Wonders of the Universe

WHAT IS GRAVITY?

Mercury’s unpredictable orbit has caused real problems for scientists researching Newton’s theory of gravity within the Solar System.

NASA

When Newton first published his Law of Universal Gravitation in 1687 he transformed our understanding of the Universe. As we have seen, his simple mathematical formula is able to describe with unerring precision the motion of moons around planets, planets around the Sun, solar systems around galaxies, and galaxies around galaxies. Newton’s law is, however, only a model of gravity; it has nothing at all to say about how gravity actually is, and it certainly has nothing to say about a central mystery: why do all objects fall at the same rate in gravitational fields? This question can be posed in a different way by looking again at Newton’s famous equation:

This states that the gravitational force between two objects is proportional to the product of their masses – let’s say that m₁ is the mass of Earth and m₂ is the mass of a stone falling towards Earth. Now look at another of Newton’s equations: F = ma, which can be written with a bit of mathematical rearrangement as a = F/m. This is Newton’s Second Law of Motion, which describes how the stone accelerates if a force is applied to it. It says that the acceleration (a) of the stone is equal to the force you apply to it (F) divided by its mass (m). The reason why things fall at the same rate in a gravitational field, irrespective of their mass, is that the mass of the stone in these two equations (labelled m2 in the first equation and m in the second), are equal to each other. This means that when you work out the acceleration, the mass of the stone cancels out and you get an answer which only depends on the mass of Earth – the famous 9.81 m/s². We said this earlier in the chapter in words: if you double the mass of something falling towards Earth, the gravitational force on it doubles, but so does the force needed to accelerate it. But there is a very important assumption here that has no justification at all, other than the fact that it works: why should these two masses be the same? Why should the so-called inertial mass – which appears in F = ma and tells you how difficult it is to accelerate something – have anything to do with the gravitational mass, which tells you how gravity acts on something? This is a very important question, and Newton had no answer to it.

Newton, then, provided a beautiful model for calculating how things move around under the action of the force of gravity, without actually saying what gravity is. He knew this, of course, and he famously said that gravity is the work of God. If a theory is able to account for every piece of observational evidence, however, it is very difficult to work out how replace it with a better one. This didn’t stop Albert Einstein, who thought very deeply about the equivalence of gravitational and inertial mass and the related equivalence between acceleration and the force of gravity. At the turn of the twentieth century, following his great success with the Special Theory of Relativity in 1905 (which included his famous equation E=mc²), Einstein began to search for a new theory of gravitation that might offer a deeper explanation for these profoundly interesting assumptions.

Although not specifically motivated by it, Einstein would certainly have known that there were problems with Newton’s theory, beyond the philosophical. The most unsettling of these was the distinctly problematic behaviour of a ball of rock that was located over 77 million kilometres (48 million miles) from Earth.

The planet Mercury has been a source of fascination for thousands of years. It is the nearest planet to the Sun and is tortured by the most extreme temperature variations in the Solar System. Due to its proximity to our star, Mercury is a difficult planet to observe from Earth, but occasionally the planets align such that Mercury passes directly across the face of the Sun as seen from Earth. These transits of Mercury are one of the great astronomical spectacles, occurring only 13 or 14 times every century. Mercury has the most eccentric orbit of any planet in the Solar System. At its closest, Mercury passes just 46 million kilometres (28 million miles) from the Sun; at its most distant it is over 69 million kilometres (42 million miles) away. This highly elliptical orbit means that the speed of the movement of this planet varies a lot during its orbit, which means in turn that very high-precision measurements were necessary to map its orbit and make predictions of its future transits. Throughout the seventeenth and eighteenth centuries, scientists would gather across the globe to watch the rare transits of Mercury. These scientists used Newton’s Law of Gravity to predict exactly when and where they could view the spectacle, but it became a source of scientific fascination and no little embarrassment when, time after time, Mercury didn’t appear on cue. The planet regularly crossed the Sun’s disc later than expected, sometimes by as much as several hours.

Mercury’s unusual orbit was a real problem, but because of the observational uncertainties it wasn’t until 1859 that the French astronomer Urbain Le Verrier proved that the details of Mercury’s orbit could not be completely explained by Newtonian gravity. To solve the problem, many astronomers reasoned there must be another planet orbiting between the Sun and Mercury. This planet had to be invisible to our telescopes, but it must also exert a gravitational force large enough to disturb Mercury’s orbit. Encouraged by the recent discovery of the planet Neptune, based on a similar anomaly in the orbit of Uranus, they named the ghost planet Vulcan

For decades astronomers searched and searched for Vulcan, but they never found it. The reason for this is that Vulcan doesn’t exist. The errors in the predictions in fact signalled something far more profound: Newton’s Theory of Universal Gravitation is not correct.

This image shows an artist’s impression of the hypothetical planet Vulcan, which was once believed to orbit in an asteroid belt closer to the Sun than Mercury. Vulcan was supposedly first sighted by amateur astronomer Lescarbault on 26 March 1859, but further observations were inconclusive and Vulcan was later proved to be a ghost planet.

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