Review of some Basics

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Review of some Basics
T.J.Turner Extragalactic Astronomy and
Cosmology Review A few examples of Newtonian
Physics Light Thermal Radiation - Black
Body Continuum/Emission/Absorption Spectra
Doppler Effect Luminosity and Flux Extinction


Lecture 4
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Recap of Lecture 3

• We discussed Galileos Principle of Equivalence,
• because mi A G mg M R-2 and inertial and
  gravitational masses are equivalent
• A G M R-2
• If all forces apart from gravity can be ignored,
  all objects fall at the same rate

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Recap lecture 3

• Isaac Newton discovered that it is gravity which
  plays the vital role of determining the motion of
  the planets - concept of action at a distance
• Newtons law of universal gravitation
• Every mass attracts every other mass
• Force drops off with square of distance
• Keplers laws are a direct consequence of
  Newtons law of gravity

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Recap lecture 3
Newtons 3 laws of motion 1Every body
continues in its state of rest or (straight-line)
motion until compelled to do otherwise
by an external force (inertial
frames) 2Force equals Mass times Acceleration
Fma or Fnet dp/dt 3To every Force there is
an equal ( opposite) Reaction F12 -F21 We
also derived the Law of Universal Gravitation
found by Newton F GMm/r2
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Recap lecture 3
We derived a formula for the escape
velocity and discussed Newtons
generalization of Keplers third law as P24?2
R3 /G(M1M2) Allowed Keplers Laws to be
applied to moons and (much later) binary stars
and extrasolar planets.
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Recap lecture 3
Reading assignment Chapter 3 (Newton) Chapter
4 (pages 90 - 105)
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From Newtonian Physics-Escape Velocity

• vesc ?(2GM/r) M is mass of object from which we
  are escaping, r is dist or radius
• Example 1 Calc the escape velocity from the moon
  compare to that of the Earth
• Moon has M7.4 x 1022 kg, R1.7 x 106 m
• vesc ?(2Gx 7.4 x 1022 / 1.7 x 106 )
• 2409.7 m/s 2.4 km/s

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From Newtonian Physics-Escape Velocity

• Example 2 A space station orbits Earth in
  geosynchronous orbit at 42,000 km from the center
  of the Earth. At what velocity must a probe be
  launched from the station to escape Earths
  gravity? Is there an advantage launching the
  probe from the station rather than direct from
  Earth?
• Earth has M6.0 x 1024 kg, R4.2 x 107 m
• vesc ?(2Gx 6.0 x 1024 / 4.2 x 107 )
• 4365 m/s 4.4 km/s
• much less than 11.2 km/s for escape from Earths
  surface!!

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From Newtonian Physics - g

• Example3 What is the acceleration of gravity on
  the surface of the moon?
• Moon has M7.4 x 1022 kg, R1.7 x 106 m
• FGMm/r2
• gmoon G x M/r2
• gmoon G x 7.4 x 1022 /(1.7 x 106) 2
• 1.7 m s-2
• about 1/6 that of the earth

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From Newtonian Physics - K3

• Example 4 Use the fact the Earth orbits the Sun
  in 1 year at an average distance 150 x106 km to
  calc the mass of the Sun. R? 150 x106 km.
• can use Newtons general version of Keplers 3rd
  law
• P24?2 R3 /G(M1M2)
• and M? M? M?
• to give
• P2 ? 4 ?2 R3 ?/ G M ?

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From Newtonian Physics - K3

• P2 ? 4 ?2 R3 ?/ G M ?
• rearrange
• M? 4 ?2 R3 ?/ G P2 ?
• P ? 1 year 3.15x107 s R? 150 x106 km
  1.5 x 1011 m
• gives
• M? 2 x 1030 kg

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From Newtonian Physics - K3

• Example 5 A satellite orbits Earth in 86,164 s,
  calculate its height above the center of the
  Earth. The mass of the earth is M ? 6.0 x 1024
  kg
• Msatellite M? M ? again, can use Newtons
  general version of Keplers 3rd law
• P2 satellite 4 ?2 R3 satellite/ G M?
• R3 satellite G M? P2 satellite / 4 ?2
• Psatellite 86,164 s M ? 6.0 x 1024 kg,
  gives
• R satellite 4.2 x 107 m

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Understanding Keplers 3rd Law

• Example 6 Use Newtons version of Keplers 3rd
  Law to answer the following
• Imagine another solar system with star the same
  mass as the Sun. Suppose there is a planet in
  that system with mass twice that of Earth and
  orbiting at 1 AU from the star. What is the
  orbital period of the planet? Explain.
• Solution
• The planet mass is small compared to the star
  (which has mass of our Sun). In this case the
  orbital period is indep. of planets mass, as
  Newtons version of K3 contains the sum of masses
  (P24?2 R3 /G(M1M2) ). Thus the orbital period
  of the planet would be 1 year, same as Earth.

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Understanding Keplers 3rd Law

• Example 7 Use Newtons version of Keplers 3rd
  Law to answer the following
• Suppose a solar system has a star four times as
  massive as our Sun. If that system has a planet
  the same mass as Earth orbiting at a distance 1
  AU, what is the orbital period of the planet?
  Explain.
• Solution
• The period squared varies inversely with the sum
  of masses, so the period itself goes as the
  inverse square root of the masses P ?4?2 R3
  /G(M1M2)
• Thus if the star is four times that of the Sun,
  and the planets mass is negligible in comparison,
  then the period will be half that of earth, 6
  months.

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A Few Quick Reminders

• Speed of Light is constant
• Thermal Radiation - Black Body properties
• Continuum/Emission/Absorption Spectra
• Doppler Effect for velocity ltlt c
• Luminosity and Flux - whats the difference?
• Extinction - what does this mean?

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The Speed of Light

• Maxwells equations
• Predict waves of electromagnetic energy
  quickly realized that these were light waves!
• Sometimes light acts a wave and sometimes like a
  particle- wave-particle duality
• The speed of light c appears as a fundamental
  constant in the equations.
• T? x f c 3x 105 km/s 3x 108 m/s
• Energy of a photon E?h? h is
  Plancks constant

c denotes the speed of all EM waves in a vacuum
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Light
Radiation refers to the emission of energy from
an object
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THE SPEED OF LIGHT PROBLEM

• Relativity tells us how to relate
  measurements in different frames.
• Galilean relativity
• Simple velocity addition law
  vtotalvrunvtrain

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Speed of Light

• However, the speed of light is absolute. Cannot
• make an EM wave appear to travel faster by
  emitting it on a moving train !
• Initially, people did not worry about the lack
  of Galilean Invariance for EM waves, most
  physical waves needed a medium to propagate, and
  speeds relate to the medium. Light was thought to
  propagate in the lumniferous Ether (19th century)
• Hypothetical substance that fills space - a
  medium through which light can travel.
• Was presumed that c should be measured with
  respect to the rest frame of the Ether.
• Albert Michelson Edward Morley attempted to
  measure motion of Earth through ether

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Michelson-Morley Experiment 1887
Aim to measure differences in speed of light in
different directions w.r.t ether M-M showed
speed of light same in any direction So,
whats going on??
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M-M

• Major mystery (crisis) in 19th century physics
  two successful theories seemed incompatible!
• Mechanics Galilean Relativity Newtons laws
  did not fit with Electromagnetism Maxwells
  eqns
• Need some new theory (Special Relativity)

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Absoluteness of the Speed of Light

• Absoluteness of the speed of light verified
  today in many ways. E.g., observing a binary star
  system we see distinct stars. If Galilean
  velocity addition applied light from the
  approaching side may catch up with that from the
  receding side, producing a double-image of a
  single star!

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Other remindersthermal radiation
Thermal radiation is emitted from objects with
temperature gt 0 K. The atoms/molecules have
kinetic energy. In opaque objects (like stars)
the photons bounce off atoms before escaping,
makes the shape of the emitted spectrum depend
only on temperature, this radiation is known as a
black body.
Black Body radiation occurs a lot and the
universe is filled with BB radiation at 2.7 K
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Key Properties of Black Bodies
Hotter objects emit more total radn /unit area
(T in Kelvin)
Hotter objects peak at higher energyshorter
wavelength
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Emission/Absorption

Continuum Emission
Continuum Emission
Continuum Emission
Emission Spectrum
Absorption Spectrum
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Emission/Absorption

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Emission/Absorption

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Flux/Luminosity

Flux simply refers to the apparent brightness of
a source
Obeys inverse square law, source twice as far is
x4 dimmer
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Flux/Luminosity

Luminosity is the total energy emitted an object
radiates into space per unit time
Flux luminosity surface area of sphere
Flux luminosity 4? x distance2
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Extinction

Gas/dust between stars between galaxies absorbs
light decreases observed flux
Such a decrease due to interaction with matter
is called extinction
Decrease in flux is a function of freq depends
on the composition of the matter
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Extinction

Decrease in flux is a function of freq depends
on the composition of the matter
read chapter 4 of Hawley Holcomb
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Doppler Shift

Sound waves ffrequency ( of waves passing
fixed point in 1 second) ?wavelength (distance
between two crests of wave) csspeed of the wave
?
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Doppler Shift

• Suppose source is moving towards you with speed V
• Waves get squeezed in dirn of motion (L
  decreases)
• cs stays same (speed of sound)
• So, frequency must go up

blueshift
redshift
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Doppler Shift

Non-relativistic formula (v ltlt c) v/c ??/ ?rest
Works on light too
Review Doppler tutorial at www.astronomyplace.com
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Doppler Shift

For v ltlt c radial velocity shifted wavelength
- rest wavelength speed of light
rest wavelength gt0 redshift, moving away from
us lt0 blueshift, moving towards us
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Doppler Shift

Example The rest wavelength of one of the
visible lines of H is 656.285 nm. The line is
easily identifiable in the spectrum, but is
observed at a wavelength of 656.255 nm. What is
the radial velocity and direction of Vega? The
observed wavelength is shorter than expected so
Vega is moving towards us and the line is
blueshifted. (656.255 - 656.285) x 300,000
-13.7 km/s
656.285 Vega is moving towards us at 13.7 km/s
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Doppler Shift

• Example 2 In H, the transition from level 2 to
  level 1 has a rest wavelength 121.6 nm. Suppose
  you see this line at 120.5 nm in Star A, 121.2 in
  Star B, 121.9 nm in C and 122.9 nm in D. Which
  stars are approaching, receding, and at what
  speeds?
• Solution v/c ??/ ?rest
• v(120.5-121.6)/121.6 x 3x105 -2714 km/s
  (towards us)
• v(121.2-121.6)/121.6 x 3x105 -987 km/s (toward
  us)
• v(121.9 - 121.6)/121.6 x 3x105 740 km/s (away)
• v(122.9 - 121.6)/ 121.6 x 3x105 3207 km/s
  (away)

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Can find more on all this

Doppler tutorial and others at www.astronomyplace
.com also see text under Browse the Book menu