Math Is Fun Forum

The equation provided is a parabolic equation, but it is not the equation of the comet trajectory!! Since to derive the equation of the comet path, you have to introduce first a plane coordinate system (choosing a certain point as the origin) in which both variavbles are distances, or if you like to use time, you can use a parametric representation of the trajectory with time taken as the parameter. The equation which is provided has nothing to do with the trajectory (if it is the equation of the trajectory in a coordiate system other then the cartesian, then it must has different form). It just relates time to the distance of the comet from the center of jupiter's moon, and since the comet is at equal distances from jupiter's moon at symmetrical points (taking the axis of the parabola as the symmetrical line), each distance from the moon has two values, "equal in magnitudes and different in signs" depending on the side which the comet occupied.