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Vis-Viva Equation

The vis-viva equation, also referred to as the 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.

The speed equals the square root of the product of the gravitational constant, the mass of the orbit center and the difference between twice the reciprocal of the distance from the focus and the reciprocal of the semimajor axis.

Formula

QuantityVariable["v", "Speed"] == Sqrt[Quantity[1, "GravitationalConstant"]*QuantityVariable["M", "Mass"]*(-QuantityVariable["a", "Length"]^(-1) + 2/QuantityVariable["r", "Length"])]

symbol description physical quantity
v speed "Speed"
M mass of orbit center "Mass"
a semimajor axis "Length"
r distance from focus "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Vis-Viva Equation"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Vis-Viva Equation"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Vis-Viva Equation"], {QuantityVariable["v","Speed"] -> Quantity[24.64`, ("Kilometers")/("Seconds")]}]
Out[3]=

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