On May 1, the opposition of Mars came. At some point on the Earth, at the moment of opposition, the Sun and Mars simultaneously rose above the horizon. Find the latitude of a given point and determine which sides of the horizon the Sun and Mars were located. The inclination of the Mars orbit plane to the ecliptic and refraction should be neglected.
It would seem that there is a contradiction in the condition of the problem: Mars entered into opposition with the Sun, being at this time on the ecliptic, that is, exactly in the opposite point of the sky to the Sun. Wherever we are, the sunrise in the eastern semicircle of the horizon should occur simultaneously with the setting of Mars in the western sky. However, this contradiction can be avoided if we move to some point in polar latitudes, where the Sun and Mars will be located in the points of the north and south, their daily movement will be directed along the horizon, and the Sun and Mars will cross it due to their movement along the sky relative to the stars.
Let’s remember that during opposition, Mars moves backward among the stars, towards the movement of the Sun. On May 1, the Sun has a declination of about + 15 °, and it continues to increase. Mars, at the opposite point of the sky, has a declination of -15 °, but it also increases. Therefore, if we find ourselves at a latitude of + 75 ° at solar midnight, we, to our surprise, will see the Sun rising in the north and Mars rising in the south.