There are five Lagrange points for the Earth-Sun system - unique balance points where the gravitational forces caused by the Sun and Earth equal the centrifugal force acting on a mass at that point. The Lagrange points are shown in the figure below. The L4 and L5 Lagrange points are outside the scope of this class, but the other three points represent stable orbits where the radial forces are balanced. Perhaps the most interesting way to think about Lagrange points is that they represent locations where satellites can be placed that remain fixed relative to the positions of Earth and the Sun. (a) Find the location of L₁ relative to the Sun as a fraction of the Earth's orbital radius RĘ. (b) Find the location of L2 relative to the Sun as a fraction of the Earth's orbital radius RE. L4 L3 60° 60° L5 L1 L2