# The Naked Scientists Forum

### Author Topic: How fast do objects move away from Earth?  (Read 2673 times)

#### thedoc

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##### How fast do objects move away from Earth?
« on: 22/05/2015 13:50:02 »
Martin Fennell asked the Naked Scientists:

http://www.telegraph.co.uk/news/science/space/11436236/Astronomers-find-black-hole-12bn-times-bigger-than-the-sun.html

The thing that blows my mind are these two numbers:

"The new object, named SDSS J0100 2802, is 12.8 billion light years from Earth and was formed just 900 million years after the Big Bang"

As the Universe is 13.8 billion years old, does this mean the object is moving away from the earth at 12.8/13.8 = 92% of the speed of light?

Thanks and keep up the good work.

What do you think?
« Last Edit: 22/05/2015 13:50:02 by _system »

#### jccc

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##### Re: How fast do objects move away from Earth?
« Reply #1 on: 22/05/2015 17:13:46 »
i think i will read those like stories.

#### Bill S

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##### Re: How fast do objects move away from Earth?
« Reply #2 on: 23/05/2015 02:05:24 »
Quote
As the Universe is 13.8 billion years old, does this mean the object is moving away from the earth at 12.8/13.8 = 92% of the speed of light?

It's not as straightforward as that, because of the expansion of the Universe.

There's quite a good calculator, which might help, at:

http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html

#### PmbPhy

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##### Re: How fast do objects move away from Earth?
« Reply #3 on: 23/05/2015 04:15:53 »
Quote from: thedoc
As the Universe is 13.8 billion years old, does this mean the object is moving away from the earth at 12.8/13.8 = 92% of the speed of light?
Where did this come from? I.e. why is he taking the ratio and assuming that it's traveling at 92% the speed of light away from us?

#### evan_au

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##### Re: How fast do objects move away from Earth?
« Reply #4 on: 23/05/2015 11:49:01 »
Quote from: Bill S
There's quite a good calculator, which might help
Bill, I'm afraid that I find the calculator a bit overwhelming.
Could you please describe what values you would plug into which field, and where to read the answer?

#### jeffreyH

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• The graviton sucks
##### Re: How fast do objects move away from Earth?
« Reply #5 on: 23/05/2015 12:20:57 »
To determine this relationship you have to take into account the Weyl postulate. This proposes that no geodesics in the universe will cross and that they originated from a singular point in the finite or infinite past. So in essence you would have to start the calculations at the big bang. Taking into account the period of inflation. This is complicated by the fact that matter as we know it would not have existed early in the process so that the path of any object is incomplete and made up of the trajectories of incomplete parts. So a simple ratio will never work.

#### Bill S

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##### Re: How fast do objects move away from Earth?
« Reply #6 on: 23/05/2015 21:03:57 »
Astronomical Calculator

A few years ago I was helping a friend who was trying to explain some of the complications of the expansion of the Universe to a group of young people.  I found a slightly simpler form of the calculator and did a bit of "swatting".  I'm afraid I've "blanked out" most of it since , but here are some of the key points from the notes I made for him.  It seemed to make sense then:

In terms of light travelling through the Universe this means that there is a distance (usually referred to as a horizon) beyond which we may never be able to see.

Figure 1 is a simplified form of a chart of cosmic times and distances.  It can be created, in varying degrees of complication, on line at: http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html.  In order to demonstrate the use of the table in the context of the present discussion, we do not need all the columns, but anyone wishing to investigate further can do so by following the above link.

The information in the table all relates to the present time; that is 13.8 billion years after the Big Bang.  For a simple demonstration we will use the top line and columns 3, 5 and 6.

At 1.6 billion years post Big Bang (Col 3) something sent some light towards where Earth is now.
At that time it was 4.8 billion light years away (Col 6).  The light took 12.2 billion years to reach Earth (because 13.8 - 1.6 = 12.2).  In that time the distance between the emitting object and Earth's location increased to 23.9 billion light years (Col 5).  From these figures it will be apparent that there is no simple, practical relationship between travel time and either distance then or distance now.

Obviously there is a lot more information that could be obtained from figure 1.  For example, at every point in the history of the Universe there has been a time/distance between two specified locations when/where the Universe's expansion equalled the speed of light.  This varies with time, and is shown in column 4.  Thus, relative to here/now the recession rate equals the speed of light if the figure in column 6 divided by the figure in column 4 equals 1.   From this it might look as though it should be a simple matter to identify the horizon beyond which nothing will ever be visible to us.  Such is not the case, of course.  However, this is not an astronomy primer, and I am not an astronomer, so we will leave this table before I risk spreading too much confusion.

#### evan_au

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##### Re: How fast do objects move away from Earth?
« Reply #7 on: 24/05/2015 12:41:22 »
Thanks for explaining the table, Bill - it gives an idea of the sort of complications involved!

I think "z" is sometimes used as a measure of the redshift (the ratio of the wavelength of the radiation when it was emitted and when it is received - on Earth, in this example)?

So on the top line, S=5 and z=4. Does this mean that the received wavelength is 4 times longer than when it was emitted?
« Last Edit: 24/05/2015 12:47:19 by evan_au »

#### Bill S

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##### Re: How fast do objects move away from Earth?
« Reply #8 on: 24/05/2015 22:44:49 »
Quote from: evan
So on the top line, S=5 and z=4. Does this mean that the received wavelength is 4 times longer than when it was emitted?

That seems logical, but I think this is among the bits I blanked out.  I would have to find my original "swattings" to answer that.  Could take a while.

#### The Naked Scientists Forum

##### Re: How fast do objects move away from Earth?
« Reply #8 on: 24/05/2015 22:44:49 »