Orbiting the known Universe
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AlternateGravity
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Orbiting the known Universe
I was trying to calculate how fast an object would need to move in order to orbit an object with the mass of the observable universe at a distance of 48 billion light years away and I was getting a result of 8.4E46m/s which is much faster than the speed of light, which makes it seem to big to be the correct answer. Can anyone tell me how fast something would need to move in order to orbit an object with the mass of the observable universe at a distance of 48 light years away ignoring the fact that the universe is expanding and the effect of dark energy?
Gravitons would be my favorite particle as their existence could prove extra dimensions.
Re: Orbiting the known Universe
I took two years of physics in high school (and loved it), so I was eager to solve this for myself. I found the equation for finding the speed of an orbiting body, which is:
V = sqrt((G * m)/r)
Where G is the gravitational constant, m is the mass of the body being orbited, and r is the radius of the orbit. WolframAlpha gave me an estimate for the universe's mass, and also converted the radius from light years to meters. Then I just plugged the values in and simplified the equation. The answer I got was 7.1 x 10^8 meters/second, or 2.4 times the speed of light. I checked myself with my calculator and got the same answer, so I think my answer is correct.
Link to my work (the picture's too big to embed).
V = sqrt((G * m)/r)
Where G is the gravitational constant, m is the mass of the body being orbited, and r is the radius of the orbit. WolframAlpha gave me an estimate for the universe's mass, and also converted the radius from light years to meters. Then I just plugged the values in and simplified the equation. The answer I got was 7.1 x 10^8 meters/second, or 2.4 times the speed of light. I checked myself with my calculator and got the same answer, so I think my answer is correct.
Link to my work (the picture's too big to embed).
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A Random Player
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Re: Orbiting the known Universe
I just typed it into Wolfram.
It gives 7*10^8 m/s, or 2.3c, which matches Neal's answer.
You can't save this result by claiming a non-point-mass, because of the shell theorem.
Of course, the OU's Schwarzchild radius is 530 billion ly, so... (Something doesn't make sense. I can certainly escape the observable universe with enough energy..)
To orbit at c (ignoring relativity), you would need to be 260 billion ly away.
It gives 7*10^8 m/s, or 2.3c, which matches Neal's answer.
You can't save this result by claiming a non-point-mass, because of the shell theorem.
Of course, the OU's Schwarzchild radius is 530 billion ly, so... (Something doesn't make sense. I can certainly escape the observable universe with enough energy..)
To orbit at c (ignoring relativity), you would need to be 260 billion ly away.
$1 = 100¢ = (10¢)^2 = ($0.10)^2 = $0.01 = 1¢ [1]
Always check your units or you will have no money!
Always check your units or you will have no money!
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testtubegames
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Re: Orbiting the known Universe
Sean Carroll wrote a nice post about why the universe isn't a black hole. There aren't any numbers in the article to compare to yours... which would be helpful, since he states that the Schwartzschild radius of the observable universe is roughly the radius. So maybe you're missing something in your calculations? (Because at this point, you really, really need to use General Relativity, so perhaps the 'mass' you looked up gets extra terms from pressure/energies.)
As for the necessary orbital speed... since your answer is above c, we'll need relativistic equations instead of Newtonian ones. This wiki page is a pretty good resource, though at first glance I didn't see one simple equation you could plug into. And they are pretty heady.
But, of course, I already churned through all those equations to make a computer program that can solve them. (Yay!) So the fastest way I could think to solve this GR problem is to use the Gravity Simulator... scaled appropriately. So, once you are sure you've got an accurate measure of the mass/energy of the universe that you're orbiting... you could scale the mass/speed-of-light/radius down by some factor, create it in the GSim with relativity on, and see what happens.
As for the necessary orbital speed... since your answer is above c, we'll need relativistic equations instead of Newtonian ones. This wiki page is a pretty good resource, though at first glance I didn't see one simple equation you could plug into. And they are pretty heady.
But, of course, I already churned through all those equations to make a computer program that can solve them. (Yay!) So the fastest way I could think to solve this GR problem is to use the Gravity Simulator... scaled appropriately. So, once you are sure you've got an accurate measure of the mass/energy of the universe that you're orbiting... you could scale the mass/speed-of-light/radius down by some factor, create it in the GSim with relativity on, and see what happens.