Download If Earth had no tilt, what else would happen?

A more in depth explanation from last week:
If Earth had no tilt, what else
would happen?
•The equator would be much hotter due to the direct sunlight
which would lead to a lower survival rate and little life.
•The poles would receive less direct light and thus be colder
making the survival rate there lower as well.
•The species would have evolved differently (micro-evolution),
thus different life would be on Earth.
•But we would have a habitable zone between the poles and the
equator, but unfortunately it would be a smaller habitable region
than we have now.
Solar & Sidereal Motion and
Models of the Solar System
(Week 7)
Why does Sidereal Motion (Time) matter?
•It is a system of timekeeping used by astronomers, useful because a star rises
and sets at the same sidereal time every day, but not at the same solar
(synodic) time which is our typical time system.
•Because local sidereal time is the right ascension (RA) of a star on the
observers meridian, it is a direct indication of whether a celestial object of
known right ascension is observable at that instant.
•Our clocks are based upon Solar time and we measure stars rising about 4
minutes earlier each day.
•Why does this happen?
The short version…because of Earth’s motion around the Sun.
•What types of motion can be measured with the Sidereal system?
Sidereal Day, Sidereal Periods of Celestial Bodies to include the Sidereal
Month of the Moon
Sidereal Time vs. Solar (Synodic) Time
• A time-keeping system
astronomers use to keep
track of the direction to
point their telescopes to
view a given star in the
night sky.
• One sidereal day
corresponds to the time
taken for the Earth to
rotate once with respect
to a distant star.
•A time keeping system
based upon when the Sun is
highest in the sky (~12 pm).
•One solar day corresponds
to the time taken for the
Earth to rotate once with
respect to the Sun.
Prior to Tutorial completion, the Instructor will:
a) define parallel lines
b) define period
c) define high noon (in the diagram below)
d) in the diagram below illustrate a 360 degree rotation of
person/Earth with a ruler (students use toothpick) while Earth is
still orbiting the Sun & sketch the Earth/person in a later
snapshot
e) help students visualize distant stars (see
top of page) and have them draw similar
stars on their Tutorial
f) provide every student with a toothpick
Solar vs. Sidereal Day - Lecture Tutorial
(pg 11-12; 10-20 minutes)
• STOP the Tutorial just after the “Note:” on page 12, put
name on it and turn it in to Instructor next Tuesday.
• Be ready to struggle a little bit, this is a discovery!
•
•
•
•
•
Work with a partner!
Read the instructions and questions carefully.
Discuss the concepts and your answers with one another.
Come to a consensus answer you both agree on.
If you get stuck or are not sure of your answer, ask another
group.
• If you get really stuck or don’t understand what the Lecture
Tutorial is asking, ask one of us for help.
Follow up to Tutorial
Using the angle that the Earth sweeps out as it goes once around the Sun
and the number of days in a year, the number of degrees per day that
Earth moves in orbit about the Sun is:
A) 365 days/180 degrees = 2 days/degree
B) 365 days/180 degrees = 0.5 degrees/day
C) 360 degrees/365 days = 1 degree/day
D) 360 degrees/24 hours = 15 degrees/hour
E) none of the above
ANSWER: “C” or 1 degree/day for
Earth revolving about the Sun [Realize
that choice “D” or 15 degrees/hour is
the rotation rate of the Earth about its
axis, which is also the rate the celestial
sphere appears to rotate.]
Follow up to Tutorial
During what type of a day does the
Earth rotate through slightly
more than 360 degrees?
A) Synodic day which is 24 hrs
B) Solar day which is less than 24
hrs
C) Sidereal day which is less than
24 hrs
D) Sidereal day which is more
than 24 hrs
E) Both A) & B) above
ANSWER: “A” One solar/synodic day corresponds to the time taken for the Earth
to rotate once with respect to the Sun which is more than 360 degrees and takes 24
hours.
Follow up to Tutorial
During what type of a day does the
Earth rotate through 360
degrees?
A) Synodic day in 24 hrs
B) Solar day in less than 24 hrs
C) Sidereal day in less than 24 hrs
D) Sidereal day in 24 hrs
E) Both A) & B) above
ANSWER: “C” One sidereal day corresponds to the time taken for the Earth to
rotate once with respect to a distant star.
• One sidereal day lasts
approximately 23 hours
and 56 minutes during
which time the Earth
rotates 360 degrees
(~4 minutes shorter
than a solar day).
• One solar (synodic) day
lasts 24 hours during
which time the Earth
rotates more than 360
degrees.
Local Sidereal Time Clock
http://www.jgiesen.de/astro/astroJS/siderealClock/
Apparent Movement of a Star
http://www.jgiesen.de/elevaz/basics/astro/stposengl.htm
Synodic (Solar) vs. Sidereal Period
of
the Moon
( & brief intro. to Moon phases)
http://www.youtube.com/watch?v=fLhxF6cnUoQ
In this video, be sure to:
a) notice how the Earth’s orbit around the
Sun makes the Moon’s sidereal period
different from its synodic period
b) try to identify several Moon phases at
various points in the animation
c) read the blue writing, see next slide for a
snapshot of it
Sidereal vs. Synodic Period of the
Moon (zooming in)
Sidereal Period is 27.32 days, Moon
rotates to the purple line (which should
be parallel to the leftmost red dotted
line), 360 degrees; not back to New
Moon - same phase as leftmost image
Synodic Period is 29.53 days, Moon
rotates to the orange line, more than 360
degrees; back to the same phase (new
moon) as leftmost image.
Models of the Solar
System
•Retrograde Motion of the Planets
•Geocentric vs. Heliocentric
•Kepler’s Laws
Planets were often called wandering stars because they
seem to slowly move from one constellation to the next.
East
South
Mars prograde & retrograde motion is in red between May 1 and Dec. 31
West
Retrograde Motion
• Models of the universe MUST adequately
describe this retrograde motion!
What did the Greeks have
to say about the motion of
the Solar System?
“The astronomer must try
his utmost to explain
celestial motions by the
simplest possible
hypothesis; but if he fails to
do so, he must choose
whatever other hypotheses
meet the case.”
-Ptolemy of Alexandria
(140 A.D.)
Ptolemy
•He tried to create a model that
would account for retrograde
motion.
•He placed the planets in orbits
(deferments) using epicycles.
•What is this Earth-centered theory
called?
Geocentric theory:
(in Greek, geo means
earth) which maintained
that Earth was the center
of the universe
For most of human history, we have thought the universe was geocentric.
Copernicus devised the first
comprehensive heliocentric
cosmogony to successfully explain
retrograde motion.
Heliocentric theory:
with the Sun at the center of the
universe or solar system
Copernicus
(1473 – 1543 AD)
Retrograde motion is an apparent motion
caused when one planet moves from being
behind another planet to being in front of
the other planet.
Let’s watch a movie(s) of this motion.
http://www.astronomy.ohiostate.edu/~pogge/Ast161/Movies/#marsretro
Tycho Brahe
(1546-1601)
Tycho Brahe (1546-1601) is known
for 1. First telescope observations of
the sun
2. First sun centered scientific
model of the solar system or
universe
3. Being the world’s best nakedeye astronomer
4. Creating first a theoretical model
to explain planetary motions
5. Creating first a theoretical model
for explaining gravity
Tycho Brahe (1546-1601) is known
for 1. First telescope observations of
the sun
2. First sun centered scientific
model of the solar system or
universe
3. Being the world’s best naked-eye
astronomer
4. Creating first a theoretical model
to explain planetary motions
5. Creating first a theoretical model
for explaining gravity
What do we
mean by
“Greatest
Naked-eye
Astronomer?”
No telescope!
Scientists use parallax to measure distances.
Tycho Brahe measured distances
using parallax that disproved
ancient ideas about the heavens
• He observed a supernova in 1572 and with
this showed that the heavens were both
changing and had a dimension of distance;
this troubled scholars who previously thought
the heavens were unchanging.
• He showed that comets were objects that
occurred in the region of the planets, not in
Earth’s atmosphere.
Johannes
Kepler
1571 - 1630
He was rumored to
have hated Tycho
Brahe and was in
the relationship for
the data. With that
data he changed the
understanding of
motion of heavenly
bodies forever.
Johannes Kepler 1571 - 1630
is Known for 1. First telescope observations of the
sun
2. First sun centered scientific model of
the solar system or universe
3. Being the world’s best naked-eye
astronomer
4. Creating the first theoretical model to
explain planetary motions
5. Creating the first theoretical model for
explaining gravity
Johannes Kepler 1571 - 1630 is
Known for -
1. First telescope observations of
the sun
2. First sun centered scientific
model of the solar system or
universe
3. Being the world’s best naked-eye
astronomer
4. Creating first a theoretical model
to explain planetary motions
5. Creating first a theoretical model
for explaining gravity
Johannes
Kepler
1571 – 1630
Kepler’s Three
Laws of
Planetary
Motion
Eccentricity, e
•how squashed or out
of round the ellipse is
•a number ranging
from 0 for a circle to
1 for a straight line
e = 0.02
e = 0.7
e = 0.9
Kepler’s First Law: The orbit of a planet
about the Sun is an Ellipse with the Sun at
one focus.
What is the shape of Earth’s
orbit around the Sun?
Earth, e = 0.016
Kepler’s Second Law: A line joining a
planet and the Sun sweeps out equal
Areas in equal intervals of time.
Kepler's Second Law Movie
http://bcs.whfreeman.com/universe6e/pages/bcsmain.asp?v=category&s=00110&n=01000&i=04110.07&o=|04000|01000|&ns=
0
Kepler’s SECOND LAW
• A line drawn from the planet to the Sun
sweeps out equal Areas in equal times
• orbital speed is not constant for an
ellipse only for a circle
• planets move faster when near the
Sun (perihelion)
• planets move slower when they are
far from the Sun (aphelion)
SECOND LAW
• The speed a planet travels during its
orbit is related to the distance from the
star
– When the planet is near the sun the planet goes
faster than when the planet is farther from the sun
Planet travels slow here
Planet travels fast here
Kepler’s THIRD LAW
The size of the orbit (a is the length of its orbit’s
semi-major axis) determines the orbital period, T
3
a
=
AU
2
T
years
Thus planets that orbit near the Sun orbit with
shorter periods (T) than planets that are far from the
Sun
THIRD LAW
• The size of the orbit determines the
orbital period
– planets that orbit near the Sun orbit with
shorter periods than planets that are far
from the Sun
Kepler’s Third Law: The square of a planet’s
sidereal (orbital) period is proportional to the cube
of the length of its orbit’s semimajor axis (T2≈a3).
,T
=
T2
The Second and Third Laws
• The Third Law how
• The Second Law
the
orbital
periods
tells us what a
are related to the
particular planet
orbital distances for
does when it orbits all the planets in the
a Star
Solar System
– The planet will move
faster when it is close
to the Sun and slower
when it is farther from
the Sun
– planets that are in an
orbit located near the
Sun have short orbital
periods
– planets that are in an
orbit located far from the
Sun have long orbital
periods
THIRD LAW
• The size of the orbit determines the
orbital period
– planets that orbit near the Sun orbit with shorter
periods than planets that are far from the Sun
T = ~ 12 years
T = 1 year
THIRD LAW
• The size of the orbit determines the
orbital period
– planets that orbit near the Sun orbit with
shorter periods than planets that are far
from the Sun
– MASS DOES NOT MATTER
Both have T = 1 year
According to Kepler’s second law, a
planet with an orbit like Earth’s would:
A. move faster when further from
the Sun.
B. move slower when closer to the
Sun.
C. experience a dramatic change in
orbital speed from month to
month.
D. experience very little change in
orbital speed over the course of
the year.
E. none of the above.
Which of the following best describes what
would happen to a planet’s orbital speed if
it’s mass were doubled but it stayed at the
same orbital distance?
A. It would orbit half as fast.
B. It would orbit less that half
as fast.
C. It would orbit twice as fast.
D. It would orbit more than
twice as fast.
E. It would orbit with the same
speed.
Kepler’s second law says “a line joining a
planet and the Sun sweeps out equal areas
in equal amounts of time.” Which of the
following statements means nearly the
same thing?
A.
B.
C.
D.
E.
Planets move fastest when they are
moving toward the Sun.
Planets move equal distances
throughout their orbit of the Sun.
Planets move slowest when they are
moving away from the Sun.
Planets travel farther in a given time
when they are closer to the Sun.
Planets move the same speed at all
points during their orbit of the Sun.
If a small weather satellite and the large
International Space Station are orbiting
Earth at the same altitude above Earth’s
surface, which of the following is true?
A. The large space station has
a longer orbital period.
B. The small weather satellite
has a longer orbital period.
C. Each has the same orbital
period
Kepler’s 2nd & 3rd Laws - Lecture
Tutorials: (pg 21-27)
• Work with a partner!
• Read the instructions and questions carefully.
• Discuss the concepts and your answers with one
another.
• Come to a consensus answer you both agree on.
• If you get stuck or are not sure of your answer, ask
another group.
• If you get really stuck or don’t understand what the
Lecture Tutorial is asking, ask one of us for help.