BACKGROUND INFORMATION : Ceres is an asteroid that is about 590 miles (950 km) in diameter on average – the largest in the asteroid belt.

BACKGROUND INFORMATION : Ceres is an asteroid that is about 590 miles (950 km) in diameter on average – the largest in the asteroid belt. Its mass compromises about a third of the mass of the entire asteroid belt.

Questions :

1. The perihelion of Ceres is 2.5577 A.U. and the aphelion is 2.9773 A.U. What is the length of the major axis of Ceres orbit.
2. How far apart are the two foci of the ellipse of Ceres’ orbit?
3. What is the eccentricity of Ceres orbit?
4. What is the average distance between Ceres and the Sun?
5. How many years does it take Ceres to orbit the Sun?

Please provide your work for all questions.

The following equations may need to be used – Eccentricity, universal gravitation, acceleration due to gravity, escape velocity, Kepler’s 3rd Law, Kepler’s 3rd Law with Newton’s Update, and Universal Gravitation and Circ Motion.