Download Physics 125 Solar System Astronomy

Physics 125
Solar System
Astronomy
James Buckley
[email protected]
Lecture 3
The Big Picture from the Big Bang to
Our Solar System (Part II)
Reading
Quiz 2
Circular
acceleration
• Answer BOTH questions
-True or False: The Stars, unlike the sun, tend to rise
in the West and set in the East
-Ancient peoples built stone or wood structures to mark
•the seasons, e.g., on the summer solstice, the sun
∆⃗vthe line of site of two
appears on the Horizon along
⃗a =
∆t or two, describe why
stone monoliths. In a sentence
this alignment only occurs two times a year.
Physics 125, J. Buckley
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Angles
Circular acceleration
Arclength s = D ✓
D
✓/2
✓
a/2 = D sin(✓/2)
a/2
s
For small angles sin
⇡
a/2 ⇡ D (✓/2)
a ⇡ D✓
•
To make the following formulas work, we need to
measure angules in radians, not degrees. Recall:
there are 2⇡ radians in 360 ∆⃗
v
⃗a =
∆t
• The separation of two stars, or two sides of a planet appear to us as an
angle (that’s what cameras and eyes really see). Angles map into
positions on the film, or retina - we don’t really measure size.
Physics 125, J. Buckley
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Back-Yard
Astronomy Tip #1
Circular
acceleration
Measuring Angles
•
∆⃗v
⃗a =
∆t
• Measuring angles
Physics 312 - Lecture 4
– p.3/??
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Star Formation
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• Iconic Hubble image of the “pillars of creation’’ in the Eagle Nebula where
molecular clouds (H2, CO, even organic molecules) are collapsing under
self gravity to form new stars.
Physics 125, J. Buckley
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Jean’s acceleration
Instability
Circular
Molecule with KE>PE
•
Molecule with KE<PE
∆⃗v
⃗a =
∆t get collapse
• If pressure not sufficient to hold off gravity,
• Another way of looking at this is that there is some radius (and enclosed mass)
for which molecules (at a given Temperature) do not have enough kinetic
energy to escape gravity. This radius is called the Jean’s radius and the
enclosed ass called the Jean’s mass.
Physics 125, J. Buckley
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Star Formation
Circular acceleration
Pleiades
•
∆⃗v
⃗a =
Orion Nebula ∆t
• You can find star formation regions in Orion, or
see young stars in the Pleiades (the blue glow is
due to ionization of the surrounding gas by UV
light from the young stars)
Trapezium
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Collapse
Circular acceleration
Pressure
Gravity
•
Gravitational attraction makes cloud collapse
and heat-up, emitting black-body radiation
(protostar)
•
The heat of collapse results in an increase in
random motion of the gas atoms, increasing
temperature and pressure
•
•
Eventually random thermal velocities are high
enough and densities high enough that
Hydrogen atoms can overcome their repulsion
and fuse
∆⃗v to form Helium, liberating mass as
⃗aenergy
=
∆t
•
A star is born!
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Pressure
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• Gravity compresses gas, like a piston making particles speed up
and density and pressures increase
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Sustained
Fusion in Stars
Circular
acceleration
• As velocity (kinetic energy) and density increases, the probability of two
hydrogen nuclei hitting each other really hard increases.
• If they hit hard enough, they can overcome the electric repulsion (like
charges repel), and strong nuclear forces take over, making them stick
together in a different nucleus
⌫
1
H•
e+
2
1
H
Step 1
e
2
H
1
H
H
3
3
∆⃗v
He
⃗a =
Step 2
He
∆t
4
3
He
He
+
1
+
H
1
H
Step 3
Physics 125, J. Buckley
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Hydrogen
Bomb
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• Hydrogen bombs are the most energetic man-made terestrial
events, with typical energy release equal to 1Mton of TNT (4.2
Giga-Joules)
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Fusion Energy
Circular
acceleration
Fusion:
H-Bomb:
• Solar luminosity is 3.826x1026 Watts
•
•
1 megaton of TNT (typical H-bomb) releases 4x1015 Joules. So sun’s
∆⃗v
26
output in “H-bomb” units is (3.8 x10
/
⃗a = 4.0 x1015) J or about 100 billion
∆t
H-bombs a second!
• More than just an arbitrary unit, the sun really is 100 billion H-bombs
worth of Hydrogen fusion a second, with all the associated radiation!
Physics 125, J. Buckley
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Fusion
Power
Math
Time!
Circular acceleration
E = m c2
Mass of a hydrogen atom, mH = 1.673 ⇥ 10
Mass of a helium atom, mHe = 6.645 ⇥ 10
27
27
kg
kg
Speed of light, c = 2.998 ⇥ 108 m/s
m = (4 ⇥ mH )
E
=
m c2
=
4.7 ⇥ 10
=
=
•6⇥10
26
mHe = 4.7 ⇥ 10
29
4.22 ⇥ 10
4.22 ⇥ 10
29
kg
kg ⇥ (2.998 ⇥ 108 m/s)2
12
kg m2 /s2
12
J
hydrogen atoms in a kg
1 Joule = 1 W sec (1 hr /3600 sec)(1 kW ∆⃗
/v
1000 W)
⃗a = ✓
◆✓
◆
26
∆t
1
kW
hr
6
⇥
10
H
atoms
Energy per kg = 4.22 ⇥ 10 12 J/reaction
3.6 ⇥ 106 J
4 H atoms/reaction
=
1.8 ⇥ 108 kW hr
An average American household uses about 1000 kW hr per month, so on kg of
Hydrogen fuel could power a small city (200 thousand) households for one
month.
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Fusionacceleration
Enery on Earth
Circular
•
∆⃗v
⃗a =
∆t
• Promise of fusion energy, the ultimate clean infinite source of energy, still
remains far out of reach.
Physics 125, J. Buckley
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Discussion
question:
Circular
acceleration
•
∆⃗v
⃗a =
∆tSocrative, check ALL correct
• Discuss the answers, and using
answers (there could be more than one or zero!)
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How do you know?
Circular acceleration
• If you were an ancient Greek, with no modern technology (no telescopes,
internet, GPS, electronic clocks, computers or modern transportation how
would you know:
- The earth is round?
- How big the moon and sun are? How far away?
- That we orbit the sun, and not (what we observe) that the sun orbits us?
the earth is spinning?
- That
•
∆⃗v suns?
other
- That the points of light in the sky⃗aare
=
∆t
- How far away those stars are? Are they other suns?
- And yet, the ancient greeks DID know these things!
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Library
of Alexandria
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• World’s first Research institute, established by Aristotle, tutor
of Alexander the Great under his patronage.
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Library
of
Alexandria
Circular
acceleration
• The library of Alexandria thrived between the 4th century BC and Roman
and continued until about 400 AD (surviving several fires) until it was finally
destroyed (probably in one great fire).
• The library contained as many as a million scrolls with writings of great
astronomers and mathematicians like Euclid, Archimedes, Erastothenes,
Hipparchus, Aristarchus of Samos.
• The details remain unclear, but is likely that the library was destroyed near
the beginning of the 5th century AD. The destruction may have occurred
near the time that Hypatia, a leading (female) philosopher of the Greek
Alexandrian tradition was brutally murdered (dragged behind a carriage)
by a•Christian mob, perhaps upset by a dispute between the prefect Orestes
∆⃗v and Hypatia, or about their
and Bishop over the “pagan” beliefs⃗aof=Orestes
∆t
support of the Jewish population
• The great intellectual achievements of Hypatia, and the story of her brutal
murder (even as Christian writers of the time admired her intellect inspired
the name of the Feminist journal “Hypatia: A Journal of Feminist
Philosophy)
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Aristotle
and Plato
Circular
acceleration
Plato (424-348 BCE)
Aristotle (384-322 BCE)
•
establishing a school of
• Aristotle (and Plato) was a brilliant philosopher,
∆⃗v
⃗a =century.
thought that persisted through the 15th
∆t
• Made important contributions to Philosophy, but not so much for the Physical
sciences (and Astronomy). In fact they did some harm - so we will skip them
and get to the story of the Ancient Greeks that actually matter for Astronomy!
Physics 125, J. Buckley
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Aristarchus
of
Samos
Circular acceleration
• Aristarchus lived on the Greek
island of Samos (310-230 BC)
• Postulated that planets orbited
sun not Earth.
• Devised methods to measure
Samos
size of the Earth, size and
distance of the Moon and Sun.
• Deduced that stars are other
suns but at enormous distances
“Aristarchus
has brought out a book consisting of certain hypotheses, wherein
•
it appears, as a consequence of the assumptions made, that the universe is
∆⃗
v hypotheses are that
many times greater than the ‘universe’ just mentioned.
His
⃗a =
∆t revolves about the
the fixed stars and the sun remain unmoved, that the earth
sun on the circumference of a circle, the sun lying in the middle of the orbit,
Contributed by Vae Isakhanian, EYAD, G and others
and that the sphere of fixed stars, situated about©2014
theGoogle
same· center
as the sun, is
Basarsoft, ORION-ME, TerraMetrics · Terms of Use
100 km
so great that the circle in which he supposes the earth to revolve bears such a
proportion to the distance of the fixed stars as the centre of the sphere bears to
its surface.”
- Archimedes (287-212 BC)
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Distance
to Moon and Sun
Circular
acceleration
3 deg
87 deg
•
•
Aristarchus argued that angle between the moon and sun when the moon was exactly half full
∆⃗v estimated the angle at ~ 87 deg so
could be used to compute ratio of distances. Aristarchus
⃗a =
the ratio of distances was sin(3 deg). Trig was not invented
∆t yet, so he used an inequality
1/18>sin(3)>1/20 (based on right triangles).
•
He deduced sun was 18 to 20 times as far away as the moon. Actually, the angle between the
half moon and sun is 89.83 deg and sun is about 400 times as far as the moon - but the method
was sound (Aristarchus also estimate the radius of the Sun from the angular size)
Physics 125, J. Buckley
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Relative
Size of Earth and Moon
Circular
acceleration
•
∆⃗v
⃗a =
∆t a lunar eclipse gives a
• Curvature of shadow of Earth during
rough estimate of the relative radius of the earth and moon.
• Angular size of moon is about 0.5 deg???
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Aristarchus,
continued
Circular
acceleration
10th century copy of
Aristarchus’ calculations of
the relative sizes of the sun
earth and moon.
•
∆⃗v
⃗a =
∆t
• Knowing the ratio of distances from the Earth to the Sun and moon, Aristarchus
used the size of the shadow relative to the moon at a Lunar Eclipse, an the fact
that the Earth and Sun have about the same angular size (0.5 deg) at eclipse to
measure the relative radii of the Sun, Earth and Moon and the relative distances
Physics 125, J. Buckley
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Radiusacceleration
of Earth
Circular
•
Erastothenes of Cyrene (modern day Libya)
(276-194 BC) was a Greek mathematician,
astronomer, Librarian of Alexandria, friend of
Archimedes.
•
Sun visible at bottom of well, vertical sticks
cast no shadow in Syene on summer solstice at
local noon. In Alexandria on same day, a stick
cast a measurable shadow.
•
From measurements of shadows in Alexandria,
the zenith angle of the sun corresponded to
1/50 •circle of 7.2 deg south of zenith>
Sun’s Rays
7.2 deg
Alexandria
∆⃗v
• Assuming Alexandria due north of Syene, ⃗a =
∆t
distance to Syene must be 1/50 circumference
of the Earth. With a distance of 5000 stadia
=> 700 stadia per deg, a circumf of 252,000
stadia. 1 stadium ~ 185m giving a
circumference of 46620 km, only 16.3% too
large!
Syene
Radius of t
7.2 deg
Diamete
• Erastothenes of Cyrene (modern day Libya
Greek mathematician, astronomer, Librari
friend of Archimedes.
• Sun visible at bottom of a well, vertical sti
in Syene on the summer solstice at local n
on the same day, a stick cast a measurable
• From measurements of shadows in Alexan
elevation of the Sun corresponded to 1/50
south of the zenith at the same time.
Physics 125, J. Buckley
Alexandria was due north of Sy
• Assuming
Physics 312 - Lecture 1 – p. 25/27
Hyparchus’
Lunar Distance
Circular
acceleration
✓
Alexandria
Earth
✓
Syene
Moon
visible
Blocked from
Sun
view
(Alexandria)
• Hyparchus (190-120 BC) used the different appearance of a solar eclipse from
Syene (total) and Alexandria (partial) to determine the distance from the Earth
to•Moon.
∆⃗v
=
in Alexandria saw 1/5 of the sun.
• During the total eclipse in Syene, an⃗aobserver
∆t
• Angular size of the sun is
⇡ 0.5 , so ✓ ⇡ 1/10
• He derived that the distance to the moon Dm was related to the distance
between the two cities D, by D = Dm ✓
Physics 125, J. Buckley
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Geocentric
Universe
Circular
acceleration
Figure from a 16th
century Portugese
Cartographer showing
the Ptolemeic
geocentric system
• But
• Hipparchus rejected the ideas of Aristarchus and others, and adopted a
Heliocentric model (as introduced by Plato
∆⃗v(424-348 BC) and Aristotle (384-322)
⃗a =by Ptolemy (384-322 BC)
in the 4th century BC), and formalized
∆t
• The Planets (or Wanderers) were star-like objects that seemed to move with
respect to background stars.
• In the time of Hipparchus, and later formalized by Ptolemy
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Planetsacceleration
and Epicycles...
Circular
•
∆⃗v
⃗a =
∆t
Physics 125, J. Buckley
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Summary
Circular
acceleration
• Sun and moon have about the same angular size (0.5 deg)
• Aristarchus derived a number of geometric methods for determining the relative
size and distances of the Sun, Earth, Moon system and postulated a Heliocentric
solar system, and even that stars were other suns. His numbers were off, only due
to his limited ability to measure the angle between half moon and sun.
• Erastothenes devised an accurate method for deriving the radius of the earth.
• Hipparchus repeated and improved on Aristarchus’ methods and came up with
pretty
• accurate estimates for the size of the solar system - but he believed in a
Geocentric system
∆⃗v
⃗a =
to the destruction of many important
• The burning of the library of Alexandria led∆t
documents. Some Muslim scholars had translated some works (Aristotles, in
particular) into Arabic. These were later translated into Latin after most of the
original Greek copies were destroyed (referred to as the Recovery of Aristotle in
the middle ages)
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Parallax Distance
Parallax
Circular
acceleration
1 AU
d=
tan p
d
1 AU
p
1 pc
p”
• By definition, a star at a distance
of one parsec (1 pc) will have a
parallax angle of one arcsec (1”)
• 1 pc = 3.08568025 x 1018 cm
•
1 pc = 3.26163626 ly
•∆⃗
v
⃗a =
Nearest star, Proxima Centauri,
•∆t
has a parallax angle of 0.77” and
a distance of 1.3 pc or 4.2 ly
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Distance to Planets
Parallax distance
S un
E arth
M ercu ry
!
Venus transit, APOD July 20, 2004
Relative scales of the solar system
Planet
Period (years)
Approx. Radius (a.u.)
Earth
1.0
1.0
Mercury
0.241
0.39
Venus
0.615
0.72
Mars
1.881
1.5
Jupiter
11.86
5.2
Physics 312 - Lecture 3
– p.9/12
Venus transit, Crow Observatory, June 5, 2012
Mercury
Transit
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• Mercury transits occur more often, but Mercury is closer to the
sun and it is hard to measure the parallax
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3 Future and past
4 See also
5 References
6 External links
Nearest Stars
Nearestacceleration
Stars
Circular
List
Designation
#
1
System
Star
Solar System
Sun
Alpha Centauri
(Rigil Kentaurus;
Toliman)
Additional
references
180°
0.000015
has 8
planets
variable: the Sun travels along
the ecliptic
14h 29m 43.0s
!62° 40! 46" 0.768 87(0 29)"[5][6] 4.2421(16)
# Centauri A
(HD 128620)
2
G2V [2]
0.01[2]
14h 39m 36.5s
!60° 50! 02"
# Centauri B
(HD 128621)
2
K1V [2]
1.34[2]
5.71[2]
14h 39m 35.1s
!60° 50! 14"
4
M4.0Ve
9.53[2]
13.22[2]
17h 57m 48.5s
+04° 41! 36" 0.546 98(1 00)"[5][6] 5.9630(109)
5 M6.0V[2] 13.44[2] 16.55[2]
10h 56m 29.2s
+07° 00! 53" 0.419 10(2 10)"[5]
6 M2.0V[2]
11h 03m 20.2s
+35° 58! 12" 0.393 42(0 70)"[5][6] 8.2905(148)
06h 45m 08.9s
!16° 42! 58" 0.380 02(1 28)"[5][6] 8.5828(289)
01h 39m 01.3s
!17° 57! 01" 0.373 70(2 70)"[5]
4
Lalande 21185 (BD+36°2147)
•
Declination [2]
Distance[4]
Light-years
(±err)
11.09[2] 15.53[2]
Wolf 359 (CN Leonis)
Luyten 726-8
Right ascension[2]
Parallax[2][3]
Arcseconds(±err)
M5.5Ve
3
6
G2V [2] !26.74 [2] 4.85[2]
Epoch J2000.0
1
Barnard's Star (BD+04°3561a)
Sirius
(# Canis Majoris)
Apparent Absolute
magnitude magnitude
(m V )
(M V )
Proxima Centauri
(V645 Centauri)
2
5
Star
#
Stellar
class
4.38[2]
0.747 23(1 17)"[5][8] 4.3650(68)
7.47[2]
10.44[2]
Sirius A
7
A1V [2]
!1.46 [2]
1.42[2]
Sirius B
7
DA2 [2]
8.44[2]
11.34[2]
Luyten 726-8 A
(BL Ceti)
9
M5.5Ve
12.54[2] 15.40[2]
Luyten 726-8 B
(UV Ceti)
[7]
10 M6.0Ve
12.99[2]
7.7825(390)
8.7280(631)
15.85[2]
∆⃗v
a =23 41 54.7
14.79⃗
∆t
7
Ross 154 (V1216 Sagittarii)
11 M3.5Ve
10.43[2] 13.07[2]
8
Ross 248 (HH Andromedae)
12 M5.5Ve
12.29[2]
9
Epsilon Eridani (BD!09°697)
13
K2V [2]
3.73[2]
6.19[2]
03h 32m 55.8s
has two
!09° 27! 30" 0.309 99(0 79)"[5][6] 10.522(27) proposed
planets
10
Lacaille 9352 (CD!36°15693)
14 M1.5Ve
7.34[2]
9.75[2]
23h 05m 52.0s
!35° 51! 11" 0.303 64(0 87)"[5][6] 10.742(31)
11
Ross 128 (FI Virginis)
15 M4.0Vn
11.13[2] 13.51[2]
11h 47m 44.4s
+00° 48! 16" 0.298 72(1 35)"[5][6] 10.919(49)
16 M5.0Ve
13.33[2] 15.64[2]
12
EZ Aquarii
(GJ 866,
Luyten 789-6)
•
EZ Aquarii A
[2]
18h 49m 49.4s
h
m
s
!23° 50! 10" 0.336 90(1 78)"[5][6] 9.6813(512)
+44° 10! 30" 0.316 00(1 10)"[5]
[2] 15.58
[2]
M?
!15°encyclopedia
18! 07" 0.289 50(4 40)"[5]
13.27
22h 38m the
33.4s free
List 16
of nearest
stars
- Wikipedia,
EZ Aquarii B
List of nearest
and14.03
parallax
[2] 16.34[2] (from Wikipedia)
EZ Aquarii C stars
16
M?
Procyon
13
(# Canis Minoris)
Procyon A
19
F5VIV[2]
0.38[2]
2.66[2]
07h
39m
18.1s
10.322(36)
11.266(171)
Physics 125, J. Buckley
+05° 13! 30" 0.286 05(0 81)"[5][6] 11.402(32)
Physics 312 - Lecture 1 – p. 25/27
Local (Horizon)
Coordinates
Circular
acceleration
•
∆⃗v
⃗a =
∆t
• Zenith is the point directly over head, the Meridian is the line
going through points due south and due north, passing through
the zenith.
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Path ofacceleration
Sun Throughout Year
Circular
•
∆⃗v
⃗a =
but during the course of the year, it
• The Sun rises in the East, Sets in the West, ∆t
appears to get higher in the sky (during summer) and cross the Horizon at
different Points.
• Ancient structures marked times of year, by aligning objects with the position
that the Sun crossed the Horizon in different seasons.
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Summary
Circular
acceleration
• The Universe started with the big bang!
• There are 100 billion stars in the galaxy, and 100 billion galaxies in
the visible universe.
• Dark matter is the main gravitational mass, responsible for galaxy
formation.
• Stars are powered by nuclear fusion, ignited by very high
temperatures and pressures from gravitational collapse.
••Our solar system is composed of inner, terrestrial planets and outer
∆⃗v
gas giants, but is mostly empty space!
⃗a =
∆t
• Going back to ancient time, we have come up with many ingenious
ways to measure our Universe, without ever leaving our planet (or
surfing the web).
• Reading assignment: Sections 2.1, 2.2, 3.1 and 3.2
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Planetsacceleration
in the Night Sky
Circular
• Compared with stars, planets:
- Are often quite bright
- Twinkle less than stars
becaues they are
“extended”
Mars
•
⃗a =
- Move relative to stars over
∆⃗v the course of nights, years
∆t
• Greeks called planets “Wanderers”
• Venus, Mars, Jupiter and Saturn all clear to the naked eye.
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