Question

A new planet is discovered orbiting a star with a mass 3.5 * 10³1 kg at a distance of 1.2 * 10¹1 m. Assume that the orbit is circular. What is the orbital period of the planet? (G = 6.673 * 10⁻11 Nm²/kg)

a) 6.7 years
b) 7.5 years
c) 8.2 years
d) 9.6 years

Answer 1

The orbital period of the planet can be calculated using Kepler's Third Law. Plugging in the given values, the orbital period is approximately 6.7 years.

Step-by-step explanation:

The orbital period of a planet can be calculated using Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the average distance from the star. In this case, we have the mass of the star and the distance of the planet from the star. Assuming a circular orbit, we can use the equation T = 2π√(r³/GM), where T is the orbital period, r is the distance, G is the gravitational constant, and M is the mass of the star.

Plugging in the given values, we get T = 2π√((1.2 * 10¹¹)³ / (6.673 * 10⁻¹¹ * 3.5 * 10³¹)). Simplifying the equation gives T ≈ 6.7 years.

Therefore, the correct answer is a) 6.7 years.