Kepler’s Laws
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flagWhat you'll discover
- arrow_forwardState Kepler’s three laws in plain language
- arrow_forwardLocate the Sun at one focus of an elliptical orbit
- arrow_forwardSee equal areas swept in equal times as speed changes
- arrow_forwardConnect orbit size to orbital period (third law)
Law 1: Orbits are ellipses
Johannes Kepler, studying Tycho Brahe’s precise measurements of Mars in the early 1600s, discovered that planets do not move in perfect circles. Every orbit is an ellipse — a stretched circle — with the Sun sitting at one focus, off to the side of the centre.
The eccentricity slider controls the stretch: e = 0 is a perfect circle, and higher values make longer, thinner ellipses. Earth’s orbit has e = 0.017 (nearly circular); comets can exceed 0.9.
Law 2: Equal areas in equal times
A planet does not travel at constant speed. It moves fastest at perihelion (closest to the Sun) and slowest at aphelion (farthest away).
Kepler found the exact rule: the line from the Sun to the planet sweeps out equal areas in equal times. Near the Sun the line is short, so it must sweep a wide, fast arc; far away the line is long and a slow crawl covers the same area. Switch on "show swept area" and compare the shaded slices — different shapes, identical areas.
Law 3: Bigger orbits, much longer years
Kepler’s third law links size and time: the square of the orbital period is proportional to the cube of the orbit’s average radius (T² ∝ a³).
In numbers: an orbit 4 times wider takes 8 times longer to complete. This is why Mercury (0.39 AU) laps the Sun in 88 days while Neptune (30 AU) needs 165 years. The law is so reliable that astronomers use it backwards — measuring a moon’s period to calculate the mass of its planet.
Why the laws work
Kepler described the patterns but never knew why they held. Seventy years later Newton showed that all three laws fall straight out of his law of gravitation: an inverse-square pull from a single body produces exactly elliptical orbits, conserves angular momentum (which is the equal-area law in disguise), and yields the T² ∝ a³ relationship.
The same mathematics guides Nepal’s communication satellites, the ISS and every interplanetary probe ever launched. Four-hundred-year-old laws, still steering spacecraft today.