What is gravity?

Newton's law of gravity is one of the most important scientific advances ever. But it is misunderstood by many. For example, I've seen social media posts asking, "If the Earth's gravity is strong enough to hold down massive oceans, then why isn't it strong enough to hold down a butterfly, which flies upward with little effort?" Here is Newton's answer.

It takes two to tango

One misunderstanding is revealed in the first four words of the question: "If the Earth's gravity..." Gravity is misunderstood as a force created unilaterally by a planet. Newton tells us instead that it's a mutual attraction between any two masses. If the butterfly weighs 0.001 pounds, this means both that the Earth exerts a 0.001-pound force on the butterfly and that the butterfly exerts an equal force in the opposite direction on the Earth.

Forces on the butterfly and on the Earth

Both masses have equal say

The strength of this attraction is determined by the product of the two masses involved. To calculate the force in this example, we start by multiplying the mass of the Earth by the mass of the butterfly. Double either mass, and you double the attractive force. That means that if we could increase the mass of the butterfly to match the mass of the oceans, the butterfly would be as strongly attracted to the Earth as are the oceans. The butterfly ascends with ease because of its small mass, not in spite of it.

The distance has a say

The strength of gravitational attraction falls off as the objects get farther apart. More precisely, the second step in calculating the force is to divide the mass product by the square of their separation. Triple the separation between two objects, and the force decreases by a factor of nine.

What's this G thing?

No, I didn't say G string. Shame on you. The final step in the calculation is to multiply by a number that gives us the right value of the force in the units we're using. That factor is called G, but Newton didn't know its value. So how might we measure it?

Crude gravimeter

Imagine two massive balls suspended by wires side by side and brought close together. Their mutual gravitational attraction will cause them to move closer to one another so that they don't hang straight down.

Primitive gravimeter using two balls suspended side by side

Knowing the weights of the balls and measuring the tilt angles of the wires, one can calculate the force of attraction. We know the masses and we can measure their separation. That enables us to get a value for G by doing the above calculation in reverse, getting the value of G from the gravitational force rather than the other way around.

This is how G is measured in principle. In practice this method is too crude. If the balls have any electrical charge on them, this will create a strong force. The balls might be gravitationally attracted differently to other things in the room. Air currents and temperature changes could also disturb the measurement. And for ordinary size objects, the tilt angle would be extremely small and difficult to measure.

Cavendish experiment

Henry Cavendish (1731-1810) was a British chemist and physicist known for his extraordinary experimental skills. In 1798 he used a torsion balance to measure G. Here is a simplified picture of his apparatus:

Simplified picture of Cavendish experiment

A pair of small masses (the red balls labelled m) are at the ends of a dumbbell suspended from a torsion wire, which resists being twisted in the same way that a spring resists being stretched or compressed. A pair of large masses (the gray balls labelled M) are placed as shown to attract the small masses, twisting the dumbbell clockwise until the stiffness of the torsion wire counteracts the attractive force. The large masses are then moved around to the opposite sides of the small ones, causing the dumbbell to twist counterclockwise. G is then deduced by measuring how much the twist angle changes when the large balls are moved.

This experiment was very cleverly designed and carefully done. Cavendish could move the large balls from ouside the room using a pulley system, so that nothing else in the room was being changed. He enclosed the apparatus in a dark chamber and measured the twist by looking through a window using a telescope. While he does not explicitly say this in his paper, certain details, such as the use of silver wires in the structure suspending the dumbells, suggest that the balls were well grounded to prevent the buildup of electrical charge. He repeated the experiment 17 times, changing things to make sure that he was not being fooled by magnetic effects or thermal air currents. His measurement of G stood for a century as the most accurate and is within 1% of the modern accepted value.

Schools do this now!

The Cavendish experiment has been replicated in science labs and in classrooms. A number of companies sell Cavendish torsion balances. PASCO's apparatus, for example, has a very detailed manual walking the user through the process of setting it up, properly balancing it, and grounding and shielding it to eliminate electrostatic forces and other disturbances.

Gravity measurement is still a subject of research

Newton's theory of gravity has been superseded by Einstein's theory, known as General Relativity. Scientists have both improved the Cavendish method and come up with new techniques. To find out more, I recommend this article on gravity measurement in the Proceedings of the National Academy of Sciences.