Renaissance

Astronomy

Nicholas Copernicus1473 - 1543

(Niklas Koppernigk)

Developed a mathematical model

for a Heliocentric solar system

Nicholas Copernicus

Synodic PeriodThe orbital period of a planet as measured by a

moving observer

Sidereal Period The orbital period of a planet as measured by a

stationary observer

Planet Approximate

Sidereal Period

Mercury 88 days

Venus 7.5 months

Earth 1 year

Mars 687 day

Jupiter 12 years

Saturn 30 years

Nicholas Copernicus

Nicholas Copernicus

Planetary Configurations - Inferior Planets

Nicholas Copernicus

Planetary Configurations - Superior Planets

Planetary Distances

Planet Copernicus Modern

Mercury 0.38 0.387

Venus 0.72 0.723

Earth 1.00 1.000

Mars 1.52 1.520

Jupiter 5.22 5.200

Saturn 9.17 9.540

Tycho Brahe1546-1601

Danish Aristocrat Superb naked eye positions of planets Observations (experiment) can decide

between physical models

Kepler’s Laws

First LawPlanets orbit the Sun in ellipses

with the Sun at one focus of the ellipse

Sun

Planet

Ellipses

Focus Focus

d1 d2

d1 + d2 = constant for any point on ellipse

Ellipses

a = Semi-major axis

b = Semi-minor axis

Eccentricity

a

c

e = c/a

Kepler’s Laws

Second LawA line drawn from the planet

to the Sun sweeps out equal areas in equal intervals of time

The Search for Order

Perfect solids

The Search for Order

Music of the Spheres

Kepler’s Laws

Third LawThe orbital period of a planet

squared is proportional to the length of the semi-major axis cubed.

P2 a3

Using the Third Law

P2 a3

P2 constanta3

P2 a3

P measured in years, a in AU, object orbits Sun

Kepler’s Laws

Empirical Kepler could not explain why the

planets orbited the Sun (he thought it had something to do with magnetism)

Universal

Galileo Galilei1564-1642

Among the first to turn a telescope to the sky Developed the Scientific Method Believed in the popularization of science Developed the Law of Inertia

Telescope Discoveries

Milky Way

Objects exist that Aristotle knew nothing about - the combined light of many faint stars can produce an observable result.

The Moonb Mountains, valleys (Earthlike) features

were observed.b But the Moon was in the Celestial Realm

Telescope Discoveries

Telescope DiscoveriesThe Moons of Jupiter

g Clear example of four objects that do not orbit the Earth.

g If Aristotle was wrong here, could he not also be wrong in other areas?

Telescope DiscoveriesPhases of Venus

The full range of phases cannot happen in the Geocentric Model.

The Phases of VenusGeocentric Model

The Phases of VenusHeliocentric Model

Telescope DiscoveriesSunspots

Showed they were really on the Sun

The Sun was the physical mani-festation of God

Board of Inquisition

The Trial of Galileo

Isaac Newton1642 - 1727

Newton’s Laws

A body continues to move as it has

been moving unless acted upon by an

external force.

The 1st Law

Newton’s First Law

No mention of chemical composition

No mention of terrestrial or celestial realms

Force required when object changes motion

Acceleration is the observable consequence of forces acting

Newton’s Laws

The 2nd Law

The Sum of the Forces acting on a body is proportional to the acceleration that the body

experiences F a

F = (mass) a

Newton’s Laws

For every action force there is an equal and opposite reaction force

(You cannot touch without being touched)

The 3rd Law

Newton’s Universal Gravitation

M m

d

Two masses separated by a distance

Newton’s Universal Gravitation

2d

GMmF

2d

MmF

Newton’s Universal Gravitation

Inverse Square Law

Separation Force

R F

2R ¼F

3R 1/9F

½R 4F

¼R 16F

Newton’s Universal Gravitation

The force of gravity cannot be made zero.

G is small

•6.67 X 10-11 N m2/kg2

Mass causes gravity

•Only one kind of mass

•Contrast with the electric force

The Apple

2

R

mGMF

m

M

mgR

mGM

2

2

R

GMg

Gravity at Work

All objects fall at the same rate in a gravitational field.T Leaning Tower of Pisa - GalileoT Galileo’s Experiment on the MoonT Apparent weightlessnessT Lack supporting force

Orbiting Falling without getting closer

to the ground.T Newton’s estimate of orbital velocity

Examples:T Space ShuttleT ElevatorT Amusement Park Rides

The Earth and Moon

F

2R

mGMF

Earth

Moon

Rma

R

mGM

2

G

aRM

2

Orbiting - the Complete Story

< vorb Ellipse

Circle

vorb Circle

Ellipse

vorb<v<vesc Ellipse

Velocity Shape

Parabola

vesc Parabola Hyperbola

> Vesc Hyperbola

Link

Where was Newton Wrong?

Moving too fast Close to the speed of light Solution was Special Relativity (1905)

Too close to a large gravitational field Solution was General Relativity (1917)

On very small scales Inside the atom Solution was Quantum Mechanics (1927)

The Principle of Elegance

Physicists look for symmetry

• Occam’s Razor

End of Renaissance Astronomy