1. The Age, Size, and Expansion
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Hubble’s Law:
The Age, Size, and Expansion
of Our Universe

2. In the early 20th century, Vesto Slipher and
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In the early 20th century, Vesto Slipher and
Edwin Hubble discovered that all galaxies
outside of our Local Group are moving away
from us.
Lunarmark.blogspot.com

3. 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 every
galaxy we can see is away from us. How can we
tell this?
actual motion
proper motion
radial motion
Earth

4. The Doppler Effect If the source of light is moving away from an
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The Doppler Effect
If the source of light is moving away from an
observer, the wavelength of the light is stretched.
This is a redshift.
Image Credit:
Wikipedia
(Redshift)

5. Hubble determined the distances to many of
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Hubble determined the distances to many of
these galaxies using cepheid variable stars
as ‘standard candles.’
What he discovered was astounding:
The radial velocity of a galaxy is directly
proportional to its distance.
A galaxy 100 MLY away from us is receding
away from us twice as fast as a galaxy
50 MLY away.

6. This relationship, which has come to be known
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This relationship, which has come to be known
as Hubble’s Law, can be used to establish both
the size and the age of the universe.
Credit: imagine.gsfc.nasa.gov

7. Doppler Shift Equation: change in wavelength = speed of recession
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Doppler Shift Equation:
change in wavelength = speed of recession
unshifted wavelength speed of light
Δλ = vr
λ c

8. Example: The normal wavelength of H-α light is
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Example: The normal wavelength of H-α light is
656.3 nm. This light is observed to be shifted
to 670 nm when coming from a galaxy. What is
the recessional velocity of the galaxy?
(670 nm – nm) = vr
656.3 nm x 105 km/s
13.7 nm x 3.00 x 105 km/s = km/s
656.3 nm

9. Velocity = H0 · distance Hubble determined the distance to many such
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Hubble determined the distance to many such
galaxies, finding that their velocities and
distances were directly proportional.
Today, Hubble’s Law is written:
Velocity = H0 · distance
velocity is in km/sec distance is in MLY or MPc
H0 is the Hubble Constant.
H0 has units of 1/time.

10. Different experiments have attempted to define H0 accurately:
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Different experiments have attempted to
define 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 in
units of km/sec/MLY?

11. Velocity ÷ H0 = distance How does this determine the age and size of
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How does this determine the age and size of
the 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.

12. This value includes a number of assumptions, which
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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, which
we’ll look at when we study cosmology.

13. Ohio University - Lancaster Campus slide 13 of 17 Spring 2009 PSC 100
Credit: - ESA/ESO’s Astronomy Exercise Series

14. How fast should a galaxy be receding from us,
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Some Examples:
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 = km/sec

15. How far away is a galaxy that has a
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How far away is a galaxy that has a
recessional 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 = MLY or
1.61 billion LY or 495 MPc

17. Ohio University - Lancaster Campus slide 17 of 17 Spring 2009 PSC 100
What happens when you do too much math!
Credit: snoedel.punt.nl