// physics › Orbits
Explore Kepler's three laws of planetary motion; the third law solves for orbital period, distance or central mass.
T² = 4π²a³ / (G M)
A mind behind this: Johannes Kepler 1571–1630
First: planets travel in slightly squashed circles (ellipses) with the Sun off to one side. Second: a planet speeds up when it is near the Sun and slows down when far away. Third: planets farther from the Sun take much longer to go around — and there is an exact formula linking the two.
T is how long one orbit takes, a is the size of the orbit (its semi-major axis), M is the mass of the thing being orbited (like the Sun), and G is a fixed constant of nature. Square the period and it is proportional to the cube of the distance — so going twice as far out makes the year far more than twice as long.
Take Earth: its orbit is about 1.496 × 10¹¹ metres across and the Sun's mass is about 1.989 × 10³⁰ kg. Put those into the third law and you get a period of about 31.5 million seconds — which is one year. The formula really works.
Because of the second law: the line from the Sun to the planet always sweeps the same area in the same time. Near the Sun that line is short, so the planet has to move quickly to sweep the same area; far away the line is long, so it can move slowly.
Astronomers use the third law to weigh the universe — if you watch how long something takes to orbit and how far out it is, you can work out the mass of the star or planet it goes around. It even helps find planets around other stars.
Johannes Kepler was a German astronomer in the early 1600s. Using very careful measurements, he replaced the old idea that orbits must be perfect circles with these three laws — work that later let Newton explain gravity itself.