Born in 1643 in Woolsthorpe, England, Sir Isaac Newton began developing his influential theories on light, calculus and celestial mechanics while on break from Cambridge University. Years of research culminated with the 1687 publication of “Principia,” a landmark work that established the universal laws of motion and gravity. Newton’s second major book, “Opticks,” detailed his experiments to determine the properties of light. Also a student of Biblical history and alchemy, the famed scientist served as president of the Royal Society of London and master of England’s Royal Mint until his death in 1727.
Isaac Newton was born on January 4, 1643, in Woolsthorpe, Lincolnshire, England. The son of a farmer, who died three months before he was born, Newton spent most of his early years with his maternal grandmother after his mother remarried. His education interrupted by a failed attempt to turn him into a farmer, he attended the King’s School in Grantham before enrolling at the University of Cambridge’s Trinity College in 1661.
Newton studied a classical curriculum at Cambridge, but he became fascinated by the works of modern philosophers such as René Descartes, even devoting a set of notes to his outside readings he titled “Quaestiones Quaedam Philosophicae” (“Certain Philosophical Questions”). When the Great Plague shuttered Cambridge in 1665, Newton returned home and began formulating his theories on calculus, light and color, his farm the setting for the supposed falling apple that inspired his work on gravity.
Newton returned to Cambridge in 1667 and was elected a minor fellow. He constructed the first reflecting telescope in 1668, and the following year he received his Master of Arts degree and took over as Cambridge’s Lucasian Professor of Mathematics. Asked to give a demonstration of his telescope to the Royal Society of London in 1671, he was elected to the Royal Society the following year and published his notes on optics for his peers.
Through his experiments with refraction, Newton determined that white light was a composite of all the colors on the spectrum, and he asserted that light was composed of particles instead of waves. His methods drew sharp rebuke from established Society member Robert Hooke, who was unsparing again with Newton’s follow-up paper in 1675. Known for his temperamental defense of his work, Newton engaged in heated correspondence with Hooke before suffering a nervous breakdown and withdrawing from the public eye in 1678. In the following years, he returned to his earlier studies on the forces governing gravity and dabbled in alchemy.
In 1684, English astronomer Edmund Halley paid a visit to the secluded Newton. Upon learning that Newton had mathematically worked out the elliptical paths of celestial bodies, Halley urged him to organize his notes. The result was the 1687 publication of “Philosophiae Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy), which established the three laws of motion and the law of universal gravity. Principia propelled Newton to stardom in intellectual circles, eventually earning universal acclaim as one of the most important works of modern science.
With his newfound influence, Newton opposed the attempts of King James II to reinstitute Catholic teachings at English Universities, and was elected to represent Cambridge in Parliament in 1689. He moved to London permanently after being named warden of the Royal Mint in 1696, earning a promotion to master of the Mint three years later. Determined to prove his position wasn’t merely symbolic, Newton moved the pound sterling from the silver to the gold standard and sought to punish counterfeiters.
The death of Hooke in 1703 allowed Newton to take over as president of the Royal Society, and the following year he published his second major work, “Opticks.” Composed largely from his earlier notes on the subject, the book detailed Newton’s painstaking experiments with refraction and the color spectrum, closing with his ruminations on such matters as energy and electricity. In 1705, he was knighted by Queen Anne of England.
Around this time, the debate over Newton’s claims to originating the field of calculus exploded into a nasty dispute. Newton had developed his concept of “fluxions” (differentials) in the mid 1660s to account for celestial orbits, though there was no public record of his work. In the meantime, German mathematician Gottfried Leibniz formulated his own mathematical theories and published them in 1684. As president of the Royal Society, Newton oversaw an investigation that ruled his work to be the founding basis of the field, but the debate continued even after Leibniz’s death in 1716. Researchers later concluded that both men likely arrived at their conclusions independent of one another.
Newton was also an ardent student of history and religious doctrines, his writings on those subjects compiled into multiple books that were published posthumously. Having never married, Newton spent his later years living with his niece at Cranbury Park, near Winchester, England. He died on March 31, 1727, and was buried in Westminster Abbey.
A giant even among the brilliant minds that drove the Scientific Revolution, Newton is remembered as a transformative scholar, inventor and writer. He eradicated any doubts about the heliocentric model of the universe by establishing celestial mechanics, his precise methodology giving birth to what is known as the scientific method. Although his theories of space-time and gravity eventually gave way to those of Albert Einstein, his work remains the bedrock on which modern physics was built.
Newton himself often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree.[146][147] Although it has been said that the apple story is a myth and that he did not arrive at his theory of gravity in any single moment,[148] acquaintances of Newton (such as William Stukeley, whose manuscript account of 1752 has been made available by the Royal Society) do in fact confirm the incident, though not the apocryphal version that the apple actually hit Newton's head. Stukeley recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726:[149][150][151]
John Conduitt, Newton's assistant at the Royal Mint and husband of Newton's niece, also described the event when he wrote about Newton's life:[152]
In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree."
It is known from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory.[153] The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the Moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon's orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it "universal gravitation".
Various trees are claimed to be "the" apple tree which Newton describes. The King's School, Grantham claims that the tree was purchased by the school, uprooted and transported to the headmaster's garden some years later. The staff of the (now) National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree[154] can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale in Kent[155] can supply grafts from their tree, which appears identical to Flower of Kent, a coarse-fleshed cooking variety.[156]
5.1 Newton’s laws of motion
English natural philosopher Isaac Newton unified German astronomer Johannes Kepler’s laws of planetary motion (discussed in Chapter 3) with Italian natural philosopher Galileo Galilei’s theory of falling bodies (discussed in Chapter 4). Newton published his laws of motion and universal gravitation in The Mathematical Principles of Natural Philosophy, commonly known as the Principia, in 1687.[1]
5.1.1 Newton’s first law
Newton’s first law of motion states that objects continue to move in a state of constant velocity, which can be zero, unless acted upon by an external force. The tendency of an object to resist a change in motion is known as inertia, and objects that are moving at a constant velocity are said to be in an inertial reference frame.
Galileo had first suggested this law, but it had not been universally accepted because it contradicted Ancient Greek philosopher Aristotle’s laws of physics.
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5.1.2 Newton’s second law
Newton’s second law shows how an object will be affected if an external force does act upon it. This law states that the rate of change of momentum of a body is proportional to the resultant force acting on it, and will be in the same direction. This means that:
| F = ΔpΔt | (5.1) |
Δp = mΔv, and a = ΔvΔt and so Newton’s second law can be re-written as:
| F = ma | (5.2) |
Here, F is force, Δ can be read as ‘change in’, p is momentum, t is time, m is mass, v is velocity, and a is acceleration. This shows that less force is needed to push something lighter, which means that less massive objects have less inertia. More force is needed to push something heavier, and so more massive objects have more inertia.
5.1.3 Newton’s third law
Newton’s third law states that the force on an object is always due to another object; all forces act in pairs that are equal in magnitude and opposite in direction. This is why you feel recoil when you strike an object, and why you do not fall through the Earth due to the pull of gravity.
5.1.4 The conservation of momentum
The combination of Newton’s second and third laws shows that momentum must be conserved (as discussed in Chapter 4). This means that the total momentum of two objects will remain the same before and after a collision.
| If F = ΔpΔt and F = -F, then Δp= -Δp. | (5.3) |
5.2 Newton’s law of universal gravitation
Newton’s law of universal gravitation states that every mass attracts every other mass in the universe, and the gravitational force between two bodies is proportional to the product of their masses, and inversely proportional to the square of the distance between them.
Spherical objects like planets and stars act as if all of their mass is concentrated at their centre, and so the distance between objects should include their radius.
Here, for two objects that are orbiting a common centre of mass (like the Earth and Sun), m1 is the mass of the less massive object (like the Earth) and m2 is the mass of the more massive object (like the Sun). F1 is the gravitational force produced by m1, and F2 is the gravitational force produced by m2. ris the radius of the orbit, which is equivalent to the distance between the two masses. Finally, G is a constant that is the same for everything in the universe.
Newton stated that the force of gravity is always attractive, works instantaneously at a distance, and has an infinite range. Most importantly, it affects everything with mass - and has nothing to do with an object’s charge or chemical composition.
This means that it can account for both the force that causes the planets to orbit the Sun - as described by Kepler - and the downwards force that causes objects to accelerate towards the Earth - as described by Galileo.
5.2.1 Newton’s cannonball thought experiment
In 1728, Newton demonstrated the universality of the force of gravity with his cannonball thought-experiment.[2] Here Newton imagined a cannon on top of a mountain. Without gravity, the cannonball should move in a straight line. If gravity is present then its path will depend on its velocity. If it’s slow, then it will fall straight down. If it reaches the orbital velocity (discussed in Section 5.3) - where the gravitational force equals the centripetal force - then it will orbit the Earth in a circle or ellipse. If it’s faster than the escape velocity - when the kinetic energy is equal to the gravitational potential energy (discussed in Chapter 14) - then it will leave the Earth’s orbit.
5.3 The mass of the Sun and planets
The mass of an object in orbit (like the Earth) can be determined if you know how far away it is from the thing it is orbiting (the distance between the Earth and Sun), how long it takes to make one orbit (one year), and the mass of the thing it’s orbiting (the mass of the Sun).
This is because, for objects in spherical orbits, the centripetal force (Fc) is equal to the force of gravity. The centripetal force is the force that causes rotating objects to move in a circle, this can happen, for example, if you swing a yo-yo around:
| Fc = mac | (5.5) |
| Fc = mv2r | (5.6) |
Here, ac is the centripetal acceleration (discussed in Chapter 3).
| Centripetal force | = | m1v2r | (5.7) |
| Gravitational force | = | Gm1m2r2 | (5.8) |
| m1v2r | = | Gm1m2r2 | (5.9) |
v = dΔt, where the time period (Δt) is the period of one orbit (P), and distance is the circumference of a circle (2πr), giving:
| m1(2πr)2rP2 | = | Gm1m2r2 | (5.10) | |
| and so | P2 = (2π)2r3Gm2 | and | m2 = (2π)2r3GP2 | (5.11) |
Here, m1 is the mass of the less massive object (the Earth) and m2 is the mass of the more massive object (the Sun).
This equation assumes that m1 is orbiting in a circle around m2. In reality, both m1 and m2orbit the centre of mass between the two objects. This explains Kepler’s first law (discussed in Chapter 3), which states that ‘the orbit of every planet is an ellipse with the Sun at one of the two foci’.
The two masses balance like objects on a seesaw, a type of lever (discussed in Chapter 4), and just like a lever in balance, the torques on each side are equal so that m1g d1 = m2g d2. This is shown in Figures 5.5 and 5.6.
Here d1 is the distance between m1 and the pivot - the centre of mass - and d2 is the distance between m2 and the centre of mass. The distance, in this case, is equal to the radius of each circle around the centre of mass, and so d1 = r1 and d2 = r2. Finally, as shown in Section 5.4, g is the same for each object, giving:
| m1r1 = m2r2 | (5.12) |
If m1 = m2, then the two masses will balance - i.e. remain in a stable orbit - if they are an equal distance from the centre, and so r1 = r2. If m2 is twice the mass of m1, then it will have to be placed half the distance from the pivot - the centre of mass - in order to balance. When m2 is far greater than m1, then m2 will be placed so close to the centre of mass, that the centre will be within its radius.
This would be the case for the Earth and Sun, however in the case of objects in the Solar System, there are more than just two objects to balance. Many objects are in a stable orbit around the Sun, and the most massive of these is Jupiter. The mass of Jupiter means that the centre of mass in the Solar System is actually about 700,000 km from the centre of the Sun. This is about the same distance as the radius of the Sun, as shown in Figure 5.6.
The gravitational force only depends on the distance between m1 and m2. It’s not affected by where the centre of mass is, and so the equation remains the same, but the centripetal force is different. The centripetal force pulls both m1 and m2 towards the centre of mass, and so:
| P2 = (2π)2r1r2Gm2 | and | m2 = (2π)2r1r2GP2 | (5.13) |
Just as with a lever in balance, m1r1 = m2r2. This can be rearranged to show that r1 = r m2m1+m2 and so:
| P2 = (2π)2r3G(m1+m2) | and | m1+m2 = (2π)2r3GP2 | (5.14) |
This is known as Newton’s derivation of Kepler’s third Law.
All of this means that if you know the time it takes for an object to complete one orbit of another, and the distance between the two objects, then you can work out the total sum of their masses.
The Earth takes one year to orbit the Sun. The distance between the Earth and Sun was first accurately determined by French astronomer Jean Richer and Italian astronomer Giovanni Domenico Cassini in 1672. They did this by measuring the parallax of Mars (discussed in Chapter 3). They could then work out the distance between the Earth and Mars. Once they knew this, they could work out the distance between the Sun and every planet with a known period using the relative distances from Kepler’s third law. They concluded that the Sun is about 140 million km from the Earth, underestimating the distance by less than 10 million km.[3]
Once the mass of one planet was known, the mass of the Sun could be determined, and once the mass of the Sun was known, the mass of any planet with a known period could be calculated. The mass of the Earth was determined in 1797 using the relationship between force and acceleration given in Newton’s second law.[4]
5.4 Mass and acceleration
Newton’s law of gravitation shows that objects with different masses fall at the same rate when combined with his second law of motion. This is because an object’s acceleration due to the force of gravity only depends on the mass of the object that is pulling it:
| Force | = | m1a | (5.15) |
| Gravitational force | = | Gm1m2r2 | (5.16) |
| m1a | = | Gm1m2r2 | (5.17) |
| a | = | Gm2r2 | (5.18) |
Here, m1 is the mass of the less massive object (a feather or hammer in this case) and m2 is the mass of the more massive object (a planet or moon). This shows that very heavy and very light objects will all fall at the same rate if they are dropped in the same place and there is no air resistance.
This was proven in 1971, when Apollo 15 astronaut Commander David Scott dropped a feather and hammer at the same time on the Moon. The Moon has no atmosphere to create air resistance, and so they fell at the same rate, reaching the Moon’s surface at the same time.
The acceleration due to the force of gravity is referred to as g:
| g = Gm2r2 | (5.19) |
The law of pendulums (discussed in Chapter 2) can be derived by putting g = Gm2r2 into P2= (2π)2r3Gm2:
| If g = Gm2r2 and P2 = (2π)2r3Gm2 thenP = 2π √rg. | (5.20) |
Here, P is the period. The period of a pendulum and the period of a planet are both equal to the time it takes for them to cover a distance equal to the circumference of one full circle - 2πr. r is the radius of this circle, equal to the length of the pendulum.
5.4.1 The mass of the Earth
The mass of the Earth was first determined by British natural philosopher Henry Cavendish in 1797.[4] g = Gmr2 (where m = m2), and so:
| Mass of the Earth = gr2G | (5.21) |
The radius of the Earth can be derived from the circumference, which was first measured by Ancient Greek astronomer Eratosthenes using the angle of shadows in different locations during the solstice, when the Sun is highest in the sky (discussed in Chapter 3).[5]
On Earth, g = 9.8 ms-2. Galileo showed how you could derive g in the 1500s by measuring the acceleration of falling objects (discussed in Chapter 4)[6] and, in about 1666, English natural philosopher Robert Hooke suggested that a pendulum could be used to measure acceleration due to gravity (discussed in Chapter 2).
Cavendish showed how G could be determined by measuring the gravitational force between two objects of known masses in a laboratory, using an instrument known as a torsion balance. Once Cavendish could compare the different forces exerted by different masses, he could calculate G, and use it to work out the mass of other objects.
Cavendish found that G = 6.674 × 10-11 m3kg-1 s-2 when everything is measured in units of metres, kilograms, and seconds. The mass of the Earth was calculated to be about 5.97 × 1024 kg (this is about six million, billion, billion), the value accepted today.
5.4.2 Acceleration due to gravity on Earth
The Earth has a mass of about 5.97 × 1024kg, and so the acceleration due to gravity on the surface of the Earth, about 6,371,000 m from its centre, is:
| g on the surface of the Earth | = | Gmr2 | (5.22) |
| = | 6.674×10-11× 5.97×10246,371,0002 | ||
| = | 9.8 ms-2 | ||
| = | 1 g |
This number gets rapidly lower the further you get from the surface of the Earth, by the time you are about 400 km away (which is roughly the distance from London to Paris), it falls by about 10%. At 4000 km, it falls by about 60%, and by the time you get to the Moon, which is 384,400 km away, it has fallen by over 99.9%.
This number gets rapidly higher the closer you get to the centre of the Earth. The fact that it’s infinite at a radius of 0 is indicative of our lack of understanding about how physics works at very small lengths (discussed in Book II).
The force of gravity 10 cm from the centre of the Earth is:
| g 10 cm from the centre of the Earth | = | 6.674×10-11× 5.97×10240.12 | (5.23) |
| = | 4×1016 ms-2 | ||
| = | 4×1015 g |
If you could tunnel to the centre of the Earth, however, then you would not feel this force. At the centre of the Earth, the gravity of the Earth would be accelerating you equally in all directions, and so you would feel weightless.[7]
5.4.3 Acceleration due to gravity on an asteroid
All objects with strong enough gravitational fields become approximately spherical. This is because the surface is pulled inwards equally in all directions, and so any imperfections are smoothed out. The mass that an object needs to become spherical depends on what it is made of. It is easier to smooth out water than rock, for example.
Objects made of rock tend to be spherical if they have a mass over about 1020 kg, which is the mass of some asteroids.[8] This is about 60,000 times less massive than the Earth, and produces objects with a radius of about 300 km.[9]
| g on an asteroid | = | 6.674×10-11 × 1020300,0002 | (5.24) |
| = | 0.074 ms-2 | ||
| = | 0.0076 g |
5.4.4 Acceleration due to gravity on the International Space Station
The International Space Station (ISS) orbits the Earth from about 400 km away,[10] and so:
| g on the International Space Station | = | 6.674×10-11× 5.97×1024(6,371,000 + 400,000)2 | (5.25) |
| = | 8.7 ms-2 | ||
| = | 0.9 g |
This is 90% of the gravity on the surface of the Earth, which means that people on the ISS do not appear to be weightless because of their distance from the Earth. Instead, they appear weightless because the ISS accelerates towards the Earth at about 8.7 ms-2, which means that it’s in ‘free-fall’.
Objects in free-fall are accelerating towards the Earth at the same rate as they are accelerated by gravity. If there is no drag from the atmosphere, then objects in free-fall act as if they are weightless. You do not feel this drag if you are inside an enclosed space, like a space station or an aeroplane, and so you can experience weightlessness on a zero-G flight. Here, an aeroplane accelerates towards the Earth at 9.8 about ms-2, and so the floor appears to fall away from the people inside at the same rate as they are pulled towards it by gravity. This makes it appear as if they are hovering above a stationary floor.
Objects in orbit, like the ISS, are able to constantly fall towards the surface of the Earth without ever reaching the ground. This is because the surface is spherical, and so falling away from them at the same rate.
5.4.5 Mass and weight
You may feel weightless when in free-fall, but you still have the same mass.
In physics, mass is a fundamental property that particles have (discussed in Book II). A person’s mass is the sum of the mass of all the particles in their body, and so their body mass only changes if they add or remove some of these particles.
Weight is simply another name for the gravitational force described by Newton’s law of universal gravitation, and ‘apparent weight’ is the force you feel due to your total acceleration.
| Weight | = | Force of gravity | (5.26) |
| = | Gm1m2r2 | (5.27) |
Weight can also be described using Newton’s second law F = ma as:
| Weight | = | Mass × Acceleration due to gravity | (5.28) |
| = | m1 × g | (5.29) | |
| = | Gm1m2r2 | (5.30) |
Here, m1 and m2 are interchangeable. The weight of a 60 kg person on the surface of the Earth is:
| Weight | = | 60 kg × 9.8 ms-2 | (5.31) |
| = | 589 kg ms-2 | ||
| = | 589 N |
This means that the Earth exerts a 589 N force on a 60 kg person due to its gravitational field. If the two masses were reversed, however, and you calculated the force on the Earth caused by the gravitational field of a 60 kg person, then the equation would remain the same. This means a 60 kg person exerts a 589 N force on the Earth due to their gravitational field.
Another way of saying this is that the weightof the Earth caused by its acceleration under the gravitational field of an object is the same as the weight of that object.
What is 1 kg?
The gram was defined in 1795 as the mass of one cubic centimetre of water at the melting point of water,[11] however the terms ‘mass’ and ‘weight’ were often used interchangeably when referring to objects on Earth until the late 1800s.
The General Conference on Weights and Measures (CGPM) formed in 1875 and representatives from different countries met in Paris in order to develop a common international measuring system, known as the metric system.[12] In 1889, the CGPM created an object out of a platinum-iridium alloy that was about 1000 times the mass of a gram; this is a kilogram, where kilo refers to 1000.[13] The CGPM declared that from then on, the mass of a kilogram in the metric system would refer to the mass of this object, and copies were taken to each member country.
In 1901, the CGPM confirmed that the kilogram is a unit of mass, not weight. Weight is measured in newtons (N), the same unit as other forces.[13]
5.5 Mass and energy
As shown in Chapter 4, the amount of energy transferred (ΔE) by a force (F) is equal to the force multiplied by the distance the force acts over:
| ΔE = Fd | (5.32) |
5.5.1 Gravitational potential energy
For gravitational potential energy (GPE):
| GPE | = | Fd | (5.33) |
| = | Gm1m2r2r | (5.34) | |
| = | Gm1m2r | (5.35) |
This is the same as British engineer William Rankine’s concept of potential energy, which is the energy that is needed to keep an object from falling from a height (discussed in Chapter 4):
| GPE | = | m1gh | (5.36) |
| = | Weight × Distance | ||
| = | m1Gm2r2r | (5.37) | |
| = | Gm1m2r | (5.38) |
Here h is height, which is equal to the radius (r).
5.5.2 Kinetic energy
For kinetic energy:
| KE = Fd | (5.39) |
| KE = mad | (5.40) |
This is the same as Coriolis’ equation for kinetic energy (discussed in Chapter 4).
| v | = | dt | (5.41) | |
| = | vinitial + vfinal2 | |||
| and | ||||
| a | = | Δvt | (5.42) | |
| = | vfinal - vinitialt | |||
| giving | ||||
| t | = | vfinal - vinitiala | (5.43) | |
| so that | ||||
| d | = | (vinitial + vfinal)(vfinal - vinitial)2a | (5.44) | |
| and | ||||
| ad | = | 12 (vfinal2 - vinitial2) | (5.45) |
Kinetic energy only applies to objects that are moving, and so vinitial is always 0, giving:
| ad = 12 v2 | (5.46) |
where v = vfinal. Finally, this gives:
| KE = 12 mv2 | (5.47) |
5.6 Newton and absolute space
There’s evidence that Newton was motivated to universalise his theory of gravitation because of his religious beliefs.[14] In the 1600s, members of the Royal Society - a scientific institution based in London - typically believed that science investigated the same truth as the bible. They believed that knowledge came in two forms: revealed truth, which comes from studying scripture, and natural theology, which seeks to learn about God by studying what they considered to be God’s creation. The conclusions of natural theology were only accepted if they agreed with revealed truth.
In the second edition of the Principia, Newton stated that nature reveals a creator. He claimed that this was evident firstly, from the fact that the universe formed at all. Secondly, from the fact that the masses that did form are placed so that they do not fall together under their own mutual gravitation, and thirdly, Newton found evidence of design in the specifics of our Solar System, such as the fact that the orbits of the planets are all in the same direction and plane. Newton claimed that the eccentric orbits of comets alone reveal the existence of a creator and described God as “an intelligent and powerful being”.[15]
In private correspondence, Newton expressed his belief in the Hebrew God of the Old Testament.[14] He considered himself to be Arian, believing that scripture had been wrongly interpreted at the first Council of Nicaea, in 325, when the Trinity first became an important part of Christen theology. Newton’s belief that the Holy Trinity are not three persons remained illegal in England throughout his lifetime.
Newton stated that because a singular God “exists always and every where”,[15] space and time must be absolute. This means they provide a background in which things take place, and would continue to exist even if the universe were devoid of all physical matter. Newton argued that God’s eternal nature implies absolute and eternal time, and God’s infinite duration corresponds to absolute and infinite space.
The belief that space and time are absolute is known as spacetime substantivalism because it implies that space is composed of some kind of pseudo-substance, like Aristotle’s aether (discussed in Chapter 4).
5.6.1 Leibniz and relative space
German mathematician and philosopher Gottfried Leibniz accepted that the law of gravitation could be universalised, but objected to Newton’s concept of absolute space. Firstly, he argued that Galileo had shown there’s no such thing as absolute velocity, and so there can’t be any such thing as absolute space, from which it’s derived. Secondly, Leibniz objected to Newton’s description of absolute space as a kind of physical entity because it has no causal powers or independent existence. Leibniz claimed that space is purely a mental entity.[16,17]
The view that space only exists when physical objects are present is known as relationism. Relationism can be countered by the idea that although there is no absolute velocity, there is absolute acceleration, and absolute space can be derived from this.[18]
This argument was reassessed in the first half of the 20th century, after the publication of German-Swiss-American physicist Albert Einstein’s theory of general relativity[19](discussed in Chapter 8).
5.6.2 Olbers’ paradox
Newton’s infinite, eternal, universe posed problems for astronomers as well as philosophers. In 1720, English astronomer Edmond Halley stated that if the universe is eternal, and the stars are infinitely old, then the sky should be as bright as the surface of the Sun in all directions.[20,21] This is because the starlight from an infinite amount of stars would have reached us by now, filling every part of the sky.
This view was first considered by English astronomer Thomas Digges in the 1500s, and then by Kepler, German natural philosopher Otto von Guericke, French natural philosopher Bernard de Fontenelle, and Dutch natural philosopher Christiaan Huygens.[22] It was popularised by German astronomer Heinrich Olbers in 1823, and is known as Olbers’ paradox.[23] Olbers’ paradox was not resolved until American astronomer Edwin Hubble provided evidence of the big bang in the first half of the 20th century (discussed in Chapter 9).
5.7 The precession of Mercury
Newton’s theory was first questioned in 1859, when French mathematician Urbain Le Verrier showed that Mercury’s orbit could not be explained by Newton’s equations.[24]
Mercury does not form a closed ellipse when it orbits the Sun. Instead, the ellipse rotates. This sort of movement is known as precession, and was later explained by Einstein’s theory of general relativity
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