Example: Units of the Hubble Constant

First, an everyday example: Suppose you are told someone is driving at 100 km/hr and you want to know how long it will take them to go 130 miles to reach you. How do you figure this out.

D=Vt
so
t=D/V

But the units of speed and distance given are incompatible. Speed is length/time and distance is length, but the units for the length in the speed here is kilometers and the units for the length in the distance is miles. You must either convert the kilometers to miles or the miles to kilometers. 1 mi = 1.6 km or 1 km =0.625 mi.

time = (130 mi x 1.6 km/mi) / 100 km/hr = 208 km / 100 km/hr = 2.08 hrs

time = (130 mi) / (100 km/hr x 0.625 mi/km) = 130 mi / 62.5 mi/hr = 2.08 hrs

The Hubble Constant is typically expressed in units of

H = km/sec/MLY (km per sec per million light years)
or
H = km/sec/Mpc (km per sec per million parsecs)

This is a length divided by a time divided by a length so has units of 1 over time, but the two lengths are in different units. We need to convert the million light years (MLY) or the million parsecs (Mpc) to kilometers (km).

1 LY = 9.461 x 1015 m = 9.461 x 1012 km   (Appendix 6 & 1 km = 103 m)

1 MLY = 9.461 x 1012 x 106 = 9.461 x 1018 km

If, suppose H = 20 km/sec/MLY, then

    H = 20 km/sec/(9.461 x 1018 km) = (20/9.461) x 10-18 (km/sec/km) = 2.11 x 10-18 1/sec

Note: There are 60x60x24x365.25 = 3.16x107 sec in a year.

Updated: 2003.01.27 (Monday) 15:44:15 EST

Visions of the Universe
Bob Stein's home page, email: steinr@pilot.msu.edu