Astro 101
Fall 2013 -- Lecture #2
Ancient Observers Noticed the “Wandering Stars” (e.g., planets) …
They saw that sometimes they had “retrograde” motion. But they thought
Everything orbited the Earth. How could this be?
(example)
The hash marks
show the position
of Mars relative to
the fixed stars at
Five-day intervals
The “Geocentric Model”
Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus,
Mars, Jupiter and Saturn.
Aristotle vs. Aristarchus (3rd century B.C.):
Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth.
Aristarchus: Used geometry of eclipses to show Sun bigger than Earth
(and Moon smaller), so guessed Earth orbits Sun. Also guessed Earth
spins on axis once a day => apparent motion of stars.
Aristotle: But there's no wind or parallax.
Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the
planets".
But if you support geocentric model, you must attribute retrograde
motion to actual motions of planets, leading to loops called “epicycles”.
Ptolemy's geocentric model (A.D. 140)
13
12
7
11
10
6
9 8
Retrograde Motion –
Correct Explanation
5
4
3
2
1
13
12
11
10
9
8
7
6
5
4
1
2
3
"Heliocentric" Model
●
Rediscovered by Copernicus in 16th century.
●
Put Sun at the center of everything.
Much simpler. Almost got rid of retrograde
motion.
●
But orbits circular in his model. In reality,
they’re elliptical, so it didn’t fit the data well.
●
●
Not generally accepted then.
Copernicus 1473-1543
Galileo (1564-1642)
Built his own telescope in 1609.
400 years ago.
Discovered four moons orbiting Jupiter
=> Earth is not center of all things!
Co-discovered sunspots. Deduced Sun
rotated on its axis.
Discovered phases of Venus, inconsistent
with geocentric model.
Johannes Kepler
• (1571 - 1630)
• Born near Stuttgart
• Studied philosophy and theology at Tubingen
• Developed love for astronomy as a child
• Showed high level of mathematical skill
• Had a reputation as a skilled astrologer
• Wanted to be a minister; became instead a
teacher of astronomy and math in Graz, Austria
• Became assistant to Tycho Brahe in 1601
• Developed Laws of Planetary Motion
Orbits of Planets – Heliocentric Model
All orbit in same direction.
Most orbit in same plane.
Elliptical orbits, but low eccentricity for most, so nearly circular.
13
12
7
11
10
6
9 8
Retrograde Motion –
Correct Explanation
5
4
3
2
1
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12
11
10
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7
6
5
4
Earth
1
2
3
Jupiter
(for example)
Kepler's First Law
The orbits of the planets are elliptical (not circular)
with the Sun at one focus of the ellipse.
Ellipses
distance between foci
eccentricity =
major axis length
(flatness of ellipse)
Kepler's Second Law
A line connecting the Sun and a planet sweeps out equal
areas in equal times.
slower
Translation: planets move faster
when closer to the Sun.
faster
Kepler's Third Law
The square of a planet's orbital period, P, is proportional to
the cube of its semi-major axis, a.
P2 α a3
(for circular orbits, a=radius).
Translation: the larger a planet's orbit,
the longer the period.
With the scale of the Solar System determined, can rewrite
Kepler’s Third Law as:
P2 = a3
as long as P is in years and a in AU.
So compare Earth and Pluto:
Object
a (AU)
Earth
Pluto
1.0
39.53
P (Earth years)
1.0
248.6
Newton (1642-1727)
Kepler was playing with mathematical shapes and
equations and seeing what worked.
Newton's work based on experiments of how
objects interact.
His three laws of motion and law of gravity
described how all objects interact with each other.
Newton's Correction to Kepler's First Law
The orbit of a planet around the Sun has the common
center of mass (instead of the Sun) at one focus.
Timelines of the Big Names
Galileo
Copernicus
1473-1543
1564-1642
Brahe
1546-1601
Kepler
1571-1630
Newton
1642-1727
At this time, actual distances of planets from Sun were unknown,
but were later measured. One technique uses parallax.
“Earth-baseline parallax” uses
telescopes on either side of Earth to
measure planet distances.
The Celestial Sphere
An ancient concept, as if all
objects at same distance.
But to find things on sky,
don't need to know their
distance, so still useful today.
Features:
- Does not rotate with Earth
- Poles, Equator
- Coordinate System
Celestial Coordinates:
Right Ascension – parallel to lines of longitude, i.e.,
run from North to South
of
-- in units of Hours, Minutes, Seconds
-- why? Correspondence with sidereal rotation
the sky in 23 hr 56 min solar time
Declination – parallel to lines of latitude, i.e., parallel
to
Equator
Lines of R.A. (Right Ascension)
N Celestial
Pole
Lines of Decl.
(Declination)
+ = Northern hemisphere
- = Southern hemisphere
N Pole
Earth
S Pole
A typical celestial
coordinate would look
like this:
Earth sphere
“projected” outwards
to the sky, except, it
doesn’t rotate with the Earth
S Celestial
Pole
21h 34m 13.3 sec
+28.6 deg.
The Year
Inclined view of the Earth’s orbit
The Earth revolves around the Sun in 365.256 days (“sidereal year”).
The "Solar Day" and the "Sidereal Day"
Solar Day
How long it takes for the Sun to return to the same
position in the sky (24 hours).
Sidereal Day
How long it takes for the Earth to rotate 360o on its axis.
These are not the same!
One solar day later, the Earth has rotated slightly more than 360o .
A solar day is longer than a sidereal day by 3.9 minutes
(24 hours vs. 23 hours 56 minutes 4.091 seconds).
The Year
Scorpius
Orion
Inclined view of the Earth’s orbit
The Earth revolves around the Sun in 365.256 days (“sidereal year”).
But the year we use is 365.242 days (“tropical year”). Why?
Precession
The Earth has a bulge. The Moon "pulls down" on the side of the bulge
closest to it, causing the Earth to wobble on its axis (how do we know this?)
Vega
*
* Polaris
Spin axis
Precession Period 26,000 years!
Precession
animation
Now
Orion
Scorpius
Night
Day
Day
Summer: July
Night
Winter: January
13,000 years from now
Orion
Scorpius
Night
Night
Day
Winter: July or January?
Day
Summer: January or July?
We choose to keep July a summer month, but then in 13,000 years, summer occurs on other side of orbit!
The Motion of the Moon
The Moon has a cycle of "phases", which lasts about 29 days.
Half of the Moon's surface is lit by the Sun.
During this cycle, we see different fractions of the sunlit side.
Which way is the Sun in each case?
Q: What is a “Blue Moon” ?
A: The second Full Moon occuring within a
single calendar month. Occur, on average, once
every 2.7 years.
Some American Full Moons
September:
Harvest Moon
(Colonial
American)
October:
Corn Ripe Moon
(Taos)
November:Sassafras Moon
(Choctaw)
December:Big Freezing Moon (Cheyenne)
Cycle of phases slightly longer than time it takes Moon to do a complete
orbit around Earth.
Cycle of phases or
"synodic month"
Orbit time or
"sidereal month"
29.5 days
27.3 days
Eclipses
Lunar Eclipse
When the Earth passes directly between the Sun and the Moon.
Sun
Earth
Moon
Solar Eclipse
When the Moon passes directly between the Sun and the Earth.
Sun
Moon
Earth
Solar Eclipses
Diamond ring effect - just before
or after total
Total
Partial
Annular - why do these occur?
Lunar Eclipse
Why don't we get
eclipses every
month?
How can there be
both total and
annular eclipses?
Moon's orbit tilted compared to Earth-Sun orbital plane:
Sun
Moon
Earth
5.2o
Side view
Moon's orbit slightly elliptical:
Moon
Distance varies by ~12%
Earth
Top view, exaggerated ellipse
Types of Solar Eclipses Explained
Certain seasons are favorable for eclipses. Solar “eclipse season”
lasts about 38 days. Likely to get at least a partial eclipse
somewhere.
It's worse than this! The plane of the Moon's orbit precesses, so
that the eclipse season occurs about 20 days earlier each year.
Next total solar eclipse in N. America = August 2017
Rocket Science 101
Rocket Science 101
• The same laws that govern the motion of the planets around the
sun (Kepler’s Laws) also govern:
-- Motion of satellites (“moons”) around planets
-- Motion of artificial satellites and spacecraft around the Earth
-- Motion of spacecraft on their way through the Solar System
• What are the differences?
-- The body creating the gravity that governs the orbit (the
“central
body”) is not necessarily the same
-- This determines the period of each orbit (time for orbit)
-- Orbits may be highly elliptical, or inclined
-- This also affects the period
-- The velocity (“speed”) of something moving in an elliptical
orbit will be different than the velocity of something moving in a
circular
orbit at the same distance from the central body
Example
Central Body could be
Earth, Sun, Jupiter, …
Circular
Orbit 2
Circular
Orbit 1
P1
P2
Central
Body
Elliptical
Orbit 3
Orbits 1 and 2 are circular, so the velocity of the satellite/moon/spacecraft is the same everywhere in
each orbit, BUT  Because the orbits have different radii (sizes = distances from the body), the
velocities in the two orbits are not the same !
Velocity at P1 for Orbit 1 and Orbit 3 are also NOT the same (because they aren’t the same orbit!)
Some terminology
“Apo” –
Point of furthest
distance =
slowest speed in
the orbit
“peri” –
Point of closest
approach =
x
fastest speed in
the orbit
Central
Body
x
Elliptical
Orbit 3
Central body = Earth (satellites, Moon), we say “Perigee” and “Apogee”
Central body = Sun (planets, comets, asteroids, interplanetary spacecraft)
we say “Perihelion” and “Aphelion”
We can use Kepler to our advantage …
How to get from Orbit 1 to Orbit 2:
Circular
Orbit 2
Burn 1 =
Add velocity so that
the moving object has
the proper velocity for
the”transfer” orbit
Elliptical (“transfer”)
Orbit 3
It moves in the ellipse
Out to point 2, then
Burn 2
Burn 2 =
Add velocity so that the
moving object has the
proper velocity for
Orbit 2
All of these velocities
can be calculated from
Kepler’s Laws
Burn 1
Circular
Orbit 1
ISS - Visible Passes
You can see satellites sometimes…
ISS - Visible Passes
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ISS - Visible Passes
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ISS - Visible Passes
Search period start: 00:00 Thursday, 20 October, 2011
Search period end: 00:00 Sunday, 30 October, 2011
Observer's location: Albuquerque,
35.0840°N,
106.6510°W
00:00 Thursday,
start:
Search period
Local time zone:
Mountain Daylight Time (UTC - 6:00)
Orbit:
374 x 396 km, 51.6° (Epoch Oct 18)
Search period end: 00:00 Sunday, 30 October, 2011
Observer's location: Albuquerque, 35.0840°N, 106.6510°W
Type of passes to include:
Visible
zone:All
timeonly
Local
Mountain Daylight Time (UTC - 6:00)
x 396
Click on the date to get aOrbit:
star chart and other pass374
details.
Date
20 October, 2011
Mag
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Type
Time
altitude
to include:
of passesMax.
Alt. Az.
Time
Alt. Az.
km, 51.6° (Epoch Oct 18)
only
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All
Alt. Az.
chart and
a star
get NNW
date to 16
on the19:07:36
20 Oct -0.9 19:05:32Click
10 WNW
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10 other
NNE
22 Oct -0.5 18:45:38 10
NW
Date
18:46:30 11
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WNW
19:05:32 10GmbH
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22 Oct -0.5 18:45:38 10
NW
pass details.
N
Ends
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Time
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19:07:36 16
NNW 19:09:41 10
NNE
18:46:30 11
NNW 18:47:23 10
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ISS Pass
20 Oct 2011
Albuquerque
Sky Path
HST - Visible Passes
| Home | Info.
Search period start: 00:00 Thursday, 20 October, 2011
Search period end: 00:00 Sunday, 30 October, 2011
Observer's location: Albuquerque, 35.0840°N, 106.6510°W
Local time zone:
Mountain Daylight Time (UTC - 6:00)
Orbit:
560 x 564 km, 28.5° (Epoch Oct 16)
Type of passes to include:
Visible only
All
Click on the date to get a star chart and other pass details.
Date
Mag
Starts
Time
Max. altitude
Alt. Az.
Time
Alt. Az.
Ends
Time
Alt. Az.
20 Oct 3.4
20:06:10 10
S
20:06:15 10
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20:06:15 10
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21 Oct 3.0
20:01:59 10
SSW
20:03:44 14
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20:03:44 14
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22 Oct 2.7
19:58:23 10
SSW
20:01:10 18
SSE 20:01:10 18
SSE
23 Oct 2.4
19:55:02 10
SW
19:58:22 22
SSE 19:58:32 22
SSE
24 Oct 2.2
19:51:49 10
SW
19:55:23 26
SSE 19:55:52 26
SSE
25 Oct 2.1
19:48:42 10
SW
19:52:25 30
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19:53:11 28
SSE
26 Oct 2.0
19:45:40 10
WSW 19:49:28 32
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19:50:27 28
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27 Oct 2.0
19:42:40 10
WSW 19:46:30 33
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19:47:44 28
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28 Oct 2.0
19:39:43 10
WSW 19:43:33 33
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19:45:01 26
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29 Oct 2.1
19:36:48 10
WSW 19:40:35 31
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19:42:20 23
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