Question

# imagine we've discovered a planet orbiting another star at an average distance of 1 au with an orbital period of 6 months. the planet has a moon that orbits the planet at the same distance as our moon, but it takes 2 months to complete an orbit. what can we infer about this planet?

Answer

We can infer that the planet has a mass of approximately 0.7 times the mass of Earth based on the calculated mass from the formula for period of the planet and moon.

- Q:What is the definition of 1 AU? A:1 AU, or astronomical unit, is the average distance between the Earth and the Sun, which is about 93 million miles or 149.6 million kilometers.
- Q:What is the formula for period, or time it takes to complete one orbit? A:The formula for period is T = 2π√(a^3/Gm), where T is the period, a is the semi-major axis, G is the gravitational constant, and m is the mass of the central body.
- Q:What can we calculate using the formula for period? A:We can use the formula for period to calculate the mass of the central body.
- Q:What is the formula for the period of a moon orbiting a planet? A:The formula for the period of a moon orbiting a planet is T = 2π√(a^3/GM), where T is the period, a is the semi-major axis, G is the gravitational constant, and M is the mass of the planet.
- Q:What can we calculate using the formula for the period of the moon? A:We can use the formula for the period of the moon to calculate the mass of the planet.