Four planets of equal mass m are rotating with speed v in a circular orbit of radius R. The four planets at any instant are at the four corners of a square circumscribed by a circle of radius R as shown below. You can leave your answers in terms of radicals (i.e square roots), otherwise, you must simplify your results. V m V R m V m V (a) What is the magnitude and direction of the net gravitational force on the mass at point A as shown in the diagram? Your answer should be in terms of m, G and R. [To do this calculation you should work out the length d between two neighbouring planets in terms of R.]

Four planets of equal mass m are rotating with speed v in a circular orbit of radius R. The four planets at any instant are at the four corners of a square circumscribed by a circle of radius R as shown below. You can leave your answers in terms of radicals (i.e square roots), otherwise, you must simplify your results. V m V R m V m V (a) What is the magnitude and direction of the net gravitational force on the mass at point A as shown in the diagram? Your answer should be in terms of m, G and R. [To do this calculation you should work out the length d between two neighbouring planets in terms of R.]