A Hohmann transfer moves a satellite between two circular, coplanar, and concentric orbits by applying two separate impulsive maneuvers (velocity changes). This type of transfer is the most fuel-efficient.
The first impulse is used to bring the satellite out of its original orbit. The satellite then follows a transfer ellipse, known as a Hohmann ellipse, to its apoapsis point located at the radius of the new orbit. A second impulse is then used to return the satellite into a circular orbit at its new radius.
Let's review some equations that can be used to solve for different variables. The semi-major axis of the Hohmann ellipse can be determined by the equation at = (r1 + r2) / 2, where r1 is the radius of the original orbit and r2 is the radius of the new orbit.
To find the total change in velocity, ΔvTot, we must add Δv1and Δv2 together.
Δ𝑣Tot = Δ𝑣1 + Δ𝑣2
𝑣circ1 and 𝑣circ2 can be found by using the following equation for the velocity of a circular orbit:
Δ𝑣1 = 𝑣1 – 𝑣circ1
Δ𝑣2 = 𝑣circ2 − 𝑣2
𝑣circ1,circ2 =√(𝜇/ 𝑟1,2)
v1 and v2 can be found by rearranging the energy equation for an orbit:
𝜀= (𝑣2)/2 − 𝜇/𝑟 →
𝑣1,2 = √(2(𝜀t + 𝜇/𝑟1,2))
where the energy of the Hohmann transfer ellipse is given by εt = -μ/2at