Kepler's Laws
Elliptical orbit with Sun at focus — equal-area sweep demonstrated live.
Key Notes
Kepler's three laws (1609, 1619) describe planetary motion — empirical, derived from Tycho Brahe's data; later explained by Newton's gravity.
1st law (LAW OF ORBITS): each planet moves in an ELLIPSE with the Sun at one FOCUS.
2nd law (LAW OF AREAS): the line joining planet to Sun sweeps out equal AREAS in equal times. Consequence of conservation of angular momentum (no torque from a central force).
3rd law (LAW OF PERIODS): square of orbital period ∝ cube of semi-major axis. T² = (4π²/GM)·a³.
Applies to any small body orbiting a much larger one (planets/Sun, moons/planet, satellites/Earth).
2nd law implies planets move FASTER at PERIHELION (closest to Sun) and SLOWER at APHELION.
Newton showed Kepler's laws follow from the inverse-square attractive force.
Bonus: Kepler's 3rd law lets us measure the mass of the central body if T and a are known.
Formulas
First law
Ellipse with semi-major axis a, eccentricity e; Sun at one focus.
Second law
Areal velocity is constant ⇒ angular momentum is conserved.
Third law
Universal — same constant for all planets/satellites orbiting same M.
Solar-system Kepler form
Choosing units of Earth-year and AU absorbs the constant; convenient.
Important Points
Kepler's laws are CONSEQUENCES of Newton's universal gravitation — they were initially empirical.
Equal areas in equal times = conservation of angular momentum — the most physically deep of Kepler's three laws.
Earth's orbit is nearly circular (e ≈ 0.017). Mercury is the most eccentric major planet (e ≈ 0.21).
Comets are extreme: Halley's e ≈ 0.967, period ~ 76 years.
Using T² = a³ in AU and years makes calculations simple: Mars T = 1.88 yr ⇒ a = 1.88^(2/3) ≈ 1.52 AU. ✓
Kepler's laws strictly apply to TWO-body problem. Real planets perturb each other (slight deviations).
Kepler's Laws notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.