There are some people who believe that Earth has a twin that orbits directly opposite the sun with exactly the same orbital elements and in the saem direction and thus unseen from Earth. The two planets are exactly 180 degrees opposed when they occupy ecliptic longitudes of 90 degrees and 270 degrees. Show how this scenario is not possible by doing the following:
a. Determine the true anomalies for Earth 1 and Earth 2 when the difference in their orbital velocities is at maximum.
b. Find the greatest elongation of Earth 2, as seen from Earth 1 (the planet we live on), in degrees as measured from the center of the sun's disk.