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Day 4 Chapter 2 Gravitation and the

Motion of the Planets

Science is the key to understanding

- Science a body of knowledge and a process of

learning about nature (called the scientific

method). - Knowledge is acquired by observations and

experiments. - Scientific method is a process for gaining more

knowledge, that can be tested and accepted by

everyone. - Scientific theory is an explanation of

observations or experimental results that can be

described quantitatively and tested. - The theory must make testable predictions that

can be verified by new observations or

experiments, and can possibly be refuted. - Theories can be modified and should be the

simplest version that explains the observations

(Occams razor). - Observe, hypothesize, predict, test, modify,

economize.

The Copernican Revolution

- The model of the Greeks (attributed primarily to

Ptolemy) had the Earth at the center of

everything. - Copernicus proposed a model of the solar system

with the Sun at the center (hence a solar

system). - Galileo made a telescope and used it to view the

sky, and saw that the phases of Venus refuted the

geocentric model of the Greeks. - Tycho Brahe and Johannes Kepler developed a more

detailed heliocentric model with elliptical

orbits.

Retrograde motion of a planet occurs over several

weeks, and involves motion to the west, as

compared to prograde (direct) motion, which is

to the east (relative to the stars of the

celestial sphere).

The Geocentric Model of planetary motion (Greek

philosophy)

The Geocentric Model does explain retrograde

motion, using concepts like deferent and

epicycle. However, it does not predict the

motion with much accuracy, and does not predict

phases of Venus (seen with a telescope).

Ptolemys Model of planetary motion used

deferents (big circles) and epicycles (little

circles centered on a point that moves on the

deferent). This involved up to 80 circles to

describe 7 objects!

Occams Razor says Simplify this!

Nicholas Copernicus and his Heliocentric model of

the Solar System explained this in a simpler way

with the Sun at the center.

Retrograde motion is seen in this model, using

Earth and Mars as the example.

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Retrograde Motion of Mars as seen from Earth

Galileo Galilei and the Birth of Modern

Astronomy Galileo built a telescope in 1609 and

looked at the sky.

Four objects The Moon The Sun Jupiter Venus

(and much more)

Galileo looked at the Moon and saw mountains,

craters, valleys, and topography like you might

find on the Earth. The Moon was perhaps an

object like the Earth!

By projecting an image of the Sun, he could see

imperfections on the Sun. Sunspots could be seen

to move from east to west on the Sun and he

deduced that the Sun rotated about once a month.

Galilean Moons of Jupiter Small point of light

could be seen near Jupiter. By observation

during several weeks he deduced that these were

moons and that they revolved around Jupiter.

Perhaps this planet was like the Earth, with

several moons of its own. It also seemed like

a miniature model of the heliocentric solar

system.

Venus Phases in the Heliocentric model These are

consistent with the observations in a telescope.

Venus Phases in the Geocentric model are

obviously wrong as soon as you observe with a

telescope. This refutes Ptolemy!

Both described the positions and movement of the

Sun, Moon, and 5 visible planets, as seen without

a telescope. The geocentric theory was too

complicated (80 circles!). (Occams razor could

be invoked to seek a simpler way.) Once the

telescope was used to observe Venus, the

geocentric theory could not explain the phases of

Venus. The heliocentric theory of Copernicus

explained many of Galileos observations, but

also used circular orbits. More accurate

measurements did not agree with the simple theory

of Copernicus (circles had to be replaced by

ellipses in the newer theory of planetary

motion).

Geocentric vs. heliocentric theories

After Copernicus and Galileo, two major

figures changed the way we come to understand

the Universe Keplers laws of planetary

motion Newtons laws of mechanics

More detailed observations were made by Tycho

Brahe (commonly called Tycho, 1546 - 1601). He

made observations of a supernova in 1572 which

convinced him that it was a distant star. He

received an island and built an observatory to

measure planetary motion to high accuracy over a

period of more than 20 years. His observations

were inherited by an assistant, Johannes Kepler,

when Tycho died in 1601.

Further development of the heliocentric theory

Tycho Brahe obtained data over a period of 21

years that were later used by his assistant

Johannes Kepler to determine that planetary

orbits are NOT circles, but are ellipses.

Johannes Kepler and the Laws of Planetary Motion

Kepler used decades of Tychos observations in

his mathematical calculations, to determine the

shape of the planetary orbits, and the speed of

the planets as they went around the Sun. This

massive effort resulted in three major statements

about the characteristics of planetary orbits

Keplers three laws of planetary motion.

Keplers three laws of planetary motion

- Orbital paths of the planets are ellipses.
- An imaginary line connecting the planet with the

Sun sweeps out equal areas of the ellipse in

equal intervals of time. - The square of a planets orbital period is

proportional to the cube of its semi-major axis.

- Kepler published this in 1609, the same year that

Galileo built his first telescope.

Keplers first law The orbital paths of the

planets are elliptical, with the Sun at one

focus. Keplers second law An imaginary line

connecting the Sun to any planet sweeps out equal

areas of the ellipse in equal intervals of

time. Keplers third law The square of the

planets orbital period is proportional to the

cube of its semimajor axis.

Keplers laws of planetary motion

An Ellipse can be drawn with string and TWO foci

For an ellipse, r1 r2 2a The

eccentricity is defined as e c/a A

circle results when e 0 GeoGebra

demonstration http//people.ucalgary.ca/louro/

geogebra/ellipse.html

Some Properties of Planetary Orbits

Keplers first law The orbital paths of the

planets are elliptical, with the Sun at one

focus. Keplers second law An imaginary line

connecting the Sun to any planet sweeps out equal

areas of the ellipse in equal intervals of

time. Keplers third law The square of the

planets orbital period is proportional to the

cube of its semimajor axis.

Keplers laws of planetary motion

Keplers Second Law equal areas in equal

time This also means higher speed at closer

distances.

Another graphic on Keplers Second Law

The Astronomical Unit is about 150,000,000 km

Keplers first law The orbital paths of the

planets are elliptical, with the Sun at one

focus. Keplers second law An imaginary line

connecting the Sun to any planet sweeps out equal

areas of the ellipse in equal intervals of

time. Keplers third law The square of the

planets orbital period is proportional to the

cube of its semimajor axis.

Keplers laws of planetary motion

Keplers Third Law P2 (in years) a3 (in

a.u.) Basically, it means that large orbits have

long periods.

Real orbits have the center of mass as one

focus For the Sun and planets, this is not a

large effect. For binary stars, the center of

mass may be near the middle of the line

connecting them.

Lets review Keplers Laws. Review see if you

can tell what these are simulating

http//webphysics.davidson.edu/physlet_resources

/bu_semester1/c17_kepler2.html http//webphysics.

davidson.edu/physlet_resources/bu_semester1/c17_pe

riods_sim.html http//webphysics.davidson.edu/phy

slet_resources/bu_semester1/c17_solar_sim.html

Newtons Laws of Physics

- First law inertia
- Second law F ma
- or acceleration force / mass
- Third law Action and Reaction
- means that forces occur in pairs.
- These can be used to show that orbits should obey

Keplers 3 laws.

Isaac Newton developed a quantitative and

explanatory theory of mechanics, explaining the

motion of objects resulting from forces.

Newtons Second Law F ma The acceleration of

a mass is proportional to the total force acting

upon it, and inversely proportional to the mass

of the object.

Newtons First Law The law of inertia. An

object will continue in its motion without

change of velocity unless it is acted on by a

net external force.

Newtons Third Law Action-reaction For every

force acting upon an object (action), there is a

force acting on another object (reaction) which

has the same magnitude (size) but points (acts)

in the opposite direction.

Newton also developed the universal law of

gravity. Gravitational force varies with the

distance between the objects. It depends on the

product of the two masses, i.e., m1 x m2 and

on the inverse of the square of the distance

between the masses (assuming they are small

compared with the distance). 1/r2

The Suns gravity causes planets to move on a

path called an orbit. These orbits obey

Keplers Laws.

- Newtons Laws explain Keplers Laws
- Newtons Laws account for all three of Keplers

Laws. - The orbits of the planets are ellipses, but it is

also possible to have orbits which are parabolas

or hyperbolas. (conic sections) - Edmond Halley predicted a comet would return in

1758 and every 76 years after that. (seen in

1910, 1986, and will return in 2061) Halleys

comet has an elliptical orbit extending out past

Neptune. - William Herschel discovered Uranus in 1781 by

accident. - After 50 years it was seen to deviate from an

elliptical orbit, and a calculation led to the

discovery of Neptune in 1846. - To be precise, elliptical orbits would only occur

if there were only the Sun and one planet. There

are 8 planets and other objects which cause

deviations from the perfect elliptical orbit.

The first exam is on Thursday, Feb. 4 (next

week!) We will have about 30 minutes of class

before the exam. Then you will take the exam

(which uses a Scantron). The exam is multiple

choice and true/false questions. Coverage is

Chapters 1 and 2 in your textbook. To review,

look at the chapter summaries, my day notes, and

a study guide that I will post this weekend.