4.A satellite is placed into a circular orbit around the planet Jupiter, which has a mass M = 1.90 x 1027 kg. (a) If the radius of the orbit is R (measured from the center of Jupiter), use Newton's laws to derive an
expression for the orbital velocity.
(b) If the satellite increases its orbital radius, how it would change the orbital velocity? Explain.
(c) If the radius of the orbit is R, derive an expression for the orbital period.
(d) The satellite rotation is synchronized with Jupiter's rotation. This requires an equatorial orbit whose
period equals Jupiter's rotation period of 9 hr 51 min = 3.55 x 104 s. Find the required orbital radius.