I need only part c

Mars orbits the Sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi)
a) Suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days later, when the Earth has completed one orbit, what is the angle between the Earth-Sun line and the Mars-Sun line? (in rad)
b) The initial situation in part a) is a closest approach of Mars to the Earth. What is the time between 2 closest approaches? Assume constant orbital speeds and circular orbits for both Mars and Earth. (Hint: when angles are equal) (in days)
c) Another way of expressing the answer to part (b) is in terms of the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations. What is that angle? (in rad)

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 2π 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 (2π radians).

So, the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations is 2π radians.

Therefore, the answer to part c is 2π radians.