Only need help with 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 find the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations, we need to use the concept of angular velocity.

Let's start with part b to find the time between two closest approaches.

b) In the closest approach situation, Earth lies on a straight line between Mars and the Sun. This means that both Earth and Mars are in line with the Sun.

Since both Mars and Earth have circular orbits, they have a constant orbital speed. Therefore, the time it takes for Earth to complete one orbit is equal to the time it takes for Mars to complete one orbit.

The time it takes for Earth to complete one orbit is given as 365.26 days. Therefore, the time between two closest approaches is also equal to one Earth orbit, which is 365.26 days.

Now, let's move to part c to find the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations.

c) We know that the time between two closest approaches is equal to one Earth orbit, which is 365.26 days. Since both Earth and Mars have circular orbits with constant orbital speeds, they cover equal angles in equal periods of time.

So, to find the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations, we need to find the angle covered by Mars in the time it takes for Earth to complete one orbit.

The angle covered by Mars in 365.26 days can be found using the formula:
angle = (2pi * time) / period

In this case, the time is 365.26 days and the period is 687 days (the orbital period of Mars).

angle = (2pi * 365.26) / 687

Simplifying this expression gives us the angle between the line drawn through the Sun, Earth, and Mars in the two closest approach situations.

Therefore, to calculate the exact value of the angle in radians, you can use the above formula to substitute the values and solve the expression.