Question: A newly discovered asteroid is being tracked by astronomers for possible crossing points with Earths orbit. They have determined that its elliptical orbit brings it

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 x 1012 kg?
(c) What is the asteroid’s minimum speed?
(d) How long does it take to orbit the Sun?

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