Peek at the Gravitational Constant, But Not Too Close! You Might Change the Value

In the mid-18th century, surveyors Charles Mason and Jeremiah Dixon left Philadelphia and were tasked with demarcating the border between Maryland and Pennsylvania, creating the now-famous Mason-Dixon Line.

At around the same time, across the other side of the Atlantic Ocean in England, scientist Henry Cavendish was busy studying the gravitational effects that the Allegheny mountains would have on the surveyor’s tools. The British scientist was worried that the Allegheny’s particular gravitational attraction could throw off Mason and Dixon’s theodolite plumb-bob, rendering their measurements of local latitudes by as much as 100 meters or more.

Thankfully, word reached Mason and Dixon, and were in constant communication with both Cavendish and the Royal Society in Britain, with the surveyors updating scientists across the globe with their findings. Normally, survey work back in the 18th century required surveyors to measure from their starting point to their end point, and then back again. During this tedious but necessary process, it’s normal for surveyors to record random errors. These errors would be randomly spread out across the entire area they were surveying.

During the measurement of the Mason-Dixon line, however, the surveyors found these random errors to be not-so-random, with many of them occurring in and around the area of the Allegheny mountains, thus confirming Cavendish’s suspicions that the mountains did, indeed, have a profound effect on instruments.

This would lead Cavendish into researching and performing one of the first high-precision experiments in the history of physics and allowed future scientists to begin calculating an extremely important, albeit highly elusive, data point in physics: the Gravitational Constant.

The Gravitational Constant: How Constant is It?

The gravitational constant –referred to as ‘big G’ to differentiate it from ‘small g’, i.e. acceleration of gravity –has become an important aspect of physics, being used to calculate various theories such as Sir Isaac Newton’s law of Universal Gravitation and even Albert Einstein’s general theory of relativity.

But for such an important physical constant, the big G isn’t all that precise: with other physical constants, the margin for error can be calculated up to 12 digits. G, on the other hand, stops at 5 digits, which is roughly ‘only’ around 1,000 times more accurate than Cavendish’s original data set.

In any other physical constant, this would be disastrous because of its inaccuracy. Worse still, despite the name ‘gravitational constant’, G isn’t all that constant either: despite having a formula for calculating G, even modern attempts at measurements can yield slightly different results.

And here’s the kicker: scientists can’t really figure out why this is. Are there unknown physical attributes at play? Is there a heretofore unknown nature of reality that we aren’t aware of at the moment? Or have we yet to figure out a more precise and constant way of measurement?

The Gravitational Constant: Minimizing Uncertainty

Henry Cavendish’s original experiment back in 1798 involved using a torsion balance to measure gravitational pull. This torsion had a deceptively simple yet fairly accurate (for its time) set-up: two small lead balls were attached to the ends of a beam and then suspended horizontally via a thin wire. Near the lead balls, he placed large 158-kg lead spheres.

Over time, Cavendish noted that the smaller lead balls were, indeed, attracted to the heavy lead weights, and this effect was recorded via the twists in the wire. Cavendish also noted that, while the force of attraction between the lead weights was ‘excessively minute’, it was enough to create a deviance in their position, which means that any physics experiment involving measuring between two areas with significantly different densities (say, a path between a forest and a mountain) that doesn’t take this into account will yield wildly inaccurate results.

Decades later, scientists will build on the then-famous Cavendish Experiment to come up with a formula: 6.674×10−11 m3⋅kg−1⋅s−2, a value that’s surprisingly close to modern accepted values. In fact, modern experiments to measure G haven’t really deviated much from Cavendish’s torsion balance experiment. Sure, we use newer materials and can find more precise values (by like 1%), but the essence remains the same: measure the attraction between two objects of different densities while making sure that the objects are kept away from the gravitational interference of other objects.

As a fundamental force of the universe, gravity is pretty much present in pretty much everything. However, while the pull of gravity becomes weaker the smaller the object is, the pull is always going to be there. Unlike electromagnetism (another fundamental force of the universe), there is no way to protect, shield from, or minimize the pull of an object’s gravity. This is why the Cavendish experiment is so sensitive: the values of the experiment will change depending on how many people passed the experiment, and even the effects of tidal forces of the sun and moon during that time.

This is what makes measuring G extremely difficult. In fact, it was only in 2000, around 200 years since Cavendish’s original experiment, were scientists able to propose a value for G with an uncertainty of ‘only’ 0.0014%, roughly 1,000 times better than ol’ Cavendish. This might seem admirable but consider that other physical constants have, at minimum, 9 digits of zeroes after the decimal point.

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Photo by Antoine Dautry on Unsplash

The Gravitational Constant: But What is it Good For? Absolutely a Lot of Things

In essence, though, even if scientists were able to measure G so precisely that it matches the precision of other physical fundamental constants, it honestly wouldn’t matter: the level of precision will not change our basic understand of one of the fundamental forces of nature. To put it simply: we know that gravitational constant proves the existence of gravity in all objects, we just don’t know what the value of G is precisely.

However, the fact that it has been more than 200 years since scientists started trying to measure G and coming up short has led many to believe that there is a very real possibility that the discrepancies in determining the absolute value of gravitational constant is due to an exotic explanation. After all, we can measure the constants in the quantum realm, yet an everyday force such as gravity eludes us.

This means that the inaccuracy of G might actually be a good thing: scientists are coming up with varying theories as to why the value of G differs, ranging from the effects of time to the effects of extra dimensional distortions. That being said, there aren’t any theories compelling enough for scientists to abandon our current understanding of gravity. Despite the discrepancies, the variances, and the inaccuracy, the gravitational constant is, well, constant enough that it doesn’t disturb the primary workings of our universe.

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