(Solved): According to Kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (w ...

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 \( (r, \vartheta) \) of a comet satisfies an equation of the form \( r=\beta+e(r \cdot \cos \vartheta) \), where \( \beta \) is a constant and \( e \) is the eccentricity of the orbit, with \( 0 \leq e<1 \) for an ellipse, \( e=1 \) for a parabola, and \( e>1 \) 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 \( \vartheta=4.3 \) (radians). a hyperbolic orbit. When \( \vartheta=4.3 \) (radians), the comet will be at \( r= \) (Round to two decimal places as needed.)