Orbital Velocity

 

            Orbital velocity refers to the speed at which an orbiting mass is traveling as it orbits the central body. This velocity, while only constant for circular orbits, can be calculated at any position along the masses orbit if the distance to the central body is known along with the specific orbital energy.

 

Specific Orbital Energy:

 

            Specific orbital energy is referred to as the sum of the potential and kinetic energies per unit mass of the orbiting body. It is represented by the equation below.

 

\epsilon=\epsilon_k+\epsilon_p={v^2\over{2}}-{\mu\over{r}} =-{1\over{2}}{\mu^2\over{h^2}}\left(1-e^2\right)

                        V = orbital speed

                        r= orbital distance

                        u= GM

                        h = specific relative angular momentum

                        e = orbital eccentricity

 

            While the above equation can be used to calculate an approximate velocity, the following equation can also be used if the eccentricity of the orbit is very small.

v_o \approx \sqrt{\mu \over a}

            When one takes regard to the masses of the two objects in orbital synchronization, the following equation can be used.

v_o \approx \sqrt{m_2^2 G \over (m_1 + m_2) r}

 

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