According to legend, the first experiment to show that all objects fell at the same rate, irrespective of mass, was performed by Galileo Galilei atop the Leaning Tower of Pisa. Any two objects dropped in a gravitational field, in the absence of (or neglecting) air resistance, will accelerate down to the ground at the same rate. This was later codified as part of Newton’s investigations into the matter. (Getty Images)

Scientists Admit, Embarrassingly, We Don’t Know How Strong The Force Of Gravity Is

Every physical theory has constants in it. The gravitational constant is remarkably uncertain.

When we first began formulating physical laws, we did so empirically: through experiments. Drop a ball off a tower, like Galileo may have done, and you can measure both how far it falls and how long it takes to hit the ground. Release a pendulum, and you can find a relationship between the pendulum’s length and the amount of time it takes to oscillate. If you do this for a number of distances, lengths, and times, you’ll see a relationship emerge: the distance of a falling object is proportional to the time squared; the period of a pendulum is proportional to the square root of the pendulum’s length.

But to turn those proportionalities into an equal sign, you need to get that constant right.

The orbits of the planets in the inner solar system aren’t exactly circular, but they’re quite close, with Mercury and Mars having the biggest departures and the greatest ellipticities. In the mid-19th century, scientists began noticing departures in the motion of Mercury from the predictions of Newtonian gravity, a slight departure that was only explained by General Relativity in the 20th century. The same gravitational law, and constant, describes gravity’s effects on all scales, from Earth to the cosmos. (NASA / JPL)

In these examples, as well as many others, that constant-of-proportionality is related to G, the gravitational constant. The Moon orbits the Earth, the planets orbit the Sun, light bends due to gravitational lensing, and comets lose energy as they…