One classic theme in science fiction is a twin planet ("Planet X") to Earth that is identical in mass, energy, and momentum but is located on the orbit 180∘ out of phase with Earth so that it is hidden from the Sun. However, because of the elliptical nature of the orbit, it is not always completely hidden. Assume this twin planet is in the same Keplerian orbit as Earth in such a manner that it is in aphelion when Earth is in perihelion. Calculate to first order in the eccentricity e the maximum angular separation of the twin and the Sun as viewed from the Earth. Could such a twin be visible from Earth? Suppose the twin planet is in an elliptical orbit having the same size and shape as that of Earth, but rotated 180∘ from Earth's orbit, so that Earth and the twin are in perihelion at the same time. Repeat your calculation and compare the visibility in the two situations.