Mathematics

### Question Description

The orbit of a comet around the sun is shaped like an ellipse in which the sun is at one focus. The two extremities of the major axis of a comet's orbit are called the comet's perihelion (closest distance to the sun) and aphelion (furthest distance from the sun). These distances from the sun are usually expressed in astronomical units (AU), where 1 AU is defined as the average distance between the sun and the earth, or about 93 million miles. The most famous comet in the solar system is Halley's comet, which has a perihelion of 0.59 AU and an aphelion of 35.09 AU. For the following problems, assume that the orbit of Halley's comet is centered at the origin, and the sun is located on the x-axis to the right of the origin. Give your answers to 2 decimal places.

I) What is the length of the major axis of the orbit of Halley's comet?

II) What are the coordinates of the sun?

III) Find an equation for the ellipse that describes the comet's orbit.

IV) Find the eccentricity of the orbit to two decimal places from your equation.