phys 3380 - astronomy exam wednesday september 21 the exam will cover anything that was covered in...

PHYS 3380 - AstronomyExam Wednesday September 21

The exam will cover anything that was covered in the notes

The exam will be closed book.

You will be allowed to have one 8/12 X 11 sheet of notes for the exam.

Good Luck!

PHYS 3380 - Astronomy

Hipparchus (c. 190 - 120 B.C.)-placed Earth away from center of perfect spheres

- developed a star catalog

- method to predict positions of sun and moon

- discovered precession of earth’s axis of rotation - estimated precession of equinoxes at 46”/year - actually 50.26”

Ptolemy (c. A.D. 100 - 170)

- combined all available astronomical information into 13 volume work, the Almagest - a geometrical model of solar system with Earth in center that predicted positions of Sun, Moon and planets - used for 1,500 years

- used idea of Apollonius (c. 240 - 190 B.C.) that planets move on small circle that turns upon larger circle around the Earth explained retrograde motion of planets - fully developed by Hipparchus - accurately predicted planetary positions within a few degrees of arc


Retrograde Motion of Planets

Apparent retrograde motion - reversal of planetary motion through the zodiac from eastward to westward

Apparent retrograde motion of Jupiter


Ptolemaic Model

Deferent - main circle of planet path

Epicycle - small circles on deferent along which planet moved


Ptolemaic Model Animation


Ptolemy's model of the motions of the Sun, Moon, and planets around Earth.


Mars Retrograde Motion

Earth’s orbital speed is faster than Mars’. When Earth catches up with Mars, Mars appears to move backwards against the background of the stars


Mars Retrograde Motion Animation


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 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 -ratio between distance from the center of the ellipse to the focus of the ellipse and the semi-major axis.


€

x 2

a2+y 2

b2=1

or

x = acos t

y = bsin t

0 ≤ t < 2π

The eccentricity is :

e = 1-b2

a2=c

a


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

Kepler’s Second Law


Area and Time 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


Planet Semimajor

Axis (1010 m)

Period

(T yr)

T2/a3

(10-34 y2/m3)

Mercury 5.79 0.241 2.99

Venus 10.8 0.615 3.00

Earth 15.0 1 2.96

Mars 22.8 1.88 2.98

Jupiter 77.8 11.9 3.01

Saturn 143 29.5 2.98

Uranus 287 84 2.98

Neptune 450 165 2.99

Pluto 590 248 2.99

PHYS 3380 - AstronomyNote:

- Kepler's third law needs to be modified when the orbiting body's mass is not negligible compared to the mass of the body being orbited.

- Kepler's laws assume a two-body system - particularly bad approximation in the case of the Earth-Sun-Moon system

for calculations of the Moon's orbit, Kepler's laws are far less accurate than the empirical method invented by Ptolemy.

- Kepler's laws do not consider the emission of radiation or relativity

- Because electrical forces, like gravity, obey an inverse square law, Kepler's laws also apply to bodies interacting electrically.

Kepler did not understand why his laws were correct - Isaac Newton discovered the answer more than fifty years later. For instance, the second law also a statement of conservation of angular momentum.


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


A New View of Nature

Sir Isaac Newton (1642 - 1727)

- followed Galileo’s lead - developed fundamental laws of motion - revolutionized mathematics and science

- experienced moment of inspiration at 24 years old - saw apple fall from tree and suddenly understood gravity

- published most famous book in science in 1687 - Philosophiae Naturalis Principia Mathematica - Principia for short

- built first reflecting telescope

- invented calculus

- discovered three laws of motion

- discovered universal law of mutual gravitation


First law:

A body remains at rest or moves along a straight line with constant velocity so long as no external force acts upon it.

Second law:

A body (m) acted upon by a force (f) will accelerate (a) in the direction of the applied force. The greater the force or the smaller the mass, the greater will be the acceleration .

F =ma

Third law:

A body subjected to a force reacts with an equal counter force to the applied force: That is, action and reaction are equal and oppositely directed, but never act on the same body.

Newton's Three Laws of Motion


1st LawA body moves along a straight line with constant velocity so long as no external force acts upon it.

2nd LawForce equals mass times acceleration

3rd LawFor every force, there is an equal and opposite force


Velocity and Acceleration

Newton showed that acceleration (a) is the change of a body’s velocity (v) with time (t):

1. Acceleration in the conventional sense (i.e. increasing speed)

a = Dv/Dt

Differential calculus!

Different cases of acceleration:

Velocity and acceleration are vectors.

3. Change of the direction of motion (e.g., in circular motion)

2. Deceleration (i.e. decreasing speed)

a

v


Feather and Hammer Movie

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.

phys 3380 - astronomy exam wednesday september 21 the exam will cover anything that was covered in...

Documents

planetary motion

planetary positions

heavenly motion

orbited earth

placed earth

terms of earth

planetary system

planets orbited sunphys