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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”

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

Lady with an ermine, Vinci

The drape of the alb is basic

More liberal period

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

Rediscovery of sculpture

Middle Age bas-relief

Figures hardly stick out of the stone

Gothic art

David, Michelangelo

Perfect knowledge of the human body

Greek art

A time of conquests and adventure

Magellan’s travel around the Earth: 1519

Europe was ready for the birth of modern science

Young Frankenstein

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

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)

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

Very complex calculations !

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











A overtakes B. What does A see of B?

B seems to be moving backward



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

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

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?










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.

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

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

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

Anyway astronomers had no telescope…

Tycho Brahe (1546 – 1601)

Born three years after Copernicus’ death

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

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

Five planets orbiting around the Sun

He believed in a modified geocentric model




All planets orbit around the Sun but the Earth!

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)

Theology student

Became convinced that all the planets are actually orbiting the Sun

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

The orbit of a planet is an ellipse


top view



How to draw an ellipse?

Position of the Sun



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?

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

Semimajor axis

Which of the following ellipses has the largest semimajor axis?

Which of the following ellipses has the largest semimajor axis?

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


Experiment: stool and weights

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

Where is this comet the fastest?


Where is this spacecraft the fastest?


Kepler’s third law

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


a: semimajor axis, in AU

a3 = P2

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?








Closer to the Sun

Which planet has the longest orbital period?







Farther away from the Sun


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

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

R) Earth

S) Mars

T) Venus

U) Mercury



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