HIPPARCHUS (c.190 – c.125 BC)

134 BCE – Nicea, Turkey

‘Observation of a new star in the constellation Scorpio’

The ‘Precession of the Equinoxes’

By the time Hipparchus was born, astronomy was already an ancient art.

Hipparchus plotted a catalogue of the stars – despite warnings that he was thus guilty of impiety. Comparing his observations with earlier recordings from Babylonia he noted that the celestial pole changed over time.
He speculated that the stars are not fixed as had previously been thought and recorded the positions of 850 stars.

Hipparchus‘ astronomical calculations enabled him to plot the ecliptic, which is the path of the Sun through the sky. The ecliptic is at an angle to the Earth‘s equator, and crosses it at two points, the equinoxes (the astronomical event when the Sun is at zenith over the equator, marking the two occasions during the year when both hemispheres are at right angles to the Sun and day and night are of equal length).

The extreme positions of summer and winter mark the times in the Earth’s orbit where one of the hemispheres is directed towards or away from the Sun.

Solstice

The Sun is furthest away at the solstices.

From his observations, he was able to make calculations on the length of the year.
There are several ways of measuring a year astronomically and Hipparchus measured the ‘tropical year’, the time between equinoxes.

Hipparchus puzzled that even though the Sun apparently traveled a circular path, the seasons – the time between the solstices and equinoxes – were not of equal length. Intrigued, he worked out a method of calculating the Sun’s path that would show its exact location on any date.

To facilitate his celestial observations he developed an early version of trigonometry.
With no notion of sine, he developed a table of chords which calculated the relationship between the length of a line joining two points on a circle and the corresponding angle at the centre.

By comparing his observations with those noted by Timocharis of Alexandria a century and a half previously, Hipparchus noted that the points at which the equinox occurred seemed to move slowly but consistently from east to west against the backdrop of fixed stars.

We now know that this phenomenon is not caused by a shift in the stars.
Because of gravitational effects, over time the axis through the geographic North and South poles of the Earth points towards different parts of space and of the night sky.
The Earth’s rotation experiences movement caused by a slow change in the direction of the planet’s tilt; the axis of the Earth ‘wobbles’, or traces out a cone, changing the Earth’s orientation as it orbits the Sun.
The shift in the orbital position of the equinoxes relative to the Sun and the change in the seasons is now known as ‘the precession of the equinoxes’, but Hipparchus was basically right.

Hipparchus‘ only large error was to assume, like all those of his time except ARISTARCHUS that the Earth is stationary and that the Sun, moon, planets and stars revolve around it. The fact that the stars are fixed and the Earth is moving makes such a tiny difference to the way the Sun, moon and stars appear to move that Hipparchus was still able to make highly accurate calculations.

These explanations may show how many people become confused by claims that the Earth remains stationary as was believed by the ancients – from our point-of-view on Earth that IS how things could appear.
a) demonstration of precession.

youtube=https://www.youtube.com/watch?v=qlVgEoZDjok
b) demonstration of the equinoxes, but not of the precession, which takes place slowly over a cycle of 26,000 years.

youtube=http://www.youtube.com/watch?v=q4_-R1vnJyw&w=420&h=315

Because the Babylonians kept records dating back millennia, the Greeks were able to formulate their ideas of the truth.

Hipparchus gave a value for the annual precession of around 46 seconds of arc (compared to a modern figure of 50.26 seconds). He concluded that the whole star pattern was moving slowly eastwards and that it would revolve once every 26,000 years.

Hipparchus also made observations and calculations to determine the orbit of the moon, the dates of eclipses and devised the scale of magnitude or brightness that, considerably amended, is still in use.

PTOLEMY cited Hipparchus as his most important predecessor.

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HEINRICH 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’ 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. 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.

diagram explaining reduced light intensity as the observer travels further from the source

What is light intensity?

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EDWIN HUBBLE (1889-1953)

1929 – USA

‘Galaxies are moving away from each other and us at an ever-increasing rate. The more distant the galaxy, the faster it is moving away’

Photo portrait of EDWIN HUBBLE with pipe ©

EDWIN HUBBLE

This means that the universe is expanding like a balloon. The principle of an expanding cosmos is at the heart of astronomical theory.

Before 1930, astronomers believed that the Milky Way was the only galaxy in the universe. The discovery of Cepheid variables, which brightened and dimmed in a regular rhythm gave a clue as to the true size of the universe.

In 1923, Hubble spotted a Cepheid variable in the Andromeda Nebula, previously supposed to be clouds of gas. This led to the conclusion that Andromeda was nearly a million light years away, far beyond the limits of the Milky Way and clearly a galaxy in its own right. Hubble went on to discover Cepheids in other nebula and proved that galaxies existed beyond our own.
He began to develop a classification system, sorting galaxies by size, content, distance, shape and brightness. He divided galaxies into elliptical, spiral, barred spiral and irregular. These are subdivided into categories, a, b and c according to the size of the central mass of stars within the galaxy and the tightness of any spiraling arms.

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The Earth’s atmosphere alters light rays from outer space; the Hubble Space Telescope, being above the atmosphere, receives images with far greater clarity and detail than any Earth-based optical instrument and its camera can achieve a resolution ten times greater than the largest Earth based telescope.
Construction began on the HST in 1977 and it was launched by the space shuttle Discovery on 25 April 1990. The instruments can detect not only visible light but also infra-red and ultra-violet.

Hubble noticed that the galaxies appeared to be moving away from the region of space in which the Earth is located. It appeared that the further away a galaxy was, the faster it was receding. The conclusion was that the universe, which had previously been considered static is in fact expanding.

In 1915, EINSTEIN’s theory of relativity had suggested that owing to the effects of gravity, the universe was either expanding or contracting. Einstein knew little about astronomy and had introduced an anti-gravity force into his equations, the cosmological constant. Hubble’s discoveries proved Einstein had been right after all and Einstein later described the introduction of the gravitational constant as ‘the biggest blunder of my life’.

Hubble’s discovery that the universe is expanding led to the development of the ‘big-bang’ model of the universe.

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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’

portrait of NEWTON ©

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.

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 Newton’s genius that allowed him to derive Kepler’s laws of planetary motion from 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

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.

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.

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.

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HEINRICH SCHWABE (1789-1875)

1843 – Germany

‘The number of visible sunspots varies in a regular cycle that averages about 11 years’

image of the Sun from space

GALILEO was the first to study sunspots. Schwabe made careful records of sunspots almost daily for 17 years before announcing his theory. He continued his observations for another 25 years.

Wherever magnetic fields emerge from the sun, they suppress the flow of surrounding hot gases, creating relatively cool regions that appear as dark patches in the sun’s shallow outer layer, the photosphere.

Sunspots vary in size from 1000 to 40,000 kilometres across and may last from a few days to many months.

Near a solar minimum there are only a few sunspots. During a solar maximum, solar flares can produce dramatic changes in the emission of ultraviolet rays and X-rays from the sun.

Hot plasma of several thousand degrees rises upwards from within the Sun, then cools down and sinks back into the depths. Where the strong magnetic fields hold the plasma, dark sunspots emerge.

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GALILEO GALILEI (1564-1642)

1632 – Italy

‘Discounting air resistance, all bodies fall with the same motion; started together, they fall together. The motion is one with constant acceleration; the body gains speed at a steady rate’

Portrait of GALILEO GALILEI ©

GALILEO GALILEI

From this idea we get the equations of accelerated motion:
v = at and s = 1/2at2
where v is the velocity, a is the acceleration and s is the distance traveled in time t

The Greek philosopher ARISTOTLE (384-322 BCE) was the first to speculate on the motion of bodies. He said that the heavier the body, the faster it fell.
It was not until 18 centuries later that this notion was challenged by Galileo.

The philosophers of ancient Greece had known about statics but were ignorant of the science of dynamics.
They could see that a cart moves because a horse pulls it, they could see that an arrow flies because of the power of the bow, but they had no explanation for why an arrow goes on flying through the air when there is nothing to pull it like the horse pulls the cart. Aristotle made the assumption that there must be a force to keep things moving. Galileo contradicted. He believed that something will keep moving at the same speed unless a force slows it down.

He contended that an arrow or a thrown stone had two forces acting upon it at the same time – ‘momentum’ pushes it horizontally and it only falls to the ground because the resistance of the air (a force) slows it down enough for it to be pulled to the ground by another force pushing downwards upon it; that which we now know as ‘gravity’.
This is the principle of inertia and led him to correctly predict that the path of a projectile is a parabola.

His insights were similar to the first two of the three laws of motion that Newton described 46 years later in ‘Principia’. Although he did not formulate laws with the clarity and mathematical certainty of Newton, he did lay the foundations of the modern understanding of how things move.

Galileo resisted the notion of gravity because he felt the idea of what seemed to be a mystical force seemed unconvincing, but he appreciated the concept of inertia and realized that there is no real difference between something that is moving at a steady speed and something that is not moving at all – both are unaffected by forces. To make an object go faster or slower, or begin to move, a force is needed.

Galileo would take a problem, break it down into a series of simple parts, experiment on those parts and then analyse the results until he could describe them in a series of mathematical expressions. His meticulous experiments (‘cimento‘) on inclined planes provided a study of the motion of falling bodies.

He correctly assumed that gravity would act on a ball rolling down a sloping wooden board that had a polished, parchment lined groove cut into it to act as a guide, in proportion to the angle of the slope. He discovered that whatever the angle of the slope, the time for the ball to travel along the first quarter of the track was the same as that required to complete the remaining three-quarters. The ball was constantly accelerating. He repeated his experiments hundreds of times, getting the same results. From these experiments he formulated his laws of falling bodies.
Mathematics provided the clue to the pattern – double the distance traveled and the ball will be traveling four times faster, treble it and the ball will be moving nine times faster. The speed increases as a square of the distance.
He found that the size of the ball made no difference to the timing and surmised that, neglecting friction, if the surface was horizontal – once a ball was pushed it would neither speed up nor slow down.

His findings were published in his book, ‘Dialogue Concerning the Two Chief World Systems’, which summarised his work on motion, acceleration and gravity.

His theory of uniform acceleration for falling bodies contended that in a vacuum all objects would accelerate at exactly the same rate towards the Earth.

Legend has it that Galileo gave a demonstration, dropping a light object and a heavy one from the top of the leaning Tower of Pisa. Dropping two cannonballs of different sizes and weights he showed that they landed at the same time. The demonstration probably never happened, but in 1991 Apollo 15 astronauts re-performed Galileo’s experiment on the Moon. Astronaut David Scott dropped a feather and a hammer from the same height. Both reached the surface at the same time, proving that Galileo was right.

Another myth has it that whilst sitting in Pisa cathedral he was distracted by a lantern that was swinging gently on the end of a chain. It seemed to swing with remarkable regularity and experimenting with pendulums, he discovered that a pendulum takes the same amount of time to swing from side to side – whether it is given a small push and it swings with a small amplitude, or it is given a large push. If something moves faster, he realised, then the rate at which it accelerates depends on the strength of the force that is moving it faster, and how heavy the object is. A large force accelerates a light object rapidly, while a small force accelerates a heavy object slowly. The way to vary the rate of swing is to either change the weight on the end of the arm or to alter the length of the supporting rope.
The practical outcome of these observations was the creation of a timing device that he called a ‘pulsilogium’.

Drawing by GALILEO of the surface of the moon

Galileo confirmed and advanced COPERNICUS‘ Sun centered system by observing the skies through his refracting telescope, which he constructed in 1609. Galileo is mistakenly credited with the invention of the telescope. He did, however, produce an instrument from a description of the Dutch spectacle maker Hans Lippershey’s earlier invention (patent 1608).

He discovered that Venus goes through phases, much like the phases of the Moon. From this he concluded that Venus must be orbiting the Sun. His findings, published in the ‘Sidereal Messenger‘ (1610) provided evidence to back his interpretation of the universe. He discovered that Jupiter has four moons, which rotate around it, directly contradicting the view that all celestial bodies orbited Earth, ‘the centre of the universe’.

‘The Earth and the planets not only spin on their axes; they also revolve about the Sun in circular orbits. Dark ‘spots’ on the surface of the Sun appear to move; therefore, the Sun must also rotate’

1610 – Galileo appointed chief mathematician to Cosmo II, the Grand Duke of Tuscany, a move that took him out of Papal jurisdiction.

1613 – writes to Father Castelli, suggesting that biblical interpretation be reconciled with the new findings of science.

1615 – a copy of the letter is handed to the inquisition in Rome.

1616 – Galileo warned by the Pope to stop his heretical teachings or face imprisonment.

1632 – when Galileo published his masterpiece, ‘Dialogue Concerning the Two Chief World Systems’ – (Ptolemaic and Copernican) – which eloquently defended and extended the Copernican system, he was struggling against a society dominated by religious dogma, bent on suppressing his radical ideas – his theories were thought to contravene the teachings of the Catholic Church. He again attracted the attention of the Catholic Inquisition.
His book took the form of a discussion between three characters; the clever Sagredo (who argues for Copernicus), the dullard Simplicio (who argues hopelessly for Aristotle) and Salviati (who takes the apparently neutral line but is clearly for Sagredo).

In 1633 he was tried for heresy.

‘That thou heldest as true the false doctrine taught by many that the Sun was the centre of the universe and immoveable, and that the Earth moved, and had also a diurnal motion. That on this same matter thou didst hold a correspondence with certain German mathematicians.’
‘….a proposition absurd and false in philosophy and considered in theology ad minus erroneous in faith…’.

Threatened with torture, Galileo was forced to renounce his theories and deny that the Earth moves around the Sun. He was put under house arrest for the rest of his life.

After Galileo’s death in 1642 scientific thought gradually accepted the idea of the Sun-centered solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.

Galileo’s thermoscope operated on the principle that liquids expand when their temperature increases. A thermoscope with a scale on it is basically a thermometer and in its construction Galileo was probably following directions given by Heron of Alexandria 1500 years earlier in ‘Pneumatics’. As with the telescope, Galileo is often incorrectly given credit for the invention of the thermometer.

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PRELUDE

IMHOTEP (c.2650 BCE)

Photograph of King Huni pyramid at Maydoum the 3rd dynasty Old Kingdom at Elfayom (427 x 500) ©

‘Architect of civilisation’

Medical sage, astronomer, mathematician, architect

Architect of the first pyramid built during the reign of the second pharaoh of the Third Dynasty, with the unification of Upper and Lower Egypt.
Came to be revered as a god of healing and identified by the Greeks with their own Aesculapius.

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