Question

Using kepler's 3rd law, what is the period for a planet that is 48 AUs away from the star its orbiting? Don't include units.

Answer 1

To find the orbital period for a planet that is 48 AUs from the star it's orbiting using Kepler's third law, you would calculate P = 48³½, with P being the period in years and a being the average distance in AUs.

Step-by-step explanation:

Using Kepler's third law, which states that the orbital period (P) in years is proportional to the square root of the cube of the mean distance (a) in astronomical units (AU) from the star (P ≈ a³½), we can calculate the period for a planet that is 48 AUs away from the star it's orbiting. The law is often expressed as P² = a³, so P = a³½. Hence for a = 48 AU, P would be 48³½, which equals 48¹⅓ or approximately 48·⅓.

Let's calculate the exact value:

• a = 48 AU
• P = a³½
• P = 48¹⅓ ≈ 48·⅓ years

After calculating, we get the period P as the answer.