Question

is the path shown below elliptical or not? use keplers laws to explain how you know.

Explanation:

Kepler's Second Law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. In the given diagram, if the path were elliptical (which is the shape of planetary orbits according to Kepler's First Law), the areas swept by the line - object Kappa and Sun should be equal for equal time intervals. But visually, the areas between \(K - \text{Sun}\), \(L - \text{Sun}\), \(M - \text{Sun}\), and \(N - \text{Sun}\) do not appear to be equal.

Answer:

The path is not elliptical. According to Kepler's Second Law, a line segment joining a planet (or an object in orbit) and the Sun should sweep out equal areas in equal time intervals. The areas formed by the segments \(K - \text{Sun}\), \(L - \text{Sun}\), \(M - \text{Sun}\), and \(N - \text{Sun}\) in the given diagram are not equal, so the path does not follow Kepler's Second Law for an elliptical orbit.