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 a_{t} = (r_{1} + r_{2}) / 2, where r_{1} is the radius of the original orbit and r_{2} is the radius of the new orbit.

To find the total change in velocity, Δv_{Tot}, we must add Δv_{1}and Δv_{2} together.

Δ𝑣_{Tot} = Δ𝑣_{1} + Δ𝑣_{2}

𝑣* _{circ1}* and 𝑣

Δ𝑣_{1} = 𝑣_{1} – 𝑣_{circ1}

Δ𝑣_{2} = 𝑣_{circ2 }− 𝑣_{2}

𝑣* _{circ1,circ2}* =√(𝜇/ 𝑟

v_{1} and v_{2} can be found by rearranging the energy equation for an orbit:

𝜀= (𝑣_{2})/2 − 𝜇/𝑟 →

𝑣_{1,2} = √(2(𝜀_{t} + 𝜇/𝑟_{1,2}))

where the energy of the Hohmann transfer ellipse is given by ε_{t} = -μ/2a_{t}