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Announcements
Astro 101, 12/4/08
• Last OWL homework:
up tomorrow around
noon
• Study materials for final
exam will appear over
the weekend (on course
web page)
• Practice exam up
midweek next week
• Final exam: Monday,
Dec. 15, 10:30 AM,
Hasbrouck 20
Three hypotheses about the
origin of the Earth’s Moon
Each of the these hypotheses makes
different predictions:
1. The Moon was an independent
planet that was captured by the
Earth in a gravitational encounter
2. The Moon and Earth formed as
“twins” in the same place in the
protosolar disk
3. The Earth was originally spinning
so rapidly that a chunk broke off
and became the Moon.
Different composition
from Earth
Same composition
as the Earth
Same composition
as the Earth’s crust
All of these hypotheses fail compared to observations!
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Formation of the Moon
(Giant Impact Theory)
• The Earth was struck by a Marssized planetesimal
• A part of Earth’s mantle was
ejected
• This coalesced and turned into
the Moon.
• Rocks returned to Earth by
astronauts on Apollo missions
support this theory: The
composition of the Moon is very
similar to the composition of the
Earth’s crust, but the easily
vaporized stuff is missing (Moon
rocks are dominated by materials
with a high melting point; low
melting point materials are
missing)
The age of the Earth
and the Moon are
similar...
How can we determine the
age of the Solar System?
Radiometric dating: by measuring
the proportions of selected atoms and
isotopes in a solid, we can determine
the age of the solid.
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Recall from previous lectures:
Hydrogen
The number of protons
in the nucleus identifies
the element.
e-
p+
atomic number = 1
atomic mass number = 1
Recall from
previous lectures:
Hydrogen
Deuterium
e-
isotope
p+
n
atomic number = 1
atomic mass number = 2
Isotopes of a
particular element
all have the same
number of protons
but have differing
numbers of neutrons
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How can we determine the
age of the Solar System?
Radiometric dating: by measuring
the proportions of selected atoms and
isotopes in a solid, we can determine
the age of the solid.
Radioactive isotope: an isotope
that tends to spontaneously change
the number of protons or neutrons
(or both) in its nucleus.
Radioactive Decay
• When a radioactive isotope suddenly changes, the
process is called radioactive decay.
• Most common carbon isotope: carbon-12 (6
protons & 6 neutrons). Stable isotope.
• Radioactive carbon isotope: carbon-14
(6
protons & 8 neutrons)
• Energy is released when radioactive decay occurs.
The energy can be carried away by particles (e.g.,
electrons) or light (typically gamma rays).
“Parent” isotope
14C
radioactive
decay
“Daughter” isotope
14N
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14N
is a stable isotope with atomic
number = 7 and atomic mass = 14
What happens when carbon-14 radioactively decays
into nitrogen-14?
PRS question
1.
2.
3.
4.
The carbon becomes ionized
A proton turns into a neutron
A neutron turns into a proton
Neutrons and protons both change forms
“Parent” isotope
14C
radioactive
(6 protons, 8 neutrons)
decay
“Daughter” isotope
14N
Radioactive Decay
• When a radioactive isotope suddenly
changes, the process is called radioactive
decay.
• Most common carbon isotope: carbon-12
(6 protons & 6 neutrons). Stable isotope.
• Radioactive carbon isotope: carbon-14
(6 protons & 8 neutrons)
“Parent” isotope
14C
radioactive
(6 protons, 8 neutrons)
decay
“Daughter” isotope
14N
(7 protons, 7 neutrons)
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Radioactive decay half-life
• Half-life: the amount of time required for half
of the parent nuclei in a solid to decay
PRS QUESTION. Suppose that one year you put 10 kilograms of a
radioactive isotope in a cabinet in your laboratory. The stuff has a
half-life of 10 years. If 30 years later you stumble across that stuff,
you will find that you still have
1.
2.
3.
4.
5.
7.5 kilograms of the radioactive isotope
5.0 kilograms of the radioactive isotope
2.5 kilograms of the radioactive isotope
1.25 kilograms of the radioactive isotope
0.625 kilograms of the radioactive isotope
10 years
10 kg
10 years
5 kg
10 years
2.5 kg
1.25 kg
We can see that there is an precise
equation that governs the amount of
radioactive substance that remains
versus time:
Current amount
Original amount
()
= 1
2
time
half-life
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Radioactive decay half-life
• Half-life: the amount of time required for half
of the parent nuclei in a solid to decay
• Half-lives range from small fractions of a
second to billions of years
40
40
Decay rate
is precise!
K
Ar
Half-life = 1.25 billion yrs
• Start with 1 gram of pure
potassium-40
• After 1.25 x 109 years, it
will have turned into 0.5
g of argon-40 and 0.5 g of
potassium-40
• 40K decays exponentially;
40Ar grows exponentially
Radiometric dating requires
chemistry knowledge!
• How do we know the initial composition of a rock?
• Argon-40 does not combine with other elements into
solids and does not condense in the protosolar nebula
• If we see 40Ar “trapped” inside a rock, we know that
it started out as 40K and decayed into 40Ar. This is
why this only works for solids - after the decay,
the 40Ar has to be trapped in place.
• Radioactive isotopes have been intensively studied,
so many parent-daughter duos can be analyzed to
infer a consistent age of a solid.
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Examples
• Some rocks brought back from the Moon contain lead206, but these minerals cannot contain lead when they
initally form.
• However, they can form with uranium-238, which decays
into lead-206 with a half-life of 4.5 billion years.
• Laboratory measurements show that these Moon rocks
contain equal amounts of uranium-238 and lead-206.
Therefore these lunar rocks are 4.5 billion years old!
• The radiometric date only goes back to the last time the
rock solidified. Rocks often melt on Earth, so they only
provide lower limits on the age. Oldest Earth rocks: >4
billions years old
Meteorites are ideal for determining
when the protosolar disk formed
• Leftovers from initial protosolar disk
• Oldest known meteorites: 4.55 billion years
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Xenon-129 in meteorites
• Like argon, xenon refuses to condense
into rocks.
• But, xenon-129 is found in meteorites.
• Iodine, on the other hand, can
chemically bind and become part of
rocks
• Iodine-129 radioactively decays into
xenon-129, but the half-life is “only” 17
million years.
• Iodine must be quickly incorportated
into a rock before it turns into xenon129
• Iodine-129 is produced inside stars, so
these meteorites must have
formed relatively soon after some
nearby star had exploded.
A nearby star
explosion likely
provided the
iodine-129 as well
as the “trigger” for
the initial collapse
Extrasolar Planets
(Unit 34)
• Our Sun has a family of planets. Do other
stars have them as well?
• First direct evidence of the existence of an
extrasolar planet was obtained in 1995.
– A planet was discovered in orbit around the star 51
Pegasi.
– Over 300 such extrasolar planets are now known to
exist.
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Most extrasolar planets cannot be
observed directly in pictures for two
reasons:
• The angle between a
star and its planets,
as seen from Earth,
is too small to
resolve with our
biggest telescopes.
• A star like the Sun
would be a billion
times brighter than
the light reflected
off its planets.
Background: binary stars orbit
around the center of mass
• Some stars (e.g., Sirius A
& B) are binary stars;
they orbit each other like a
planet orbits a star
• They both orbit around the
center of mass
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Background: binary stars orbit
around the center of mass
• Some stars (e.g., Sirius A
& B) are binary stars;
they orbit each other like a
planet orbits a star
• They both orbit around the
center of mass
Planets and stars like the Sun
and Earth also both orbit a
center of mass, but the center of
mass is very close to the star
due to its greater mass.
Background: binary stars orbit
around the center of mass
• Some stars (e.g., Sirius A
& B) are binary stars;
they orbit each other like a
planet orbits a star
• They both orbit around the
center of mass
Planets and stars like the Sun
and Earth also both orbit a
center of mass, but the center of
mass is very close to the star
due to its greater mass.
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Detecting Extrasolar Planets by
the Doppler Effect Wobble
• We can detect the
planets indirectly by
observing the motion
of the host star.
• The planet
gravitationally tugs
the star, causing it to
wobble.
• This periodic wobble
is measured from the
Doppler Shift of the
star’s spectrum.
The size and period of a binarystar orbit
(or a planet-star orbit)
are governed by Kepler’s 3rd law
P 2 = a3
However, this version of Kepler’s 3rd law only applies to the
Solar System, and only if P is in years and a is in AU
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Newton’s Version of Kepler’s Third Law
Using the calculus, Newton was able to derive
Kepler’s Third Law from his own Law of
Gravity.
In its most general form:
P2 = 4π2 a3 / G (m1 + m2)
If you can measure the orbital period of two
objects (P) and the distance between them (a),
then you can calculate the sum of the masses
of both objects (m1 + m2).
Measuring the Properties of
Extrasolar Planets
Amplitude
Period
• A plot of the radial velocity shifts forms a wave.
– Its wavelength tells you the period and size of the
planet’s orbit.
– Its amplitude tells you the mass of the planet.
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Source of uncertainty: the tilt of the
orbit
• If the orbit is “face-on”,
there will be no
measurable Doppler effect
• The mass that we infer for
the planet depends on the
tilt of the orbit
• In general, the method
provides a robust lower
limit on the mass of the
planet, and usually the true
mass will be less than 2
times larger than the lower
limit
Measuring the Properties of Extrasolar Planets
• The Doppler technique yields only planet masses and orbits.
• Planet must eclipse or transit the star in order to measure its radius.
• Size of the planet is estimated from the amount of starlight it blocks.
• We must view along the
plane of the planet’s orbit for
a transit to occur.
– transits are relatively rare
• They allow us to calculate
the density of the planet.
– extrasolar planets we
have detected have
Jovian-like densities.
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Properties of Other Planetary Systems
• planets appear to be Jovian
• more massive than our system
• planets are close to their stars
• many more highly elliptical
orbits than in our Solar
System
Above: many of the extrasolar
planets so far discovered
Implications for the Nebular Theory
• Extrasolar systems have Jovian planets orbiting close to their
stars.
– Theory predicts Jovian planets form in cold, outer regions.
• Many extrasolar planets have highly eccentric (i.e., not circular)
orbits.
– Theory predicts planets should have nearly circular orbits.
• Is the nebular theory wrong?
–
–
–
–
–
–
Not necessarily; it may be incomplete.
Perhaps planets form far from star and migrate towards it.
Doppler technique biased towards finding close Jovian planets
Are they the exception or the rule?
Migrating Jovians could prevent terrestrials from forming
Is our Solar Solar System rare?
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