Hohmann transfer orbit

In orbital mechanics, a Hohmann transfer orbit moves a spacecraft between orbiting heights. It is the most fuel-efficient method to do so, because the spacecraft is not trying to escape the planet's gravity, using an elliptical orbit for the transfer. 
A ship using this would have to apply two velocities, one to enter the elliptical orbit, and one to enter the second orbit. 
Calculation.
Assuming the mass of the spacecraft is much lower than that of the orbiting planet, the two velocities, formula_1 and formula_2, can be solved for as:formula_3formula_4where