The planet Mars has two moons. Phobos and Delmos (i) phobos has period `7` hours, `39` minutes and an orbital radius of `9.4 xx 10^(3) km`. Calculate the mass of Mars. (ii) Assume that Earth and mars move in a circular orbit around the sun, with the martian orbit being `1.52` times the orbital radius of the Earth. What is the length of the martian year in days? `(G = 6.67 xx 10^(-11) Nm^(2) kg^(-2))`

Explanation

To solve the problem, we will break it down into two parts as indicated in the question.

### Part (i): Calculate the mass of Mars

1. **Convert the orbital period of Phobos into seconds**:
- Phobos has a period of 7 hours and 39 minutes.
- Convert hours to minutes: \( 7 \text{ hours} = 7 \times 60 = 420 \text{ minutes} \).
- Total time in minutes: \( 420 + 39 = 459 \text{ minutes} \).
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