NATS 1311 - From the Cosmos to Earth Nicholas Copernicus (1473-1543) - wanted better way to predict planetary positions - adopted Sun-centered planetary

NATS 1311 - From the Cosmos to Earth

Nicholas Copernicus (1473-1543) - wanted better way to predict planetary positions - adopted Sun-centered planetary system suggested by Aristarchus

- worked out simple geometric relationships that allowed calculation of planet’s true orbital period and distance from Sun in terms of Earth-Sun distance (AU)

- still believed that heavenly motion must still be perfect circles - had to add circles upon circles as in the Ptolemaic model - did not make substantially better predictions and was not accepted for another 50 years

Heliocentric World View - The Copernican Revolution


Tycho Brahe (1546 - 1601) - observed alignment of Jupiter and Saturn in 1563 - occurred two days later than Copernicus prediction - decided to compile precise measurements of stellar and planetary positions

- compiled best set of naked-eye observation ever made - to within 1 arcminute (thickness of a fingernail at arm’s length)

- observed supernova of 1572 - proved it was farther away than the Sun - called it a nova (“new star”)

- observed comet - proved was in the heavens

- believed planets must orbit Sun but never succeeded in explaining planetary motion. Inability to detect stellar parallax led him to believe that Sun orbited Earth while all other planets orbited Sun


A Complete Reformation of Astronomy

Johannes Kepler (1571 - 1630)

- hired by Tycho Brahe to explain observations

- years of calculations trying to find circular orbit for Mars that matched Tycho’s observations - succeeded in matching Mars’ position in ecliptic - could not match position north or south of ecliptic

- finally realized planetary orbits were not circular but elliptical - developed three laws of orbital motion - accurately predicted planetary motions and matched Tycho’s data


:

Law 1: Law of elliptical orbits

Each planet moves in an elliptical orbit. Law 2: Law of areas

The imaginary line connecting any planet to the sun sweeps over equal areas of the ellipse in equal intervals of time.

Law 3: Law of periods

The square of any planet's period of orbital revolution is proportional to the cube of its mean distance from the sun.

Kepler’s Laws of Planetary Motion


Kepler’s First Law

The orbit of each planet around the Sun is an ellipse with the Sun at one focus


(a) Drawing a circle.

(b) Drawing an ellipse.

(c) Eccentricity

describes how much an ellipse deviates from a perfect circle.


Drawing an Ellipse Animation


Eccentricity and Semi-Major Axis Animation


As a planet moves around its orbit, it sweeps out equal areas in equal times.

Kepler’s Second Law


Area and Time Animation


Velocity vs Orbit Animation


The square of any planet's period, P, of orbital revolution is proportional to the cube of its mean distance, r, from the sun.I.e., the more distant a planet, the slower it moves on average.

Example:For earth, r E= 1 AU, PE = 1 year.For Mars, r M= 1.52 AU, PM = 1.88 years

€

PM2

PE2 =

rM3

rE3

1.882

12 =1.523

13

3.53≅3.51

Kepler’s Third Law


A plot of the cube of the averageplanetary distance vs the squareof the orbital period is a straightline

The average orbital speed isinversely proportional to theaverage distance from the sun


Orbital Period vs Distance Animation


Galileo Galilei (1564 - 1642)- demonstrated that a moving object remains in motion unless acted on by an outside force (Newton’s 1st law) - contradicted Aristotle’s claim that the natural tendency of any moving object is to come to rest. Birds, falling stones, clouds, etc.. would stay with the Earth unless knocked away by some force

- used telescope that he built (invented by Hans Lippershey) - - saw sunspots on the Sun, craters and valleys on the moon - proved that the heavens were not perfect and unchanging - observed moons orbiting Jupiter- observed the phases of Venus- showed that Milky Way resolved into countless

individual stars - argued stars far more numerous and distant than imagined - reason stellar parallax not observed

- recanted before Church inquisition in Rome in 1633 - formerly vindicated by the Church in 1992

The Death of the Earth Centered Universe


Major Discoveries of Galileo

• Moons of Jupiter

(4 Galilean moons)

• Rings of Saturn

(What he really saw)

(What he really saw)


• Surface structures on the moon - shadows; first estimates of the height of mountains on the moon


Sun spots (proving that the sun is not perfect!)


Phases of Venus (including “full Venus”) - In the Ptolemaic system, phases would only range from new to crescent. Proved that Venus orbits the sun, not the Earth!


Phases of Venus Animation


Speed, Velocity, and Acceleration

Speed - rate of travel - distance per unit timeVelocity - speed of travel in a certain direction

- a vector - has magnitude and directionAcceleration - rate of change of velocity - change in velocity per unit time


Acceleration of Gravity

All objects in a gravitational field fall at a constant acceleration - g -regardless of mass

On Earth - g=9.8 m/s2 or 32 ft/s2

On the Moon - g=1.63 m/s2 or 1/6th that of Earth

Calculate height of building -drop a rock and time

‘ its fall - h=1/2gt2


Gravity and Acceleration Animation

Galileo demonstrated that acceleration of gravity is independent of the mass of the falling object - supposedly dropped balls of different mass from Leaning Tower of Pisa - Newton showed why.



Feather and Hammer Animation

Documents

NATS 1311 - From the Cosmos to Earth Nicholas Copernicus (1473-1543) - wanted better way to predict planetary positions - adopted Sun-centered planetary