# Back to the Beginning of Time

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We know if we have traveled 100 miles steadily at 50 miles per hour, we must have left 2 hours earlier. From the redshift z we have learned how to find the velocity v. From the Hubble Law we have learned we have learned the distance d for several galaxy clusters. We should be able to learn when each one left us.

Virgo Cluster of Galaxies

The Virgo cluster's velocity is 1143 km/s and its distance is 16 Mpc.

Virgo Cluster

First we change 16 Mpc to kilometers.

one parsec = 30,900,00,000,000 km

one megaparsec, a million parsecs = 30,900,000,000,000,000,000 km

An easier way to write this is

1 Mpc = 3.09 x 1019km

(Note: 19 is the number of decimal places you moved to get 3.08.)

16 Mpc must be 16 times this, or 4.94 x 1020 km.

The time to travel those 16 Mpc was

distance 4.94 x 1020 km / speed 1143 km/s = 4.32 x 1017 seconds

Since there are 3.156 x 107 (365.26x24x60x60 = 31,558,464) seconds in a year, it took 13,860,000,000 years for the galaxy cluster to reach 16 Mpc.

The Virgo cluster of galaxies started its journey over 13 billion years ago !!!

Hydra Cluster of Galaxies

The Hydra Cluster is 49 Mpc away, receding at 3420 km/s.

Hydra Cluster

This is the same as we did with Virgo, but let's make it simpler to follow. We know the velocity v and the distance d. We want to find the time t to travel this distance by dividing distance by velocity

t = d / v

The first step is to convert the distance in Mpc to km. Since a megaparsec is 3.09 x 1019 km, we just multiply 49 x 3.09 x 1019

49 Mpc must be 1.51 x 1021 km

We divide the distance 1.51 x 1021 km by the speed 3420 km/s, and find it took the galaxy cluster 4.42x1017seconds to travel 49 Mpc. Since there are 3.16x107 seconds in a year, it took 1.39x1010 or 13.9 billion years for the galaxy cluster to reach 49 Mpc. That is, the Hydra cluster of galaxies started its journey over 13 billion years ago !!!

Coma Cluster of Galaxies

The Coma Cluster of Galaxies is 90 Mpc distant, traveling away at 6300 km/s.

Coma Cluster

d = 90 Mpc x 3.09 x 1019 km/Mpc = 2.78 x 1021 km

t = 2.78 x 1021 km / 6300 km/s = 4.41 x 1017 seconds

Since there are 3.16x107 seconds in a year, we find it took 1.39x1010 or 13,900,000,000 years for the galaxy cluster to reach 90 Mpc. That is, the Coma cluster of galaxies started its journey over 13 billion years ago !!!

Hercules Cluster of Galaxies

The Hercules Cluster of Galaxies is 154 Mpc away, receding at 10,800 km/s.

Hercules Cluster

d = 154 Mpc x 3.09 x 1019 km/Mpc = 4.76 x 1021 km

t = 4.76 x 1021 km / 10800 km/s = 4.41 x 1017 seconds

Since there are 3.16x107 seconds in a year, we find it took 1.39x1010 or 13,900,000,000 years for the galaxy cluster to reach 154 Mpc. That is, the Hercules cluster of galaxies started its journey over 13 billion years ago !!!

Corona Borealis

The Corona Borealis Cluster of Galaxies is 180 Mpc distant, receding at 12600 km/s.

Corona Borealis Cluster

Since a megaparsec is 3.09 x 1019 km, then 180 Mpc must be 5.56 x 1021 km.

d = 180 Mpc x 3.09 x 1019 km/Mpc = 5.56 x 1021 km

t = 5.56 x 1021 km / 12600 km/s = 4.41 x 1017 seconds

Since there are 3.16x107 seconds in a year, we find it took 1.39x1010 or 13,900,000,000 years for the galaxy cluster to reach 180 Mpc. That is, the Corona Borealis cluster of galaxies started its journey over 13 billion years ago!!!

The Beginning of Time

Every cluster of galaxies began moving away from us at the same moment ... from the same place ... from the BIG BANG!!!