During the period of evening visibility, the planet Venus entered a conjunction with Mars twice. Could Venus be at the point of greatest eastern elongation:
a) before the first conjunction with Mars?
b) between two conjunctions with Mars?
c) after the second conjunction with Mars?
During the period of evening visibility, from upper to lower conjunction, the angular velocity of motion of Venus among the stars gradually decreases. Until the moment of the greatest eastern elongation, it is greater than that of the Sun, after this moment it is less, and after passing the standing point, it changes sign, becoming negative. Mars, being near the Sun (in conjunction with Venus), moves only straight, and the angular velocity of its motion is always less than the angular velocity of the Sun.
It is obvious that two conjunctions of Venus with Mars can occur if in the first of these conjunctions Venus overtakes Mars in its motion among the stars, and in the second Mars overtakes Venus, which is slowing down or is already moving backward (enter into a second conjunction with Mars, overtaking it by a whole circle , Venus will not have time, as it will take her more than a year). But in this case, the second conjunction cannot occur until the moment of the greatest elongation, when Venus moves across the sky faster than Mars. Therefore, option c) in the problem statement is impossible. Options a) and b) are possible and often implemented.