I met a question when I try to solve a twin-planet problem in "Classical mechanics" by Goldstein 3rd edition. Chap3-17. As followings: One of the classic themes of 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 would be hidden by the Sun. However because of the elliptical nature of the orbit it would not always be completely hidden. Assume there is such a planet in the same Keplerian orbit as Earth in such a manner that it is in aphelion (furthest from the Sun) when Earth is in perihelion (closest to the Sun). Calculate to first order in eccentricity e the maximum angular separation of the twin and the Sun as viewed from Earth. Could such a twin be visible from Earth? Suppose the twin planet were in an elliptical orbit having the same size and shape as that of Earth, but rotated 180° from the orbit of Earth, so that Earth and the twin would be in perihelion at the same time. Repeat your calculation and compare the visibility in the two situations. Would you like to give some hint to solve this problem? I will be very appreciated for your great help.