Neptune lies about thirty times farther from the Sun than Earth. Yet its year is not thirty Earth years: it is 165 Earth years.
This lesson states Kepler's third law: how a planet's period grows with its distance.
From the circular-motion topic: the time for one full orbit is called the period, T.
A moon takes 7 days to complete one full orbit. What are the 7 days called?
Kepler compared the planets' periods with their average distances from the Sun. He found a precise pattern.
In T² ∝ r³, T is the orbital period and r is the average orbital radius.
Because r is cubed while T is only squared, the period grows faster than the radius.
Double the radius, and T² grows eight times. So T grows by more than double: about 2.8 times.
That is why Neptune, thirty times farther out than Earth, takes not 30 years but 165 years.
Kepler's third law links a planet's period to which quantity?
Jupiter orbits about five times farther from the Sun than Earth. Is its year closer to 5 Earth years or to 12 Earth years?
The period grows faster than the radius, because r is cubed while T is only squared.
So Jupiter's year must be well beyond 5 Earth years.
Closer to 12. Jupiter's year is about 12 Earth years.
Farther out always means a longer period: no exceptions among bodies orbiting the same center.
The law compares bodies orbiting the same central body: planets around the Sun, or moons around one planet. Two moons of one planet follow it too: the moon at the larger radius has the longer period.
Viktor says a planet twice as far from the Sun as another takes more than twice as long to orbit. Is he correct?
Which statement is Kepler's third law?
Neptune orbits about 30 times farther out than Earth, yet takes 165 years rather than 30. Which statement explains the mismatch?
Two planets circle one star. The inner planet's period is 10 days. What is true of the outer planet's period?