Back to the Beginning of Time: Difference between revisions
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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. | 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. | The Virgo cluster's velocity is 1143 km/s and its distance is 16 Mpc. | ||
[[File:virgo_cluster_z|600px|center]]] | |||
First we change 16 Mpc to kilometers. | First we change 16 Mpc to kilometers. | ||
<center> | |||
one parsec = 30,900,00,000,000 km | one parsec = 30,900,00,000,000 km | ||
one megaparsec, a million parsecs = 30,900,000,000,000,000,000 km | one megaparsec, a million parsecs = 30,900,000,000,000,000,000 km | ||
<center> | |||
An easier way to write this is | An easier way to write this is | ||
1 Mpc = 3.09 x | <center> | ||
1 Mpc = 3.09 x 10<sup>19</sup>km | |||
</center> | |||
(Note: 19 is the number of decimal places you moved to get 3.08.) | (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 | <center> | ||
16 Mpc must be 16 times this, or 4.94 x 10<sup>20</sup> km. | |||
</center> | |||
The time to travel those 16 Mpc was | The time to travel those 16 Mpc was | ||
distance 4.94 x 1020 km / speed 1143 km/s = 4.32 x | <center> | ||
distance 4.94 x 1020 km / speed 1143 km/s = 4.32 x 10<sup>17</sup> seconds | |||
</center> | |||
Since there are 3.156 x 10<sup>7</sup> (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 | == Hydra Cluster of Galaxies == | ||
The Hydra Cluster is 49 Mpc away, receding at 3420 km/s. | The Hydra Cluster is 49 Mpc away, receding at 3420 km/s. | ||
[[File:hydra_galaxy_cluster_z.jpg|600px|center]] | |||
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 | 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 | <center> | ||
'''t = d / v''' | |||
</center> | |||
The first step is to convert the distance in Mpc to km. Since a megaparsec is 3.09 x | The first step is to convert the distance in Mpc to km. Since a megaparsec is 3.09 x 10<sup>19</sup> km, we just multiply 49 x 3.09 x 10<sup>19</sup> | ||
49 Mpc must be 1.51 x | 49 Mpc must be 1.51 x 10<sup>21</sup> km | ||
We divide the distance 1.51 x | We divide the distance 1.51 x 10<sup>21</sup> km by the speed 3420 km/s, and find it took the galaxy cluster 4.42x10<sup>17</sup>seconds to travel 49 Mpc. Since there are 3.16x10<sup>7</sup> seconds in a year, it took 1.39x10<sup>10</sup> 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 | |||
== Coma Cluster of Galaxies == | |||
The Coma Cluster of Galaxies is 90 Mpc distant, traveling away at 6300 km/s. | The Coma Cluster of Galaxies is 90 Mpc distant, traveling away at 6300 km/s. | ||
[[File:coma_cluster_of_galaxies_z.jpg|600px|center]] | |||
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t = 2.78 x 1021 km / 6300 km/s = 4.41 x 1017 seconds | 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 !!! | 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 | Hercules Cluster of Galaxies | ||
The Hercules Cluster of Galaxies is 154 Mpc away, receding at 10,800 km/s. | The Hercules Cluster of Galaxies is 154 Mpc away, receding at 10,800 km/s. | ||
[[File:hercules_galaxy_cluster_z.jpg|600px|center]] | |||
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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 !!! | 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''' !!! | ||
Revision as of 18:11, 19 March 2012
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.
]
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.
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.
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.
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!!!