Kepler's third law links a planet's period to which quantity?
Jupiter has dozens of moons, each circling at its own distance. Mission planners can put their orbital periods in order without a single calculation.
This lesson turns Kepler's third law into a ranking routine: farther out, longer period.
Kepler's third law: the square of the period is proportional to the cube of the average orbital radius. Squares and cubes both grow steadily, so the link never reverses: a larger radius always means a longer period.
The routine has two steps. Step 1: read off each body's orbital radius. Step 2: put the bodies in order of radius. That order is also the order of their periods.
The table lists three moons of Uranus and their orbital radii. Rank them by period, shortest first.
Write down the values in the question:
Miranda 130,000 km; Ariel 191,000 km; Titania 436,000 km
Write down the rule:
a larger radius always means a longer period
Put the radii in order, smallest first:
Miranda, Ariel, Titania
Shortest period first: Miranda, then Ariel, then Titania.
The real periods agree: about 1.4 days for Miranda, 2.5 days for Ariel, and 8.7 days for Titania.
The table lists three moons of Jupiter and their orbital radii. Which has the longest period?
Three satellites orbit Earth at the listed distances from Earth's center. Which has the shortest period?
The routine needs the same central body for every entry: moons of one planet, or planets of one star.
Equal radii mean equal periods: the law leaves no room for a difference.
The table lists three planets and their average distances from the Sun. Rank them by period, shortest first.
The table lists three moons of Saturn and their orbital radii. Rank them by period, shortest first.
Three moons of one planet have periods of 2 days, 8 days, and 30 days. Which orbits closest to the planet?
Two satellites circle Earth at the same orbital radius. How do their periods compare?