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This animation shows transfers from perigee to apogee when `r_1ltr_2` and from apogee to perigee when `r_1gtr_2`. At the transition from circular orbit `r_1` to Hohmann ellipse, there is a short rocket burn and at the transition from Hohmann ellipse to circular orbit `r_2` there is also a short rocket burn. These burns are needed to match the circle `r_1` speed to that of the ellipse and to match the speed on the ellipse to circular orbit `r_2`. Depending on whether `r_2gtr_1` or `r_2ltr_1`, 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, `deltat`, required to provide the needed speed change, `deltav`,
`deltat=(deltav)/a`
where `a` is the acceleration. Then I compute the average orbit angle change, `deltatheta`, 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 `(d^2Theta)/(dt^2) of the orbit angle is computed`(d^2theta)/(dt^2)=(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 `(d^2theta)/(dt^2)` is applied which results in speed at the end required to continue in the subsequent orbit.