Question

A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55 earth years to complete one orbit around the star. Vega's mass is 2.1 times the sun's mass. What is the radius of the planet's orbit? Give your answer as a multiple of the radius of the earth's orbit.

Answer 1

To find the radius of the planet's orbit around the star, you can use Newton's version of Kepler's third law. The radius of the planet's orbit is approximately 1.60 times the radius of the Earth's orbit.

Step-by-step explanation:

To find the radius of the planet's orbit around the star, we can use Newton's version of Kepler's third law:

T2/R3 = 4π2/GM

Where T is the period of the planet (55 years), R is the radius of the orbit, G is the gravitational constant, and M is the mass of the star (2.1 times the mass of the Sun).

Rearranging the equation, we have:

R = (T2/GM)1/3

Plugging in the values, we get:

R = (552/[6.67 × 10-11 × 2.1 × 1.99 × 1030])1/3

R ≈ 2.38 × 1011 meters

Since the radius of the Earth's orbit is about 1.49 × 1011 meters, the radius of the planet's orbit is approximately 1.60 times the radius of the Earth's orbit.