Hubble’s Law

Edwin Hubble(1889-1953)

• Measured distances to nearby galaxies using Cepheid variables

• Galaxies are islands of stars• Developed a classification scheme

for galaxies.• Discovered the Expansion of the

Universe• Space telescope named after him!

We measure galaxy distances using a chain of techniques!

Hubble’s Law

v = Ho x d

V = 0 2800210014007007001400

km/sec

10 Mpc 20 Mpc 30 Mpc 40 MpcMilky Way A B C

V = 02800 2100 14007007001400

km/sec

10 Mpc 20 Mpc30 Mpc40 Mpc

Milky Way A B C

10 Mpc20 Mpc Alien’s Galaxy

Recessional Velocity is Proportional to Distance

The Universe is Expanding!!

y = mx + b

m = slope = Hubble’s Constant (Ho)

y - recessional velocity(v) x - distance(d)

Equation of a Straight Line

v = Ho x d

Hubble’s Law

Hubble DiagramHubble Diagram

Hubble’s LawHubble’s Law

v = Ho x dHubble DiagramHubble Diagram

Finding a Galaxy’s Finding a Galaxy’s Distance Distance Hubble’s LawHubble’s Law

d = v / Ho

To Find Distance: Measure recessional velocity (red shift)

132 Mpc

Sample Galaxies

• Distance– images

• Recessional Velocity– spectra

S

mm 49.4Mpc 15.6d

S

mm 49.4Mpc 15.6d

Measuring Distance

• Elliptical galaxies - same physical size (0.032 Mpc)• Distances inversely proportional to angular size• Virgo – known distance of 15.6 Mpc

d = 15.6 Mpc49.4 mm

S

Measuring Recessional Velocity

388.8 nm 501.5 nm

H line

112.7 nm

L – measure distance (mm) between the 388.8 nm and the 501.5 nm emission lines

x – measure distance (mm) between the 388.8 nm line and the H line

λo = 396.8 nm (laboratory wavelength of the H line)

λobs = 388.8 nm + (112.7 nm)x

L

c (λobs – λo)

λo

v =

Observed Wavelength of H LineRecessional Velocity

v = Ho x dHubble DiagramHubble Diagram

Hubble DiagramHubble Diagram

Procedure- plot data

- draw best fit line

- find slope (Ho)x

x

x

x

x

rise

runslope = rise/run

End