A space shuttle astronaut in a circular orbit around the Earth has an assembly consisting of two small dense spheres, each of mass in, whose centers are connected by a rigid rod of length ( and negligible mass. The astronaut also has a device that will launch a small lump of clay of mass mat speed vo, Express your answers in terms of m, v, 4, and fundamental constants.

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?