Earth, planets and orbits
1609–1619
Kepler’s laws of planets
Johannes Kepler, using Tycho Brahe’s observations
What if the planets don’t move in perfect circles at all?
Kepler spent years trying to fit Mars to circles, and failed by 8 arcminutes, about a quarter of the Moon’s width. He trusted Tycho Brahe’s data over perfect circles and found that planets move in ellipses. Later he found a rule linking each planet’s year to its distance from the Sun.
First, make a guess
A planet four times further from the Sun than Earth. How long is its year?
- Fastest ÷ slowest speed
- 4.00×
- Closest ÷ furthest distance
- 0.25
Each shaded wedge takes the same time to sweep, so all wedges have equal area: the planet races near the Sun and dawdles far away. The chart uses measured years and distances of the eight planets.
How they figured it out
Kepler first tried to explain the planets with nested geometric solids, sure that God had used beautiful geometry. In 1600 he joined Tycho Brahe in Prague, and after Tycho’s death in 1601 inherited the most accurate observations ever made.
His best circle for Mars missed Tycho’s data by 8 arcminutes, about a quarter of the Moon’s width. Many would have blamed the data. Kepler wrote that those eight minutes alone pointed the way to a reform of all astronomy. After years of what he called his war on Mars, he found the ellipse. Nearly a decade later, on 15 May 1618 by his own note, he found the third law linking years and distances.
The equation
Square a planet’s year and it is proportional to the cube of its average distance from the Sun.
See it in real life
Why your satellite dish never moves
A TV satellite dish points at one fixed spot because the satellite orbits once a day, keeping pace with Earth’s spin. Kepler’s third law says only one orbit does that: about 36,000 km above the equator. Every geostationary satellite sits on that single ring.
Where engineers use it
Satellite orbits
Geostationary satellites sit where the orbit takes exactly one day: about 36,000 km up, straight from Kepler’s third law.
Finding planet masses
Timing a moon’s orbit gives the planet’s mass.
Worked example: Mars’s year
- Mars: AU.
- years.
- Measured: 687 days years.
Where it came from
- The Sun in the centre 1543
Led to
Kepler started as a Copernican and replaced its circles with ellipses.
What it led to
- Universal gravitation 1687
Led to
Newton showed that an inverse-square pull produces exactly Kepler’s ellipses and his third law.
- A planet around another sun 1995
Built on
51 Pegasi b obeys Kepler’s laws; its year and its star’s wobble give its orbit and mass.