Question

In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of Earth, which orbits the Sun (mSun = 1.99 × 10³⁰ kg) at a distance of 1.50 × 10¹¹ m, called 1 astronomical unit (1 AU). Others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows a circular orbit around its star. What is the mass of the star?

1) 1.99 × 10³⁰ kg
2) 1.50 × 10¹¹ m
3) 1 astronomical unit
4) Cannot be determined

Answer 1

To find the mass of the star, we can use Newton's version of Kepler's Third Law. The mass of the star can be calculated using the equation (0.71 Earth-years)^2 / (1 AU)^3 * mSun, where mSun is the mass of the Sun.

Step-by-step explanation:

In order to find the mass of the star, we can use Newton's version of Kepler's Third Law. This law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the star. Since the planet in question has an orbital period of 0.71 Earth-years and an average distance of 1 AU, we can set up the following proportion:

(0.71 Earth-years)^2 / (1 AU)^3 = (orbital period)^2 / (average distance)^3

Simplifying this equation, we can solve for the mass of the star:

Mass of the star = (0.71 Earth-years)^2 / (1 AU)^3 * mSun

Where mSun is the mass of the Sun, which is given as 1.99 × 10^30 kg.