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

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Ohio University - Lancaster Campus slide 1 of 17Spring 2009 PSC 100

Hubble’s Law:

The Age, Size, and Expansion

of Our Universe

Ohio University - Lancaster Campus slide 2 of 17Spring 2009 PSC 100

In the early 20th century, Vesto Slipher and

Edwin Hubble discovered that all galaxies

outside of our Local Group are moving away

from 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 every

galaxy we can see is away from us. How can we

tell this?

actual motion

proper motion

radial motion

Earth

Ohio University - Lancaster Campus slide 4 of 17Spring 2009 PSC 100

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)

Ohio University - Lancaster Campus slide 5 of 17Spring 2009 PSC 100

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.

Ohio University - Lancaster Campus slide 6 of 17Spring 2009 PSC 100

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

Ohio University - Lancaster Campus slide 7 of 17Spring 2009 PSC 100

Doppler Shift Equation:

change in wavelength = speed of recession

unshifted wavelength speed of light

Δλ = vr

λ0 c

Ohio University - Lancaster Campus slide 8 of 17Spring 2009 PSC 100

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 – 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

Ohio University - Lancaster Campus slide 9 of 17Spring 2009 PSC 100

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.

Ohio University - Lancaster Campus slide 10 of 17Spring 2009 PSC 100

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?

Ohio University - Lancaster Campus slide 11 of 17Spring 2009 PSC 100

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.

Ohio University - Lancaster Campus slide 12 of 17Spring 2009 PSC 100

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.

Ohio University - Lancaster Campus slide 13 of 17Spring 2009 PSC 100

Credit: www.astroex.org - ESA/ESO’s Astronomy Exercise Series

Ohio University - Lancaster Campus slide 14 of 17Spring 2009 PSC 100

- 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 = 4340 km/sec

Ohio University - Lancaster Campus slide 15 of 17Spring 2009 PSC 100

- 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 = 1613 MLY or

1.61 billion LY or 495 MPc

Ohio University - Lancaster Campus slide 17 of 17Spring 2009 PSC 100

What happens when you do too much math!

Credit: snoedel.punt.nl

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