# Back to the Beginning of Time

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.

If you need one, click this for a web scientific calculator. It accepts power of ten numbers. For example, to enter 3x10^{5} you could write 300000 or 3e5.

## Contents

## Virgo Cluster of Galaxies

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

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 10^{19} km

(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 10^{20} km.

The time to travel those 16 Mpc was

distance 4.94 x 10^{20} km / speed 1143 km/s = 4.32 x 10^{17} seconds

Since there are 3.156 x 10^{7} (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.

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 10^{19} km, we just multiply 49 x 3.09 x 10^{19}

49 Mpc must be 1.51 x 10^{21} km

We divide the distance 1.51 x 10^{21} km by the speed 3420 km/s, and find it took the galaxy cluster 4.42x10^{17}seconds to travel 49 Mpc. Since there are 3.16x10^{7} seconds in a year, it took 1.39x10^{10} 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.

d = 90 Mpc x 3.09 x 1019 km/Mpc = 2.78 x 10^{21} km

t = 2.78 x 10^{21} km / 6300 km/s = 4.41 x 10^{17} seconds

Since there are 3.16x10^{7} seconds in a year, we find it took 1.39x10^{10} 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.

d = 154 Mpc x 3.09 x 10^{19} km/Mpc = 4.76 x 10^{21} km

t = 4.76 x 10^{21} km / 10800 km/s = 4.41 x 10^{17} seconds

Since there are 3.16x10^{7} seconds in a year, we find it took 1.39x10^{10} 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.

Since a megaparsec is 3.09 x 10^{19} km, then 180 Mpc must be 5.56 x 10^{21} km.

d = 180 Mpc x 3.09 x 10^{19} km/Mpc = 5.56 x 10^{21} km

t = 5.56 x 10^{21} km / 12600 km/s = 4.41 x 10^{17} seconds

Since there are 3.16x10^{7} seconds in a year, we find it took 1.39x10^{10} 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**!!!