Hohmann transfer from circular orbit of radius r1 to another circular orbit of radius r2 This animation shows transfers from perigee to apogee when r1<r2 and from apogee to perigee when r1>r2. At the transition from circular orbit r1 to Hohmann ellipse, there is a short rocket burn and at the transition from Hohmann ellipse to circular orbit r2 there is also a short rocket burn. These burns are needed to match the circle r1 speed to that of the ellipse and to match the speed on the ellipse to circular orbit r2. Depending on whether r2>r1 or r2<r1, these speed changes are opposite and that will be shown by the direction of the rocket when the burn occurs. In this animation all length units are in screen pixels and all time units are in computer frame times. In most descriptions of the math of Hohmann transfers, the speed changes at the transitions are called impulse burns. Obviously the speed can't change instantaneously with only finite rocket acceleration available. Therefore, I first compute the time, dt, required to provide the needed speed change, dv, dt=dv/a where a is the acceleration. Then I compute the average orbit angle change, dTheta, associated with this time increment. This is the angle prior to the transition at which the orbit angle acceleration will start. Then the required angular acceleration d2Theta/dt2 of the orbit angle is computed d2Theta/dt2=dv/(dt*r) where r is the apogee or perigee radius from the large mass about which the spacecraft orbits. Between the beginning of the speed change and its end (at either theta=0 or theta=pi), the angular acceleration d2Theta/dt is applied which results in speed at the end required to continue in the subsequent orbit.
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r1 r2 GM burnAccel Single Step