Earth’s position in space – how has it changed over
thousands of years….
Background:
• Pre-1500’s – Geocentric model of the universe (Earthcenter)
•Models were generally wrong because they were
based on wrong “first principles”, believed to be
“obvious” and not questioned:
1.
Geocentric Universe: Earth at the Center of
the Universe.
•1500’s Nicolaus Copernicus challenged the Geocentric
model of the solar system. He described a HELIOCENTRIC
(sun-centered) model of the solar system, which placed
Earth and the other planets in circular orbits. He
proposed that all planets orbit in the same direction, but
each planet orbits at different speed and distance from
the Sun.
•1600’s Galileo Galileo’s observations confirmed a
Copernicus’ model.
Earth’s position in space – how has it changed over thousands of years….
• Johannes Kepler used Tycho Brahe’s observations in mathematical terms and
Developed the 3 Laws of Planetary motion.
•
Kepler’s First Law of Motion – Planet move
around the sun in ellipses with the sun at
one focus. An ellipse is an oval-shape
geometric figure whose shape is determined
by two points with the figure. Each point is
called “focus”. In the solar system, the Sun
is at one focus of the orbit of each planet;
the second focus is empty .
•
Eccentricity – is the amount of flattening of
an ellipse, or how much the shape of the
ellipse deviates from a perfect circle. A
circle which has only one central focus has
an eccentricity of 0. The greater the
eccentricity, the less circular the ellipse.
Essential Question: How has Earth’s Position Changed over Time?
Kepler’s first law:
You will examine this by drawing 3 ellipses with foci that are at different distances apart.
(0.5 cm, 2 cm, and 4 cm)
Hypothesis:
•If the distance between foci ___________, then the eccentricity _________, because
_______________________________________________________________________
Procedure:
1. Obtain a piece of string approximately 12-14 cm long. Tie the ends
Of the string into a loop about 6-7 cm across.
2. Fold the “drawings” paper in thirds, then flatten it out. The folds
Divide the paper into spaces where you will draw and compare ellipses.
Measure and mark two dots 0.5 cm apart in the center of the top third,
mark two more 2 cm apart in the middle third, and in the bottom third,
Make two dots 4 cm apart.
3. Put the paper over the cardboard, and push thumbtacks into one set
of points, far enough to be firm, but not flat against the paper. These
are the ellipses foci. Put the string around the foci, pulling the string
tight against the tacks. Have one partner hold the tacks steady if needed.
4. Repeat step 3, for the other two set of foci. It is okay If the ellipse goes
off the paper at the top and bottom, as long as the major-semi axis (across the tacks) is on the paper.
Put some scrap paper down so You don’t draw on the desk.
Kepler’s first law continued….
5. Calculate the Eccentricity(“out-of-roundness)
Eccentricity – is the amount of flattening of an ellipse, or how much the shape of the ellipse deviates
from a perfect circle. A circle which has only one central focus has an eccentricity of 0. The
greater the eccentricity, the less circular the ellipse.
a.
b.
c.
Measure the distance between thumbtacks for each ellipse. Put the data in the chart below (a)
Draw a line across the foci to the edges of the ellipse. This is the major axis. Measure that (b)
Calculate the eccentricity (c). Eccentricity (e)=F÷A. It should be between 0 and 1. SHOW ALL
WORK IN THE DATA TABLE!
Why does the elliptical eccentricity have no units? ___________________________
____________________________________________________________________
Ellipse
(a)Distance between
foci (mm)
(b)Length of major
axis (mm)
A
B
C
6. Look at the planet table in the back of your textbook
Which planet has the most elliptical orbit?
Which planet has the most circular orbit?
(c) Eccentricity : a÷b
Show all work!
Which is roundest?
Least roundest?
Kepler’s first law continued…
7. Because a planet’s orbit is elliptical, its distance from the Sun varies throughout its “year”
(one revolution around the Sun). Label the points that represent perihelion and aphelion
on the ellipse diagram below.
Answer the following questions:
a. Earth is at perihelion on ______________;
on that date, Earth is approximately
___________km from the sun.
b. Earth is at aphelion on ______________;
on that date, Earth is approximately
___________km from the sun.
c. Based on your understanding of Kepler’s
First law, explain why the distance from a
Planet to the Sun is typically given as an
AVERAGE DISTANCE.
Equal Area …Equal Time?
•
Kepler’s second law of motion states that a line drawn from the Sun to a planet sweeps equal area in equal
time. A planet’s orbital velocity (speed at which it travels around the Sun) changes as its position in its
orbit changes. Its velocity is fastest when it is closest to the Sun and slowest when it is farthest from the
Sun.
1. If Area A = Area C on the diagram, what can be
inferred about the orbital velocities as the planet
travels along its orbit through area A compared to area
C? Which is faster?
2. A planet’s orbital velocity is fastest at the position
it orbits called Perihelion/Aphelion (circle on). During
what season (in the northern hemisphere) is Earth at
this position?________________ Therefore, Earth moves
Fastest/Slowest (circle one) in the summer than in the
winter, so summer in the Northern hemisphere must be
Longer/Shorter (circle one) than winter.
Kepler’s third law of planetary motion…..
Kepler’s 3rd Law relates a planets period of revolution (the time it takes to complete on
orbit of the Sun) to its average distance from the Sun. Kepler determined the mathematical
Relationship between period and distance and concluded that the square of the planet’s period is
proportional to the cube of its mean distance from the Sun. The formula used to determine this
relationship for any planet is T2=R3, where T is the planet’s period in Earth years and R is the
planet’s mean distance from the Sun in astronomical units (AU, where 1 AU equals the mean
distance from the Earth to the Sun =150 million km).
Sample problem: Planet X has an average distance from the Sun of 1.76AU. What is the planet’s
period of revolution, in Earth years?
T2=R3
T2=(1.76)3
T2=5.45
T = 5.45
T = 2.33 Earth years
Calculate the period
of revolution of each
of the following planets
Planet
Mean distance to
Sun (AU)
Mercury
0.387
Mars
1.524
Saturn
9.539
Pluto
39.440
Planet Unknown
1
Period of
Revolution
(Earth years)
Haley's Comet's last appearance was in 1986, and its average period of revolution around the
Sun is 76 years. What is Haley’s Comets average distance from the Sun (in AU)? Calculate the
average distance of Haley’s Comet in AU and SHOW ALL YOUR WORK!
Earth’s Motions
1,000 mph. The Earth rotates on
its axis, and we rotate along with it
Speeds in highest at the equator.
26,000 years. The earth isn't perfect--it has a
wobble! When a top spins we can see it vary
its spin a little with a wobble. The earth does
the same as it spins on its axis. It is, however,
a very slow wobble. It takes approximately
26,000 some years to occur and this motion is
known as Precession
Earth’s Motions
Earth’s Revolution – 67,000 mph:
The Earth circles the sun once a year as it
completes the 587 million mile orbit
The Earth is located about
30,000 Ly from the center of
the Milky Way Galaxy (which
is 100,000). We travel
500,000 mph around the
black hole located at the
center of the galaxy. At this
rate it takes approximately
250 million years to make
one complete revolution.
1,300,000 mph – The Milky
Way galaxy is speeding out
into space! WOW! We have
traveling partners – our Local
Group (a group of about 4
large galaxies and 30 small
galaxies). We are hurling
toward our sister galaxy, the
Andromeda Galaxy at about
290,000 mph and will collide
with it in a couple billion
years!
The Milky Way Galaxy the size of
Universe until the 1920’s
The Milky Way Galaxy is a giant disk of
stars 100,000 light-years across and
1,000 light-years thick.
The Sun is located at the edge of a spiral
arm, 30,000 light-years from the center
It takes 250 Million years for the Sun to
complete one orbit
There are over 100 Billion stars in the Milky
Way
The Spiral arms are only 5% more dense
than average, and are the locations of new
star formation
Before 1929 – the Universe was only the
Milky Way…Hubble Discovered….More
galaxies than the Milky Way
1920’s
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Big Bang Theory 1920’s… Lemaitre (just ideas needs evidence)
Evidence #1 - Hubble’s Law (1929)
Visualizing the Expansion of Space – Early in this century Edwin Hubble
discovered that the universe is expanding. Galaxies are moving outward from
us, and the farther out they are, the faster they are moving. In fact if you
compare the speed of a galaxy with another one twice as far away, the one twice
as far out will be moving twice as fast. In other words, the speed is proportional
to the distance. This effect has become known as Hubble’s Law. The
proportional nature of the expansion has interesting consequences.
1. We appear to be at the center of the expansion because galaxies are
moving away from us symmetrically in all directions. However, “observers”
in other galaxies far away would observe the same symmetric expansion and
perceive the center is an illusion. There really is NOT a center to the
expansion. Everything is moving away from everything else.
2. If we trace the expansion backward in time, all the matter is in the universe
would arrive at the same point at the same time in the past. Matter coming
from twice as far away is moving twice as fast, matter coming 10 times as
far away is moving 10 times as fast, so everything catches up at once. Thus
appears that the universe got to its present state by expansion from a tiny,
hot dense fireball by what is popularly called the “Big Bang”.
3. Go to Mrs. Fischl’s website, graph the distance vs. velocity of 17 galaxies.
Once you have graphed the data – analyze the data. What is the
relationship between the galaxies velocity and their distance.
What Is a Redshift?
How do I know which
direction a galaxy rotates?
Hubble’s Law describes the observations in cosmology that the velocities of galaxies are receding
from Earth proportional to their distances.
Blue Shift (to
higher
frequencies,
Shorter
wavelength)
Red Shift (to
lower
frequencies,
Longer
wavelength)
Hubble’s law continued…..
4. SPUD…BANG! We are going to simulate how galaxies distances are proportional to
their velocities. You will symbolize a galaxy or an object in space. As a class we are
going to go outside and huddle in a mass (to represent a primeval fireball). Mrs. Fischl
will yell BANG – everyone should run, skip, crawl….move outwards ‘til Mrs. Fischl yells
stop! Once all has stopped turn and count how many paces you are away from Mrs.
Fischl (the center of the universe). Once back in the classroom, record your data on
google doc. Calculate the velocity of “galaxies” (velocity = distance/time). Finally,
graph your classes data (distance vs. velocity).
•What is the relationship
between Distance and Velocity?
•Compare and Contrast the
simulated graph of Hubble’s
Law to the graph, question
number 4 of Hubble’s law you
constructed in question number
3.
Evidence # 2 to support Big Bang…. Abundance of Hydrogen & Helium
380,000 years until the universe was cool enough
for atoms to form at that time – Hydrogen (the
lightest element) formed …
73% of visible universe is Hydrogen
25% of visible universe is Helium
Where did all the other elements form?
Evidence #3 for the Big Bang Theory…Background Radiation
Technology played a vital
role in developing &
supporting the Big Bang
Theory…Inflationary Theory.
Astronomy is now a science
with empirical data instead
of wild plausible ideas.
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Our understanding of Earth’s place in the Universe has changed time!
What is most likely true about the Big Bang Theory or The Inflationary Theory
as technology improves?
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