The orbit equation which defines the trajectory of a spacecraft after it has departed the earth's atmosphere is solved in this video. An auxiliary variable is used to solve the second order ordinary differential equation. The solution is shown to be the general equation of a conic section in polar coordinates. The possibility of circular, elliptical, parabolic and hyperbolic trajectories for the space vehicle orbit or trajectory is shown. The concept of burnout and burnout velocity for a rocket booster is explained.
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