= Solution
Use a <Hohmann transfer orbit>. At the initial radius $r_0$, make a short prograde burn parallel to the existing <velocity>. The increased speed changes the <circular Kepler orbit> into an <elliptic orbit> whose <periapsis> is the burn point and whose <apoapsis> lies on the desired larger circle. Coast for half the transfer <orbital period> to <apoapsis>.
At that point the transfer <velocity> is again tangent to the target circle, but its magnitude is smaller than the circular speed there. A second short prograde burn raises it to the required circular speed. Thus \b[both burns increase the instantaneous speed and preserve its direction at the burn], even though the final circular speed is lower than the original one. During the coast the spacecraft loses <kinetic energy> while gaining gravitational <potential energy>.
\Image[/past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2021/paper-1-b6-hohmann-transfer.png]
{title=Original transfer-orbit construction for the later example with outer radius three times the inner radius; arrows show the two prograde burns}
The figure illustrates $3r_0$ for the subsequent parts, but the same construction works for any larger target radius. The impulsive approximation neglects the distance travelled during each burn and keeps both circles and the transfer <ellipse> coplanar.
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