You have discovered the planet Zoltron. It is 6.0 times farther from the Sun than Earth (6.0 AU). How long does it take this planet to go once around the Sun?

Answer 1

Using Kepler's 3rd law to find its period T.

 

T² / a³ = constant for all planets orbiting the sun

 

You know that for the earth,

 

T² / a³ = (1 year)² / (1 AU)³ = 1 year²/AU³

 

Then for Zoltron,

 

T² / (6.0 AU)³ = 1 year²/AU³

 

T = √[(6.0 AU)³ (1 year²/AU³)] = √216 = 14.7 years