2 5 renaissance naissance birth
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2-5 Renaissance “naissance” = “birth”. The belief that the cosmos is ultimately understandable slowly emerges again. Revival of art. The Birth of Venus, Botticeli, 1485. Rediscovery of perspective (and geometry). Delphic Sybil, Michelangelo,1510 - 1512. Rediscovery of light.

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2-5 Renaissance “naissance” = “birth”

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2 5 renaissance naissance birth

2-5 Renaissance“naissance” = “birth”

The belief that the cosmos is ultimately understandable slowly emerges again


Revival of art

Revival of art

The Birth of Venus, Botticeli, 1485


2 5 renaissance naissance birth

Rediscovery of perspective (and geometry)


2 5 renaissance naissance birth

Delphic Sybil, Michelangelo,1510 - 1512


2 5 renaissance naissance birth

Rediscovery of light

Lady with an ermine, Vinci


2 5 renaissance naissance birth

The drape of the alb is basic


2 5 renaissance naissance birth

More liberal period

The creation of the planets, the Sun and the Moon, Michelangelo


2 5 renaissance naissance birth

Rediscovery of sculpture

Middle Age bas-relief

Figures hardly stick out of the stone


2 5 renaissance naissance birth

Gothic art


2 5 renaissance naissance birth

David, Michelangelo

Perfect knowledge of the human body

Greek art


2 5 renaissance naissance birth

A time of conquests and adventure

Magellan’s travel around the Earth: 1519


2 5 renaissance naissance birth

Europe was ready for the birth of modern science

Young Frankenstein


Giordano bruno 1548 1600

Giordano Bruno (1548 – 1600)

Early champion of the heliocentric model: “the Sun, not the Earth, is the centre of the universe”

Also believed:

In the existence of inhabited planets

That the universe is infinite

But before all, dreamt of a radical reform of Christianity


2 5 renaissance naissance birth

Bruno went to Rome to convince the Pope himself!

?

1600: Bruno was burnt by the Holy Inquisition

Often portrayed by scientists as a martyr of science


Nicolas copernicus 1473 1543

Nicolas Copernicus (1473 – 1543)

Priest interested in mathematics and astronomy

Understood that stellar parallax is not observed because stars are too far

Goal: to predict the position of the planets


Ptolemy s geocentric model

Ptolemy’s geocentric model

Very complex calculations !


2 5 renaissance naissance birth

Copernicus proposed a simplified mathematicalmodel in which the Earth was orbiting the Sun


2 5 renaissance naissance birth

Mars

Earth

Moon

Jupiter

Saturn

Venus

Mercury

Sun


2 5 renaissance naissance birth

A

B

A overtakes B. What does A see of B?

B seems to be moving backward


2 5 renaissance naissance birth

A

B

Now B overtakes A. What does A see of B?

B is moving forward

A: “B has moved back and forth”


He could reproduce the retrograde motion of mars in very simple manner

He could reproduce the retrograde motion of Mars in very simple manner

Like in a car race, the Earth is sometimes overtaking Mars, giving us the impression that Mars is moving backward


2 5 renaissance naissance birth

Copernicus also deduced that the nearer a planet is to the Sun, the greater its orbital speed

Mercury orbits at a higher speed than Mars


Which planet has the smallest orbital speed

Which planet has the smallest orbital speed?

Jupiter

Earth

Mercury


2 5 renaissance naissance birth

Jupiter

Earth

Mercury


2 5 renaissance naissance birth

Jupiter

Earth

Mercury


2 5 renaissance naissance birth

Copernicus was a priest and had no intention to contradict the Scriptures

He did not claim his model described the actual motion of the Earth. It was just a mathematical trick.


2 5 renaissance naissance birth

Nevertheless, he chose to publish his De Revolutionibusafter his death

His model: no better accuracy than Ptolemy’s => was not widely accepted until more than a century


2 5 renaissance naissance birth

People were not ready to believe that the Earth was moving

They argued that if the Earth were rotating, we would feel its motion


Some even claimed that a rotating planet would fly into pieces

Some even claimed that a rotating planet would fly into pieces


2 5 renaissance naissance birth

At that time, logical reasoning had more weight than any observation or experiment

Anyway astronomers had no telescope…


Tycho brahe 1546 1601

Tycho Brahe (1546 – 1601)

Born three years after Copernicus’ death


2 5 renaissance naissance birth

Established a fine astronomical observatory on the North Sea island of Hven


2 5 renaissance naissance birth

He made a continuous record of the position of the Sun, Moon and planets for almost 20 years

Found that the predictions of Ptolemy’s model were inaccurate

Tycho measuring the altitude of a celestial object, 1587


2 5 renaissance naissance birth

Five planets orbiting around the Sun

He believed in a modified geocentric model

Sun

Earth

Moon

All planets orbit around the Sun but the Earth!


2 5 renaissance naissance birth

In 1597, Brahe’s patron the Danish King Frederick II died

Brahe had to find a new job…

He became court astronomer to the Emperor Rudolf of Bohemia, in Prague, Austria

There he met a diligent assistant: Johannes Kepler


Kepler 1571 1630

Kepler (1571 - 1630)

Theology student

Became convinced that all the planets are actually orbiting the Sun


2 5 renaissance naissance birth

Brahe was reluctant to give full access to data to Kepler, fearing his bright assistant would discover the secret of the universal motion

When Brahe died, Kepler got full access to Brahe’s records, that he studied for more than 20 years

At the age of 38, he finally published his first results


Kepler s first law

Kepler’s first law


2 5 renaissance naissance birth

The orbit of a planet is an ellipse

ecliptic

top view

Sun

planet


How to draw an ellipse

How to draw an ellipse?

Position of the Sun

Focus

Focus


2 5 renaissance naissance birth

Eccentricity of an ellipse: e

An ellipse which does not differ much from a circle is not “very eccentric”

e is close to zero

An ellipse which is very elongated has an eccentricity close to 1


The eccentricity of the earth s orbit is 0 017 what is its shape

The eccentricity of the Earth’s orbit is 0.017. What is its shape?


2 5 renaissance naissance birth

Very similar to a circle

Caution: same orbit seen from two different points of view

Top view

Side view


A semimajor axis of an ellipse

a: semimajor axis of an ellipse

Semimajor axis


Which of the following ellipses has the largest semimajor axis

Which of the following ellipses has the largest semimajor axis?


Which of the following ellipses has the largest semimajor axis1

Which of the following ellipses has the largest semimajor axis?


Kepler s second law

Kepler’s second law

A planet:

Speeds up as it comes closer to the Sun

Slows down as it moves away from the Sun

Lowest speed

Highest speed

Sun


2 5 renaissance naissance birth

Experiment: stool and weights


2 5 renaissance naissance birth

Kepler’s laws also apply to a satellite orbiting the Earth


Where is this comet the fastest

Where is this comet the fastest?


2 5 renaissance naissance birth

Sun


Where is this spacecraft the fastest

Where is this spacecraft the fastest?


2 5 renaissance naissance birth

Earth


Kepler s third law

Kepler’s third law

P: orbital period (time needed for one revolution), in years

a

a: semimajor axis, in AU

a3 = P2


2 5 renaissance naissance birth

The farther away a planet, the smaller its speed, and the longer it takes to orbit the Sun


Which planet has the largest orbital speed

Which planet has the largest orbital speed?

Mercury

Mars

Jupiter


2 5 renaissance naissance birth

Mercury

Mars

Jupiter


2 5 renaissance naissance birth

Mercury

Closer to the Sun


Which planet has the longest orbital period

Which planet has the longest orbital period?

Mercury

Mars

Jupiter


2 5 renaissance naissance birth

Mercury

Mars

Jupiter


2 5 renaissance naissance birth

Farther away from the Sun

Jupiter


2 5 renaissance naissance birth

Kepler knew the orbital periods of the planets (P)

He could estimate the distance from each planet to the Sun (a), in AU

This was a nice model, but yet it did not explain why the planets were orbiting the Sun

Meanwhile, a genius was at work in Florence, Italy…


Self assessment

Self assessment


2 5 renaissance naissance birth

11 - Which planet takes the longest time to orbit the Sun?

R) Earth

S) Mars

T) Venus

U) Mercury


Answers

Answers

NUMISMATICS


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