Two stars each of mass M form a binary star system such that both stars move in the same circular orbit of radius R. The universal gravitational constant is G. Required:
a. Use Newton's laws of motion and gravitation to find an expression for the speed v of either star in terms of R, G, and M.
b. Express the total energy E of the binary star system in terms of R, G, and M. Suppose, instead, one of the stars had a mass 2M.
c. Find the ratio of the speeds, v2M/vM.

The bubba chump shrimp company processes and packages shrimp for sale to wholesale seafood distributors. the shrimp are transported to the main plant by trucks that carry 1,000 pounds (lb) of shrimp. once the continuous flow processing of the shrimp begins, no inventory is allowed in buffers due to spoilage and all of the shrimp must be processed within 12 hours to prevent spoilage. the processing begins at the sorter, where the trucks dump the shrimp onto a conveyor belt that feeds into the sorter, which can sort up to 500 lb per hour. the shrimp then proceed to the desheller, which can process shrimp at the rate of 400 lb per hour. however, after 3 hours and 45 minutes of processing, the desheller must be stopped for 15 minutes to clean out empty shrimp shells that have accumulated. the veins of the shrimp are then removed in the deveining area at a maximum rate of 360 lb per hour. the shrimp proceed to the washing area, where they are processed at 750 lb per hour. finally, the shrimp are packaged and frozen. what is the daily process capacity of the processing plant (excluding the packaging and freezing)?