The specific energy (energy per unit mass) of a space vehicle is composed of two components, the specific potential energy and the specific kinetic energy.
The specific orbital energy of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy, divided by the reduced mass.
The formula for specific orbital energy is given as,
specific orbital energy = specific kinetic energy + specific potential energy
ϵ=ϵk + ϵp
We know value of
ϵk= v2 / 2 —— where ϵk = specific kinetic energy and v = velocity .
and
ϵp = − GM / r —— where ϵp = specific potential energy , G = the universal gravitational constant , M = the mass of the body to be escaped and r = distance from the centre of mass of the body to the object.
Therefore,
ϵ= (V2 / 2)–(GM / r)
ϵ = specific orbital energy.
v = velocity
G = the universal gravitational constant (G = 6.67×10−11 m3 kg−1 s−2)
M = the mass of the body to be escaped
r = distance from the centre of mass of the body to the object.