ohio university - lancaster campus slide 1 of 17 spring 2009 psc 100 hubble’s law: the age, size,...
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Ohio University - Lancaster Campus slide 1 of 17Spring 2009 PSC 100
Hubble’s Law:
The Age, Size, and Expansionof Our Universe
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In the early 20th century, Vesto Slipher andEdwin Hubble discovered that all galaxiesoutside of our Local Group are moving awayfrom us.
http://www.thunderbolts.info/tpod/2004/images/041109hubble-redshift.jpg Lunarmark.blogspot.com
The motion of every galaxy has 2 components:proper motion (perpendicular to our line of sight) and radial motion (along our line of sight.)
The radial motion component of nearly everygalaxy we can see is away from us. How can wetell this?
proper motionradial motion
actual motion
Earth
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The Doppler Effect
If the source of light is moving away from anobserver, the wavelength of the light is stretched.This is a redshift.
Image Credit:Wikipedia(Redshift)
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Hubble determined the distances to many ofthese galaxies using cepheid variable starsas ‘standard candles.’
What he discovered was astounding:The radial velocity of a galaxy is directlyproportional to its distance.
A galaxy 100 MLY away from us is recedingaway from us twice as fast as a galaxy50 MLY away.
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This relationship, which has come to be knownas Hubble’s Law, can be used to establish boththe size and the age of the universe.
Credit: imagine.gsfc.nasa.gov
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Doppler Shift Equation:
change in wavelength = speed of recessionunshifted wavelength speed of light
Δλ = vr
λ0 c
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Example: The normal wavelength of H-α light is656.3 nm. This light is observed to be shiftedto 670 nm when coming from a galaxy. What isthe recessional velocity of the galaxy?
(670 nm – 656.3 nm) = vr 656.3 nm 3.00 x 105 km/s
13.7 nm x 3.00 x 105 km/s = 6300 km/s 656.3 nm
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Hubble determined the distance to many suchgalaxies, finding that their velocities anddistances were directly proportional.
Today, Hubble’s Law is written:
Velocity = H0 · distance
velocity is in km/sec distance is in MLY or MPcH0 is the Hubble Constant.H0 has units of 1/time.
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Different experiments have attempted todefine H0 accurately:
70.1 ± 1.3 km/sec/MPc (WMAP)72 ± 8 km/sec/MPc (HST)70.8 ± 4 km/sec/MPc (NASA average)
What is NASA’s average value for H0 inunits of km/sec/MLY?
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How does this determine the age and size ofthe visible universe?
Re-arrange the equation:
Velocity ÷ H0 = distance
Since light moves at a finite speed (3 x 105 km/s)it takes time to cover distance.
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3.00 x 105 km/s ÷ 21.7 km/s/MLY = 13,825 MLY
Our universe has been expanding for 13.8 billion years, and our “horizon” i.e. the edge of our visible universe is 13.8 billion light years away.
This value includes a number of assumptions, whichwe’ll look at when we study cosmology.
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Credit: www.astroex.org - ESA/ESO’s Astronomy Exercise Series
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Some Examples:
1)How fast should a galaxy be receding from us,if the galaxy is 200 MLY away?
H0 · distance = velocity
21.7 km/s/MLY · 200 MLY = 4340 km/sec
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2) How far away is a galaxy that has arecessional speed of 35,000 km/sec?Give your answer in both MLY & MPc.
velocity ÷ H0 = distance
35,000 km/sec ÷ 21.7 km/s/MLY = 1613 MLY or
1.61 billion LY or 495 MPc
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What happens when you do too much math!Credit: snoedel.punt.nl