be expressed as the standard gravitational parameter using the Greek letter μ. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vis-viva equation」の詳細全文を読む スポンサード リンク
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