For this problem, you are allowed to consult with other members of the class, but not with faculty and not with anyone outside the course. Simplify all your expressions.

When placing satellites near the Earth for continuous observation of the sky, there are two points along the line from the Sun through the Earth that provide stable observation points. At each of these points the magnitude of the force of gravity from the Sun and from the Earth are equal.

a) Draw a free-body diagram for a satellite at the point between the Sun and Earth, and another for the point on the opposite of the Earth from the Sun. Clearly label which diagram is for each situation.

b) Using MSun and MEarth for the masses, show how to setup the equations symbolically to solve for the two distances from Earth at which the magnitude of the force of gravity is equal. Make it clear what each variable represents. You do not have to solve the equations symbolically.

c) Using that MSun = 1.989 X 1030 kg and MEarth = 5.972 x 1024 kg, the average distance from the Earth to the Sun is 1.496 x 1011 m, and G = 6.673 x 10-11 N·m2/kg2, find the two distances from Earth where the magnitudes of the forces of gravity are equal from each celestial body.

d) Find the names of two satellites or space telescopes that currently operate at the point that is more distant from the Sun. List the wavelengths of light they use for their observations. For example, a telescope that observes red light would record wavelengths between 620 nm and 700 nm.