To answer part c of the question, we need to find the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations.
To approach this problem, let's first understand the geometry of the situation.
1. In part a, we established that Earth lies on a straight line between Mars and the Sun after completing one orbit.
2. In part b, we determined that the time between two closest approaches is the same as the time taken for Earth to complete one orbit.
Now, let's use this information to solve part c:
Step 1: Determine the angle traversed by Earth in one orbit.
- The angle traversed by Earth in one orbit is 2Ï€ radians (a complete circle).
Step 2: Determine the angle between the line drawn through the Sun, Earth, and Mars in the closest approach situations.
- Since Earth completes one orbit in the time of closest approach, the angle between the Earth-Sun line and the Mars-Sun line will be the same angle as the angle traversed by Earth in one orbit (2Ï€ radians).
So, the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations is 2Ï€ radians.
Therefore, the answer to part c is 2Ï€ radians.