Question

You are in a circular Earth orbit with a velocity of 1 DU/TU. Your service module is in another circular orbit with a velocity of 0.5 DU/TU. What is the minimum delta v needed to transfer to the service module's orbit ? (Answer: 0.449 DU/TU).

Answer 1

For transferring from one circular orbit of radius r₁ to radius r₂, the process happens in two steps.

first, the circular of radius r₁ orbit is changed to an elliptical orbit with perihelion distance r₁ and aphelion distance r₂ , by having a small impulsive velocity change of

Then, another change in velocity is made when the object reaches r₂ with

The radius of circular orbit is given by

For the problem, units are arbitrary. So, take (this is actually the gravitational parameter G*M)

So, for the orbit with v = 1 DU/TU, (distance unit and time unit)

r₁ = 1/v² = 1/1 = 1 DU

So, for the orbit with v = 0.5 DU/TU,

r₂ = 1/v² = 1/(0.5*0.5) = 4 DU

So,

The total delta v is given by