Lesson 1 of 11 · 6 min

Kepler's laws

NCERT §7.1, §7.2

Kavya sets up her small telescope on the terrace and follows Mars for a few weeks. It drifts slowly against the stars, and one week it even seems to back up. The ancient astronomers had to explain loops like this without knowing what really moves round what.

The story this chapter follows: Kavya on her terrace with a small telescope

Kavya, who weighs 50 kg, watches the sky from her terrace with a small telescope. Mars drifting against the stars, the Moon rising over a falling guava, her weight on other worlds and down a mine, a ball fired up at 5 km/s and the space station gliding past at 400 km carry the chapter, with the same numbers throughout.

The lesson in notes

In short

Ptolemy's geocentric model put the earth at the centre with planets moving on circles riding on bigger circles. Aryabhatta (5th century A.D.) had already mentioned a sun-centred model, and Copernicus (1473–1543) proposed planets on circles around a fixed sun.

Tycho Brahe (1546–1601) recorded planetary positions with the naked eye for his whole life; his assistant Johannes Kepler (1571–1640) found three laws hidden in those records.

Law of orbits: every planet moves on an ellipse, and the sun sits at one focus of that ellipse. The circle is the special case where the two foci coincide.

An ellipse is drawn with a string pinned at two foci F₁ and F₂: for every point on the curve, the distances to F₁ and F₂ add up to the same total.

The line through the foci meets the ellipse at P (perihelion, nearest to the sun) and A (aphelion, farthest). Half of PA is the semi-major axis a.

Law of periods: T² ∝ a³, where T is the time for one revolution. The ratio T²/a³ comes out almost the same (about 3 × 10⁻³⁴ y² m⁻³) for all eight planets from Mercury to Neptune.

Most planetary orbits are very nearly circles; for the earth the ratio of semi-minor to semi-major axis is 0.99986.

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Kepler's laws

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