The equation
describes the polar coordinates of an orbit with the coordinate origin at the sun. If ∈ = 0, the orbit is circular; if 0 < ∈ < 1, the orbit is elliptical. The planets have orbits that are nearly circular; comets have orbits that are highly elongated with & nearer to 1. It is of obvious interest to determine whether a comet’s or an asteroid’s orbit will intersect that of a planet. For each of the following two cases, use MuPAD to determine whether orbits A and B intersect. If they do, determine the polar coordinates of the intersection point. The units of distance are AU, where 1 AU is the mean distance of the Earth from the sun.
a. Orbit A: p = 1, ∈ = 0.01. Orbit B: p = 0.1, ∈ = 0.9.
b. Orbit A: p = 1, ∈ = 0.01. Orbit B: p = 1.1, ∈ = 0.5.
