Science Puzzle
How Long Would a Year Be Twice as Far from the Sun?
Earth goes round the Sun once a year, at an average distance of about 150 million kilometres. Imagine a planet twice as far out, at 300 million kilometres, travelling in a circle twice as big.
How long would that planet's year be?
The Answer
About 2.8 years. Twice as far from the Sun, the year is a bit less than three times as long.
Two things change at once. The path round the Sun is twice as long, which on its own would make the year twice as long. But the planet also travels more slowly. Twice as far away, the Sun's pull is only a quarter as strong, and a weaker pull can only hold a planet in its circle if it moves more slowly. Work it through and the planet travels at only about 70 per cent of Earth's speed. Twice as far to go at 70 per cent of the speed takes 2 ÷ 0.71, about 2.8 times as long.
Johannes Kepler found the rule in 1619, from years of careful planet-watching by Tycho Brahe: the square of a planet's year is in proportion to the cube of its distance from the Sun. Two cubed is 8, and the square root of 8 is about 2.83. Mars, about 1.5 times as far out as Earth, takes 1.9 years to go round. Jupiter, 5.2 times as far, takes almost 12. Kepler didn't know why the rule worked; Newton's law of gravity explained it nearly 70 years later.
The principle: Kepler's third law. The square of a planet's year is proportional to the cube of its distance from the Sun, because a planet further out has further to go and moves more slowly.