Mercury has a mass MP = 3.18 x 1023 kg, an orbital period T = 88.0 days, and an orbital radius r = 5.79 x 10^10 m. Assume the orbit of Mercury around the Sun is approximately circular.
a) Find the angular speed of Mercury about the Sun.
b) What is the linear speed vt of Mercury?
c) Determine the centripetal acceleration aC of Mercury due to its orbit about the Sun?
d) Calculate the centripetal force FC acting on Mercury which causes its circular orbit about the Sun? Use Newton's Second Law.
e) Calculate the gravitational force acting on Mercury due to the Sun. Use Newton's Law of Universal Gravitation. How does your calculation compare to part d above?
f) Use the period T and radius r of Mercury's orbit to calculate the mass MS of the Sun. Use Kepler's Third Law. How does this compare to the mass of the Sun given in planetary data tables?
g) Find the total energy (potential and kinetic) of Mercury in its orbit about the Sun.