Finding Hubble’s Constant

Joey Schmissrauter

Hubble’s Law

v = H0d, where v is velocity in km/s, H0 is a constant and d is a distance in Mpc.

The units of H0 are km*s-1*Mpc-1

The Cepheid Distance Scale

Leavitt’s Period-Luminosity relationM<V> = -2.81log10Pd - 1.43

Where M<V> is the average absolute visual magnitude and Pd is the pulsation period in days.

Expanding Universe and Redshift

• We can calculate the speed of recession using the redshift z.– Z = (λobs-λrest)/λrest

– Z = ((1+vr/c)/(1-vr/c))1/2 – 1

– Vr/c = ((z+1)2 – 1)/((z+1)2 + 1)

d (c/H≅ 0)*((z+1)2 – 1)/((z+1)2 + 1)

H0 = 100*h km*s-1*Mpc-1

Cosmic microwave background (CMB)

[h]WMAP = 0.71 ± ~.03[H0]WMAP = 2.30 X 10-18 s-1

Hubble time

• d = v*tH = H0*d*tH

• d = H0*d*tH

• 1 = H0*tH

• 1/H0 = tH

• tH = 1/(3.24 X 10-18h-1)

• tH = 9.78 X 109 h-1 yr