According to Keplers first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational

Question:

According to Kepler’s first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational attractions from the planets ignored). In suitable polar coordinates, the position comet satisfies an equation of the form

where β is a constant and e is the eccentricity of the orbit, with 0 ≤ e 1 for a hyperbola. Suppose observations of a newly discovered comet provide the data below. Determine the type of orbit, and predict where the comet will be when (radians).³