# ISAAC NEWTON (1642-1727)

1687 – England

‘Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them’

NEWTON

The force is known as gravitation
Expressed as an equation:

F = GmM/r2

where F is Force, m and M the masses of two bodies, r the distance between them and G the gravitational constant
This follows from KEPLER’s laws, Newton’s laws of motion and the laws of conic sections. Gravitation is the same thing as gravity. The word gravity is particularly used for the attraction of the Earth for other objects.

Gravitation
Newton stated that the law of gravitation is universal; it applies to all bodies in the universe. All historical speculation of different mechanical principles for the earth from the rest of the cosmos were cast aside in favour of a single system. He demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalized that all heavenly bodies mutually attract one another. Simple mathematical laws could explain a huge range of seemingly disconnected physical facts, providing science with the straightforward explanations it had been seeking since the time of the ancients. That the constant of gravitation is in fact constant was proved by careful experiment, that the focus of a body’s centre of gravity appears to be a point at the centre of the object was proved by his calculus.

Calculus
The angle of curve, by definition, is constantly changing, so it is difficult to calculate at any particular point. Similarly, it is difficult to calculate the area under a curve. Using ARCHIMEDES’ method of employing polygons and rectangles to work out the areas of circles and curves, and to show how the tangent or slope of any point of a curve can be analyzed, Newton developed his work on the revolutionary mathematical and scientific ideas of RENE DESCARTES, which were just beginning to filter into England, to create the mathematics of calculus. Calculus studies how fast things change.
The idea of fluxions has become known as differentiation, a means of determining the slope of a line, and integration, of finding the area beneath a curve.

Newton’s ideas on universal gravitation did not emerge until he began a controversial correspondence with ROBERT HOOKE in around 1680. Hooke claimed that he had solved the problem of planetary motion with an inverse square law that governed the way that planets moved. Hooke was right about the inverse square law, but he had no idea how it worked or how to prove it, he lacked the genius that permitted Newton to combine Kepler’s laws of planetary motion with the assumption that an object falling towards Earth was the same kind of motion as the Earth’s falling toward the Sun.
It was not until EDMUND HALLEY challenged Newton in 1684 to show how planets could have the elliptical orbits described by Johannes Kepler, supposing the force of attraction by the Sun to be the reciprocal of their distance from it – and Newton replied that he already knew – that he fully articulated his laws of gravitation.

It amounts to deriving Kepler’s first law by starting with the inverse square hypothesis of gravitation. Here the Sun attracts each of the planets with a force that is inversely proportional to the square of the distance of the planet from the Sun. From Kepler’s second law, the force acting on the planets is centripetal. Newton says this is the same as gravitation.

In the previous half century, Kepler had shown that planets have elliptical orbits and GALILEO had shown that things accelerate at an even pace as they fall towards the ground. Newton realized that his ideas about gravity and the laws of motion, which he had only applied to the Earth, might apply to all physical objects, and work for the heavens too. Any object that has mass will be pulled towards any other object. The larger the mass, the greater the pull. Things were not simply falling but being pulled by an invisible force. Just as this force (of gravity) pulls things towards the Earth, it also keeps the Moon in its orbit round the Earth and the planets moving around the Sun. With mathematical proofs he showed that this force is the same everywhere and that the pull between two things depends on their mass and the square of the distance between them.

Title page of Philosophiae Naturalis Principia Mathematica

Newton published his law of gravitation in his magnum opus Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) in 1687. In it Newton analyzed the motion of orbiting bodies, projectiles, pendulums and free fall near the Earth.

The first book of Principia states the laws of motion and deals with the general principles of mechanics. The second book is concerned mainly with the motion of fluids. The third book is considered the most spectacular and explains gravitation.

Why do two objects attract each other?
‘I frame no hypotheses’, said Newton

It was Newton’s acceptance of the possibility that there are mysterious forces in the world, his passions for alchemy and the study of the influence of the Divine that led him to the idea of an invisible gravitational force – something that the more rationally minded Galileo had not been able to accept.
Newton’s use of mathematical expression of physical occurrences underlined the standard for modern physics and his laws underpin our basic understanding of how things work on an everyday scale. The universality of the law of gravitation was challenged in 1915 when EINSTEIN published the theory of general relativity.

1670-71 Newton composes ‘Methodis Fluxionum‘, his main work on calculus, which is not published until 1736. His secrecy meant that in the intervening period, the German mathematician LEIBNIZ could publish his own independently discovered version – he gave it the name calculus, which stuck.

## LAWS OF MOTION

1687 – England

• First Law: An object at rest will remain at rest and an object in motion will remain in motion at that velocity until an external force acts on the object

• Second Law: The sum of all forces (F) that act on an object is equal to the mass (m) of the object multiplied by the acceleration (a), or F = ma

• Third Law: To every action, there is an equal and opposite reaction

### The first law

introduces the concept of inertia, the tendency of a body to resist change in its velocity. The law is completely general, applying to all objects and any force. The inertia of an object is related to its mass. Things keep moving in a straight line until they are acted on by a force. The Moon tries to move in a straight line, but gravity pulls it into an orbit.
Weight is not the same as mass.

### The second law

explains the relationship between mass and acceleration, stating that a force can change the motion of an object according to the product of its mass and its acceleration. That is, the rate and direction of any change depends entirely on the strength of the force that causes it and how heavy the object is. If the Moon were closer to the Earth, the pull of gravity between them would be so strong that the Moon would be dragged down to crash into the Earth. If it were further away, gravity would be weaker and the Moon would fly off into space.

### The third law

shows that forces always exist in pairs. Every action and reaction is equal and opposite, so that when two things crash together they bounce off one another with equal force.

## LIGHT

1672 – New Theory about Light and Colours is his first published work and contains his proof that white light is made up of all colours of the spectrum. By using a prism to split daylight into the colours of the rainbow and then using another to recombine them into white light, he showed that white light is made up of all the colours of the spectrum, each of which is bent to a slightly different extent when it passes through a lens – each type of ray producing a different spectral colour.

Newton also had a practical side. In the 1660s his reflecting telescope bypassed the focusing problems caused by chromatic aberration in the refracting telescope of the type used by Galileo. Newton solved the problem by swapping the lenses for curved mirrors so that the light rays did not have to pass through glass but reflected off it.

At around the same time, the Dutch scientist CHRISTIAAN HUYGENS came up with the convincing but wholly contradictory theory that light travels in waves like ripples on a pond. Newton vigorously challenged anyone who tried to contradict his opinion on the theory of light, as Robert Hooke and Leibniz, who shared similar views to Huygens found out. Given Newton’s standing, science abandoned the wave theory for the best part of two hundred years.

1704 – ‘Optiks’ published. In it he articulates his influential (if partly inaccurate) particle or corpuscle theory of light. Newton suggested that a beam of light is a stream of tiny particles or corpuscles, traveling at huge speed. If so, this would explain why light could travel through a vacuüm, where there is nothing to carry it. It also explained, he argued, why light travels in straight lines and casts sharp shadows – and is reflected from mirrors. His particle theory leads to an inverse square law that says that the intensity of light varies as the square of its distance from the source, just as gravity does. Newton was not dogmatic in Optiks, and shows an awareness of problems with the corpuscular theory.

In the mid-eighteenth century an English optician John Dolland realized that the problem of coloured images could largely be overcome by making two element glass lenses, in which a converging lens made from one kind of glass was sandwiched together with a diverging lens made of another type of glass. In such an ‘achromatic’ lens the spreading of white light into component colours by one element was cancelled out by the other.

During Newton’s time as master of the mint, twenty-seven counterfeiters were executed.

NEXT

GRAVITY

LIGHT

# CHRISTIAAN HUYGENS (1629- 95)

1690 – Holland

HUYGENS

‘Every point on a wavefront can act as a new source of waves’

A line perpendicular to the wave fronts is called a ray and this ray shows the direction of the wave.

The Huygens construction, published in ‘Traite de la Lumiere‘ (’Treatise on Light’, 1690) gives an explanation for the way light is reflected and refracted.

Huygens said that light consists of a disturbance spreading from its source as spherical pressure waves having wave fronts perpendicular to the direction of their motion and correctly anticipated that in a denser medium light would travel more slowly. This hypothesis was largely ignored at the time as it conflicted with NEWTON‘s theory. Huygens’ view, when re-discovered and championed by THOMAS YOUNG (1773-1829) would eventually become the more commonly accepted version.

He invented a pendulum clock (1656) and also discovered Titan, the first observed moon of Saturn (1665).

Huygens discovered that a simple pendulum does not keep perfect time but completes smaller swings faster than big swings. This is because the weight or ‘bob’ of the pendulum follows a circular path. Huygens’ realisation that a pendulum mimicking a circle’s curve does not maintain a perfectly equal swing and that in order to do this it actually needs to follow a ‘cycloidal’ arc, set him on the path to designing the first successful pendulum clock.

Published ‘Horologium‘ (1658), ‘Horologium Oscillatorium‘ (1673) in which he showed that if the bob’s path were a cycloid (the curved path traced out by a point on the rim of a wheel as it rolls along) instead of a circle, it would be isynchronous (keeping equal time) no matter what the length of the swing. He made the pendulum’s swing cycloidal by suspending a rigid pendulum rod on two chords whose swing either way was limited by two plates called cycloidal checks.

GALILEO had considered the timekeeping possibilities of a swinging pendulum and Huygens successfully tied it with an escapement mechanism.
He explored the mathematics associated with pendulums – which led him, together with HOOKE, to an early prediction of the link between the elliptical orbits of the planets and the inverse square law of gravity. His work was a milestone, playing a key part in the understanding of centrifugal force. It helped to confirm Newton’s laws of motion by showing how an object will travel in a straight line unless pulled into a curved path by some other force.

Huygens was one of the founders of the French Académie des sciences in Paris.

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THE STARS

# THOMAS YOUNG (1773-1829)

1801 – England

‘Interference between waves can be constructive or destructive’

Huygens‘ wave theory was neglected for more than a hundred years until it was revived by Young in the opening years of the nineteenth century. Young rejected Newton‘s view that if light consisted of waves it would not travel in a straight line and therefore sharp shadows would not be possible. He said that if the wavelength of light was extremely small, light would not spread around corners and shadows would appear sharp. His principle of interference provided strong evidence in support of the wave theory.

Young’s principle advanced the wave theory of light of CHRISTIAAN HUYGENS. Further advances came from EINSTEIN and PLANCK.

In Young’s double slit experiment a beam of sunlight is allowed to enter a darkened room through a pinhole. The beam is then passed through two closely spaced small slits in a cardboard screen. You would expect to see two bright lights on a screen placed behind the slits. Instead a series of alternate light and dark stripes are observed, known as interference fringes, produced when one wave of light interferes with another wave of light.

Two identical waves traveling together either reinforce each other (constructive interference) or cancel each other out (destructive interference). This effect is similar to the pattern produced when two stones are thrown into a pool of water.

THOMAS YOUNG

The mathematical explanation of this effect was provided by AUGUSTIN FRESNEL (1788-1827). The wave theory was further expanded by EINSTEIN in 1905 when he showed that light is transmitted as photons.

Light, an electromagnetic radiation, is transported in photons that are guided along their path by waves. This is known as ‘wave-particle duality’.

The current view of the nature of light is based on quantum theory.

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WAVES

# HEINRICH WILHELM MATTHIAS OLBERS (1758-1840)

1823 – Germany

‘Why is the sky dark at night?’

This question puzzled astronomers for centuries and no, the answer is not because the Sun is on the other side of the planet.

Olbers pointed out that if there were an infinite number of stars evenly distributed in space, the night sky should be uniformly bright. He believed that the darkness of the night sky was due to the adsorption of light by interstellar space.

This is wrong.

OLBERS

Olbers’ question remained a paradox until 1929 when it was discovered that the galaxies are moving away from us and the universe is expanding. The distant galaxies are moving away so fast that the intensity of light we receive from them is diminished.

What is light intensity?

In addition, this light is shifted towards the red end of the spectrum. These two effects significantly reduce the light we receive from distant galaxies, leaving only the nearby stars, which we see as points of light in a darkened sky.

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THE STARS

# JOSEF VON FRAUNHOFER (1787-1826)

1823 – Germany

‘The spectroscope’

A significant improvement on the apparatus used by Newton. Sunlight, instead of passing through a pinhole before striking a prism, is passed through a long thin slit in a metal plate. This creates a long ribbon-like spectrum, which may be scanned from end to end with a microscope.

Cutting across the ribbon of rainbow colours are thin black lines. The lines are present even when a diffraction grating is used instead of a prism, proving that the lines are not produced by the material of a prism, but are inherent in sunlight.

An equivalent way of describing colours is as light waves of different sizes.
The wavelength of light is fantastically small, on average about a thousandth of a millimeter, with the wavelength of red light being about twice as long as that of blue light.

Fraunhofer’s black lines correspond to missing wavelengths of light.

By 1823 Fraunhofer had measured the positions of 574 spectral lines, labeling the most prominent ones with the letters of the alphabet. The lines labeled with the letters ‘H’ and ‘K’ correspond to light at a wavelength of 0.3968 thousandths of a millimeter and 0.3933 thousandths of a millimeter, respectively. The lines are present in the spectrum of light from stars, usually in different combinations.

Fraunhofer died early at the age of 39 and it was left to the German GUSTAV KIRCHOFF to make the breakthrough that explained their significance.

Astronomers today know the wavelengths of more than 25,000 ‘Fraunhofer lines’.

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THE STARS

1831 – England

‘A changing magnetic field around a conductor produces an electric current in the conductor. The size of the voltage is proportional to the rate of change of the magnetic field’

This phenomenon is called ‘electromagnetic induction’ and the current produced ‘induced current’. Induction is the basis of the electric generator and motor.

Faraday developed HANS CHRISTIAN OERSTED’s 1820 discovery that electric current could deflect a compass needle. In his experiment Faraday wrapped two coils of insulated wire around opposite sides of an iron ring. One coil was connected to a battery, the other to a wire under which lay a magnetic compass needle. He anticipated that if he passed a current through the first wire it would establish a field in the ring that would induce a current in the second wire. He observed no effect when the current was steady but when he turned the current on and off he noticed the needle moving. He surmised that whenever the current in the first coil changed, current was induced in the second. To test this concept he slipped a magnet in and out of a coil of wire. While the magnet was moving the compass needle registered a current, as he pushed it in it moved one way, as he pulled it out the needle moved in the opposite direction. This was the first production of electricity by non-chemical means.

In 1831, by rotating a copper disc between the poles of a magnet, Faraday was able to produce a steady electric current. This was the world’s first dynamo.

NEWTON, with his concept of gravity, had introduced the idea of an invisible force that exerted its effect through empty space, but the idea of ‘action-at-a-distance’ was rejected by an increasing number of scientists in the early nineteenth century. By 1830, THOMAS YOUNG and AUGUSTIN FRESNEL had shown that light did not travel as particles, as Newton had said, but as waves or vibrations. But if this was so, what was vibrating? To answer this, scientists came up with the idea of a weightless matter, or ‘aether’.

Faraday had rejected the concept of electricity as a ‘fluid’ and instead visualised its ‘fields’ with lines of force at their edges – the lines of force demonstrated by the pattern of iron fillings around a magnet. This meant that action at a distance simply did not happen, but things moved only when they encountered these lines of force. He believed that magnetism was also induced by fields of force and that it could interrelate with electricity because the respective fields cut across each other. Proving this to be true by producing an electric current via magnetism, Faraday had demonstrated electromagnetic induction.

When Faraday was discovering electromagnetic induction he did so in the guise of a natural philosopher. Physics, as a branch of science, was yet to be given a name.

The Russian physicist HEINRICH LENZ (1804- 65) extended Faraday’s work when in 1833 he suggested that ‘the changing magnetic field surrounding a conductor gives rise to an electric current whose own magnetic field tends to oppose it.’ This is now known as Lenz’s law. This law is in fact LE CHATELIER‘s principle when applied to the interactions of currents and magnetic fields.

Fluctuating Electromagnetic Fields and EM Waves

It took a Scottish mathematician by the name of JAMES CLERK MAXWELL to provide a mathematical interpretation of Faraday’s work on electromagnetism.

Describing the complex interplay of electric and magnetic fields, he was able to conclude mathematically that electromagnetic waves move at the speed of light and that light is just one form of electromagnetic wave.
This led to the understanding of light and radiant heat as moving variations in electromagnetic fields. These moving fields have become known collectively as radiation.

Faraday continued to investigate the idea that the natural forces of electricity, magnetism, light and even gravity are somehow ‘united’, and to develop the idea of fields of force. He focused on how light and gravity relate to electromagnetism.
After conducting experiments using transparent substances, he tried a piece of heavy lead glass, which led to the discovery of the ‘Faraday Effect’ in 1845 and proved that polarised light may be affected by a magnet. This opened the way for enquiries into the complete spectrum of electromagnetic radiation.

In 1888 the German physicist HEINRICH HERTZ confirmed the existence of electromagnetic waves – in this case radio waves – traveling at the speed of light.

The unit of capacitance, farad (F) is named in honour of Faraday.

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ELECTRICITY

# CHRISTIAN JOHANN DOPPLER (1803- 53)

1842 – Austria

‘Any source of sound or light moving away from an observer changes in frequency with reference to the observer’

The pitch of the whistle of a train is higher when the train is approaching an observer standing on a platform and lower when it is moving away from the observer.

Doppler explained the effect by pointing out that when the source of sound is moving toward the observer, sound waves reach the ear at shorter intervals, hence the higher pitch. When the source is moving away the waves reach the ear at longer intervals, hence the lower pitch. The Doppler effect also occurs when the source of sound is stationary and the observer is moving.

Doppler predicted that a similar effect would apply to light waves.

Different colours are the optical equivalent of notes of different pitch; blue light vibrates at roughly twice the pitch of red light.

In 1929 EDWIN HUBBLE suggested that the Doppler effect applied to light coming from distant stars gives a measure of the distance and speed of distant galaxies.

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