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NCERT's Class 11 gravitation chapter says the constant G "can be determined experimentally and this was first done by English scientist Henry Cavendish in 1798." If you open Cavendish's own paper, you will not find G in it. He set out to find the density of the Earth. This post explains what he actually measured, how his number gives G, and why the experiment is still a model of careful work.
Who was Henry Cavendish?
Henry Cavendish (1731–1810), as his Oxford Dictionary of National Biography entry records his dates. His paper Experiments to determine the Density of the Earth was read to the Royal Society on 21 June 1798 and printed in its Philosophical Transactions.
Whose idea was the apparatus?
Cavendish credits it at once. In the paper's first paragraph, he writes that the late Rev. John Michell had contrived a method of finding the density of the Earth by making the attraction of small quantities of matter measurable, but died before he could make any experiments with it. The apparatus passed to Francis John Hyde Wollaston at Cambridge, who gave it to Cavendish.
The design is simple. A wooden arm 6 feet long hangs horizontally from a slender wire 40 inches long, with a lead ball about 2 inches across at each end. Large lead weights are brought close to the small balls. Their attraction twists the arm, and the wire resists the twist. Michell had planned to find the force needed to twist the wire by timing the arm's swings.
How did Cavendish make such a tiny force measurable?
The force between the balls is minute, so anything else that pushes the arm, such as air currents from uneven heating, could swamp it. Cavendish decided to place the apparatus in a room that stayed shut, watch the arm from outside through a telescope, and move the lead weights without entering the room.
The arm never sat still; it kept swinging. So he observed three successive extreme points of a swing and combined them to find where the arm would come to rest. He then compared the resting points with the weights on either side.
By a mean of the experiments with his first wire, Cavendish found the density of the Earth to be 5.48 times that of water, and the same value with a second wire.
Worked example: getting G from Cavendish's density
Treat the Earth as a uniform sphere of radius R and density ρ. Its mass is M = (4/3)πR³ρ, and the gravity at its surface is g = GM/R².
Substitute M: g = G × (4/3)πR³ρ / R² = (4/3)πGρR.
Rearrange: G = 3g / (4πρR).
Use g = 9.81 m/s², ρ = 5.48 × 1000 = 5480 kg/m³, and the Earth's mean radius R = 6.371 × 10⁶ m from the NASA Earth fact sheet.
Denominator: 4π × 5480 × 6.371 × 10⁶ ≈ 12.566 × 3.491 × 10¹⁰ ≈ 4.387 × 10¹¹.
G ≈ 29.43 ÷ (4.387 × 10¹¹) ≈ 6.71 × 10⁻¹¹ N m²/kg².
The current CODATA value from NIST is 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻², so the result is about 0.5% high. NASA gives the Earth's mean density as 5513 kg/m³; Cavendish's 5480 is within about 0.6% of it.
Worked example: weighing the Earth
Now go the other way. With G known, the mass of the Earth follows from g = GM/R².
M = gR² / G = 9.81 × (6.371 × 10⁶)² ÷ (6.674 × 10⁻¹¹) ≈ 9.81 × 4.059 × 10¹³ ÷ 6.674 × 10⁻¹¹ ≈ 5.97 × 10²⁴ kg.
The common mistakes here are squaring R in kilometres instead of metres, and using the formula g = GM/R² inside the Earth, where it does not apply. NCERT's chapter and the JEE (Main) 2026 syllabus both cover how g varies with altitude and depth. Our post on gravitation and satellite problems has more practice.
What can a student take from Cavendish's way of working?
Give credit precisely. His paper opens by naming Michell's idea and Wollaston's gift. Knowing exactly what is yours and what you built on is part of doing science honestly.
Remove what you cannot control. He did not fight the air currents; he shut the room and watched from outside. In a lab practical, find the biggest source of error and design it out.
Measure what you can, then calculate the rest. He could not weigh the Earth directly, so he measured a twist, a swing time and a few distances, and let the algebra do the rest. Many numericals work the same way.
The step from g = GM/R² to G = 3g/(4πρR) is where most students lose the thread. The Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer. For the planetary side of the story, read about how Kepler found his three laws.
Try it now: use NASA's density of 5513 kg/m³ and recompute G.
