College Physics with MasteringPhysics 7th Edition by Jerry Wilson,Anthony Buffa,Bo Lou

Exercise 84

A newly discovered asteroid is being tracked by astronomers for possible crossing points with Earth's orbit. They have determined that its elliptical orbit brings it as close as 16.0 million km to the Sun and its farthest distance from the Sun is 317 million km. Ignore any gravitational affects from objects other than the Sun. Its speed at closest approach to the Sun is 126 km/s (a) How many times larger is the system's (asteroid plus Sun) gravitational potential energy (magnitude) when the asteroid is at its maximum distance, compared to its minimum distance (b) What is the system's total energy if the asteroid's mass is 3.35 × 10 13 kg (c) What is the asteroid's minimum speed (d) How long does it take to orbit the Sun Hint : You will need the Sun's mass. [Note: the R in Kepler's third law refers to the average distance from the Sun if the orbit is not circular, that is, ( R max + R min )/2]