- #1

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## Main Question or Discussion Point

Good day all,

First of all, I want to let you guys know that I'm quite new to the subject so please bear with me in case I'm asking a very basic question here. I have a struggle with the way the Age of the Universe is calculated by using Hubble's Law: V = H x D and I hope you guys could clear this up for me. Please note that my question is based on the following YouTube video where the Age of the Universe is being calculated at 5:18 :

Now, in the video he says that H has a constant of approximately 75 km/s/Mp (values may vary a bit depending on the source). I'm seeing this constant as an acceleration. An object that is within a Mp will move at 75km/s away. By the time that same object passes a distance of 1 Mp, it will move away at 150km/s. So for every Mp it reaches, it will go faster. This can be rewritten to calculate how much faster it goes for every meter which is 75000 m / 3.08567758 x 10^22 (1 Mp) = 2.43 x 10^-18 m/s/m. From this new information I can conclude that the object doesn't have a constant velocity of 75km/s over the whole Mp but that the velocity gradually increases over that Mp. By the time the object reaches the very last meter of the Mp, only then will it have reached a velocity of 75 km/s (in case that object started with velocity 0 that is)

The guy in the mentioned video calculates the Age of the Universe by giving an example of an object being at distance D1 and has a velocity of V1. From that you can say that time T = D1 / V1. Since V1 could be rewritten as the Hubble's formula (H x D1), the formula is then T = D1 / (H x D1), the D1's then cancel each other which shows that T = 1 / H. From that he then calculates 1 / (2.43 x 10^-18 m/s/m) which then gives the Age of the Universe.

Now, here's the thing I can't seem to wrap my head around. This Age calculation is based on a fact that the object had a constant velocity of V1. However, I just concluded that V1 differs for every meter an object goes, since it accelerates at 2.43 x 10^-18m/s for every meter it travels. When the guy rewrote V1 as H x D1, it will only give the velocity that the object had when it had that very distance of D1. But before it reached D1, it must have had different velocities since the velocity depends on the distance. Therefore, the time it needed for it to reach D1 would be longer (since it had smaller velocities before it reached D1). The guy in the video would therefore have underestimated the Age of the Universe.

The thing is, other video explanations -even a lecture from Yale University on this- that I found basically show the same calculation. That’s when I thought I must be missing something here but I just can’t seem to notice what. Am I doing something wrong here? If so, what exactly?

First of all, I want to let you guys know that I'm quite new to the subject so please bear with me in case I'm asking a very basic question here. I have a struggle with the way the Age of the Universe is calculated by using Hubble's Law: V = H x D and I hope you guys could clear this up for me. Please note that my question is based on the following YouTube video where the Age of the Universe is being calculated at 5:18 :

__https://www.youtube.com/watch?v=pSqJD6KF0Rw__Now, in the video he says that H has a constant of approximately 75 km/s/Mp (values may vary a bit depending on the source). I'm seeing this constant as an acceleration. An object that is within a Mp will move at 75km/s away. By the time that same object passes a distance of 1 Mp, it will move away at 150km/s. So for every Mp it reaches, it will go faster. This can be rewritten to calculate how much faster it goes for every meter which is 75000 m / 3.08567758 x 10^22 (1 Mp) = 2.43 x 10^-18 m/s/m. From this new information I can conclude that the object doesn't have a constant velocity of 75km/s over the whole Mp but that the velocity gradually increases over that Mp. By the time the object reaches the very last meter of the Mp, only then will it have reached a velocity of 75 km/s (in case that object started with velocity 0 that is)

The guy in the mentioned video calculates the Age of the Universe by giving an example of an object being at distance D1 and has a velocity of V1. From that you can say that time T = D1 / V1. Since V1 could be rewritten as the Hubble's formula (H x D1), the formula is then T = D1 / (H x D1), the D1's then cancel each other which shows that T = 1 / H. From that he then calculates 1 / (2.43 x 10^-18 m/s/m) which then gives the Age of the Universe.

Now, here's the thing I can't seem to wrap my head around. This Age calculation is based on a fact that the object had a constant velocity of V1. However, I just concluded that V1 differs for every meter an object goes, since it accelerates at 2.43 x 10^-18m/s for every meter it travels. When the guy rewrote V1 as H x D1, it will only give the velocity that the object had when it had that very distance of D1. But before it reached D1, it must have had different velocities since the velocity depends on the distance. Therefore, the time it needed for it to reach D1 would be longer (since it had smaller velocities before it reached D1). The guy in the video would therefore have underestimated the Age of the Universe.

The thing is, other video explanations -even a lecture from Yale University on this- that I found basically show the same calculation. That’s when I thought I must be missing something here but I just can’t seem to notice what. Am I doing something wrong here? If so, what exactly?

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