Imagine two planets orbiting a star with orbits edge-on to the earth. the peak doppler shift for each is 50 m/s, but one has a period of 10 days and the other has a period of 250 days. calculate the two minimum masses in units of kg and say which, if either, is larger. how do the two masses compare to the mass of the earth?

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.