The thought of increasing a satellite's (for example) speed to allow it to transfer from a "higher energy" elliptical orbit to a "lower energy" circular orbit (in reference to the effective potential energy plot that arises after introducing the concept of an effective mass to simplify the two-body problem into a one-body problem) seems a bit counterintuitive. It's easy to find this illogical with a circular orbit simply occurring at a lower energy level than an elliptical orbit in the effective potential energy plot. Examining other equations such as ΔE = Δ(-C/A) (where C = GMm) clearly depicts mathematically why, in the final stage of the Hohmann transfer process, transferring to a circular orbit with a larger major axis requires an in-take of energy, gained through the rocket engine. However, how should this be viewed with respect to the effective potential energy plot (equal to [L^(2)[/[2μr^(2)] - (GMm)/r, with the remaining term being the kinetic energy from the radial velocity; μ is the effective mass, Mm/(M+m))? Would the best way to think of this be a shift in this graph due to the work done by the propellant force on the satellite (thus a new graph that allows for the new, final energy to take a circular orbit)?