Season 17, Episode 17: How Did We Find the Mass of the Earth?

Hey StarTalkians! Episode 17 of season 17 saw Neil and Chuck sitting down with Gary O’Reilly to go through some “burning questions” from StarTalk staff. The very first question came from Gary himself:

Our Burning Questions – Simulation Debate - StarTalk Special Edition

(Starts at 2:10)

Neil answered Gary’s literal question, but nobody really addressed what he probably meant: how do we know the mass of the Earth?

The Difference Between Weight and Mass

Neil’s answer hinged on one fact: there is a difference between weight and mass.

• Your weight is the force of the Earth’s gravity acting on your mass, measured in Newtons.

• Your mass is the actual amount of matter in your body, measured in kilograms.

Often, non-specialists say “weight” when they really mean mass, as Gary surely did here.

The Real Question: How to Find the Mass of the Earth

Let’s rephrase Gary’s question: How massive is planet Earth?

Long-time StarTalkians will guess that Newton’s theory of gravity is needed to answer this question. It tells us the gravitational force, given each mass and their distance apart. This is all scaled according to a constant, called the gravitational constant.

If we have a “test” object with a known mass, we can easily measure the force of the Earth’s gravity on it. In fact, the only remaining piece of the puzzle is the size of that constant.

The Cavendish Experiment Explained

Henry Cavendish’s 1798 experiment is regarded as the first measurement of the mass of the Earth via the gravitational constant.

He used a purpose-built balance apparatus (see below). A 1.8 m wooden rod was suspended from a wire, with two lead spheres attached to either end. Like this, even the tiniest force could make the rod rotate. Cavendish placed two huge lead balls nearby to generate a gravitational force.

The gravitational force attracts the spheres, but then the tension in the now-twisted wire pulls them back. As these two forces balance, it’s possible to deduce the force due to gravity. 

After some painstaking experimental work, Cavendish isolated the gravitational effect using his apparatus. 

This gave him what we would now call an estimate of Newton’s gravitational constant. While he technically calculated the density of Earth, his estimate was only off by about 1%.