Kepler’s Third Law of Orbital Motion states that you can approximate the period P (in Earth years) it takes a planet to complete one orbit of the sun using the function p=d^((3)/(2)), where d is the distance (in astronomical units, AU) from the planet to the sun. How many Earth years would it take for a planet that is 6.76 AU from the sun?

Question

Kepler’s Third Law of Orbital Motion states that you can approximate the period P (in Earth years) it takes a planet to complete one orbit of the sun using the function p=d^((3)/(2)), where d is the distance (in astronomical units, AU) from the planet to the sun. How many Earth years would it take for a planet that is 6.76 AU from the sun?

A. 15.23
B. 17.58
C. 154.46
D. 3.58

Answer 1

To find the number of Earth years it would take for a planet that is 6.76 AU from the sun, we can use the formula P=d^(3/2), where d is the distance in AU.

P = 6.76^(3/2)

Using a calculator, we find that 6.76^(3/2) is approximately 15.23.

Therefore, it would take approximately 15.23 Earth years for a planet that is 6.76 AU from the sun.

So the answer is A. 15.23.