Physics · Ch 8 — Gravitation
Introduction
Introduction
The Universal Pull: From Falling Apples to Planetary Motion
Long before we ever study physics, we know the pull of the Earth. A ball thrown up always comes down. Walking uphill is harder than walking downhill. Rain falls from clouds, not up into the sky. These everyday experiences point to a fundamental truth: all material objects are attracted towards the Earth.
The first great leap in understanding this attraction came from Galileo Galilei (1564–1642). He recognised a profound fact: all bodies, regardless of their mass, are accelerated towards the Earth with the same constant acceleration. This was a radical idea. A heavy iron ball and a light wooden ball, dropped from the same height, were thought to fall at different speeds. Galileo, through his famous (and likely real) experiments with balls rolling down inclined planes, demonstrated otherwise. By slowing down the motion with an incline, he could measure the acceleration accurately. His value for this acceleration due to gravity was remarkably close to the modern value of .
Galileo’s inclined plane experiments were a masterclass in scientific method. By diluting gravity’s effect, he made the motion slow enough to measure with water clocks and his own pulse. This is the first time a terrestrial phenomenon (falling bodies) was linked to a universal law.
The Dance of the Planets: A Historical Puzzle
While Galileo studied objects on Earth, astronomers were obsessed with the motion of objects in the sky. For millennia, the stars appeared fixed in their patterns, but a handful of “wanderers” — the planets — moved against this fixed background in a regular, predictable way.
The first successful model to explain this was the geocentric model, proposed by the Greek astronomer Ptolemy about 2000 years ago. In this view, the Earth was the centre of the universe. The Sun, the Moon, the stars, and all the planets revolved around it in perfect circles. To explain the occasional backwards (retrograde) motion of planets like Mars, Ptolemy had to invent a complicated system of circles upon circles — epicycles — where a planet moved in a small circle whose centre itself moved in a larger circle around the Earth.
Similar geocentric ideas were also developed by Indian astronomers a few centuries later. However, a much simpler and more elegant idea had already been mentioned by the great Indian mathematician and astronomer Aryabhatta (5th century AD). In his treatise, he suggested a heliocentric model — a model where the Sun, not the Earth, was the centre around which the planets revolved.
This idea lay dormant for a thousand years until it was revived by a Polish monk named Nicolaus Copernicus (1473–1543). Copernicus’s heliocentric model was a revolutionary step. It placed the Sun at the centre and described the planets, including Earth, as moving in circular orbits around it. This single change dramatically simplified the explanation of planetary motion, eliminating the need for complex epicycles. The idea was not universally welcomed — the Church of the time rejected Copernicus’s model, and among the astronomers who publicly defended it was Galileo, who was made to stand trial by the state for holding this belief.
The shift from a geocentric to a heliocentric model was not just a change of perspective. It was a fundamental shift in humanity’s view of its place in the cosmos. It paved the way for Newton’s universal law of gravitation, which would finally unite the force that makes an apple fall with the force that holds the planets in their orbits.
From Careful Observation to Elegant Law: Tycho Brahe and Kepler
Around the time Galileo was defending the heliocentric idea, a Danish nobleman named Tycho Brahe (1546–1601) devoted his entire working life to a different task: watching the sky, night after night, and recording the positions of the planets with nothing more than his naked eye. The result was an extraordinarily precise and extensive body of data — the best that existed before the telescope.
Brahe himself never turned this data into a working model of the Solar System. That task fell to his assistant, Johannes Kepler (1571–1640). By painstakingly analysing Brahe’s observations, Kepler distilled three remarkably simple mathematical relationships that any planet’s orbit must obey — what we now call Kepler’s laws. These laws, covered next, were later the very foundation on which Newton built his universal law of gravitation.