Consider as a system the sun with venus in a circular orbit around it. find the magnitude of the change in the velocity of the sun relative to the center of mass of the system during the time venus completes half an orbit. assume the mass of the sun is 5.68 1029 kg, the mass of venus is 4.87 1024 kg, its period is 1.94 107 s, and the radius of its orbit is 1.08 1011 m. ignore the influence of other celestial objects.

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?