Wonders of the Universe - Brian Cox [76]
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