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?

•Our clocks are based upon Solar time and we measure stars rising about 4

minutes earlier each day.

Sidereal Day, Sidereal Periods of Celestial Bodies to include the Sidereal

Month of the Moon

•Why does this happen?

The short version…because of Earth’s motion around the Sun.

•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.

•What types of motion can be measured with the Sidereal system?

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 TutorialUsing 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 torotate once with respect to a distant star.

• One sidereal day lasts approximately 23 hours and 56 minutes during which time the Earthrotates 360 degrees

(~4 minutes shorter than a solar day).

• One solar (synodic) daylasts 24 hours during which time the Earthrotates more than 360 degrees.

http://www.jgiesen.de/elevaz/basics/astro/stposengl.htm

Local Sidereal Time Clock

http://www.jgiesen.de/astro/astroJS/siderealClock/

Apparent Movement of a Star

Synodic (Solar) vs. Sidereal Period

of

the Moon ( & brief intro. to Moon phases)

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

http://www.youtube.com/watch?v=fLhxF6cnUoQ

Sidereal vs. Synodic Period of the

Moon (zooming in)

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.

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

•Retrograde Motion of the Planets

•Geocentric vs. Heliocentric

•Kepler’s Laws

Models of the Solar

System

Planets were often called wandering stars because they

seem to slowly move from one constellation to the next.

WestEast SouthMars prograde & retrograde motion is in red between May 1 and Dec. 31

Retrograde Motion

• Models of the universe MUST adequately

describe this retrograde motion!

“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.)

What did the Greeks have

to say about the motion of

the Solar System?

•What is this Earth-centered theory

called?

Ptolemy•He tried to create a model that

would account for retrograde

motion.

•He placed the planets in orbits

(deferments) using epicycles.

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.

Copernicus(1473 – 1543 AD)

Heliocentric theory:

with the Sun at the center of the

universe or solar system

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.ohio-

state.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 naked-

eye 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 - 1630is 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 Moviehttp://bcs.whfreeman.com/universe6e/pages/bcs-

main.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 fast herePlanet travels slow 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

a3AU= T2

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 Second Law

tells us what a

particular planet

does when it orbits

a Star– The planet will move

faster when it is close

to the Sun and slower

when it is farther from

the Sun

• The Third Law how the orbital periods are related to the orbital distances for all the planets in the Solar System– 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 = 1 yearT = ~ 12 years

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. Planets move fastest when they are

moving toward the Sun.

B. Planets move equal distances throughout their orbit of the Sun.

C. Planets move slowest when they are

moving away from the Sun.

D. Planets travel farther in a given time

when they are closer to the Sun.

E. 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.