Why is the answer for Earth's Schwarzschild radius: the volume Earth would have to be compressed in order to form a black hole, exactly the same when derived either from Newtonian mechanics or General Relativity ? | AskScience Blog

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Saturday, May 7, 2016

Why is the answer for Earth's Schwarzschild radius: the volume Earth would have to be compressed in order to form a black hole, exactly the same when derived either from Newtonian mechanics or General Relativity ?

Why is the answer for Earth's Schwarzschild radius: the volume Earth would have to be compressed in order to form a black hole, exactly the same when derived either from Newtonian mechanics or General Relativity ?


Why is the answer for Earth's Schwarzschild radius: the volume Earth would have to be compressed in order to form a black hole, exactly the same when derived either from Newtonian mechanics or General Relativity ?

Posted: 06 May 2016 09:23 PM PDT

I saw this post and someone did a mathematical calculation for the radius :

The formula for escape velocity is Vesc = sqrt(2GM/R) where G is the gravitational constant, M is the mass (of the Earth, in this case) and R is the radius in question.

If we plug c (speed of light) in as Vesc, G = 6.67408 × 10-11 m3 kg-1 s-2, and M = 5.972 × 1024 kg, we can solve for R.

R = 0.8870 cm

Someone else later mentioned that :

The funny thing is that what you did is the classical Newtonian gravity calculation, but in a universe where Einstein's General Relativity is in effect there is no reason to expect that calculation to actually be true. It took tons of work after GR was discovered before Schwarzschild managed to do the calculation and figure this out (Einstein couldn't do it)... and the answer was exactly the same.

I want to know why? Was the general approximation in Newtonian physics relevant here or was there some other reason ?

submitted by /u/p-p-paper
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Why do we use Sodium for street lighting ?

Posted: 05 May 2016 03:25 PM PDT

Hi redditors !

Ok so coming back home today I had a thought I have frequently about how sodium is used in street lighting -at least the orange ones- and I wondered, why did we use sodium specifically ?

I know about how every atoms has its own emission spectrum -and absorption- and that sodium has a double spectral line around 589nm, which is in the 'orange part' of the visible spectrum, but I was wondering, why did we pick sodium and orange lightning specifically.

Was it for economical reasons ? Because Orange was a better choice for a reason I don't really get ?

Thanks in advance for answering !

Edit: Thanks for the answers guys ! That's almost what I thought but the reflection on the impact on astronomy is really interesting !

submitted by /u/ThatSlowBerry
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If I transported a flock of birds to the southern hemisphere, would they fly north for the winter or head further south when it starts getting cold?

Posted: 06 May 2016 07:34 AM PDT

Thus dooming themselves.

submitted by /u/1jl
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What is the absolute fastest that sound can travel, and in what medium can it obtain that speed?

Posted: 06 May 2016 12:29 PM PDT

If there was a giant ring of steel with a radius one foot greater than the Earth's radius placed around Earth, would it seemingly levitate one foot off the ground?

Posted: 06 May 2016 08:39 AM PDT

Let's just assume that the Earth is perfectly round in this situation, and the steel is unbendable and indestructible. Would it appear to float? Why or why not? What if the steel wasn't unbendable/indestructible?

submitted by /u/TheAlmightyLem
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Could a near-light-speed spacecraft travel in a loop, or only in straight lines?

Posted: 06 May 2016 08:53 AM PDT

Lets say I have a spaceship that is capable of accelerating to near light speed (and it takes a while to get going that fast), and I want to use it to experience time dilation and come back to Earth far in the future. Is the only real option to accelerate in a straight line, then come to a stop, turn around, and come back in another straight line? To me this is not ideal because you have to go through two acceleration/deceleration cycles, so the time dilation effect relative to Earth would be lessened. So, could it be possible / practical for the spacecraft to travel in a loop, by continuously adjusting its direction of thrust until it travels in a complete circle?

Intuitively I think that this would not be possible at near-light speeds, but my intuitive sense of the physics here is not too strong. Would be very interested to hear what equations or theorems are relevant here :)

Thanks in advance for any responses!

submitted by /u/Fosforus
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Do we experience less gravity during day time, because of the pull from the sun counteracting Earth's gravity? How big is this effect?

Posted: 06 May 2016 07:35 AM PDT

Is there any evidence that Uranus's axis is slowly "correcting" itself to be in line with the other planets' axes?

Posted: 06 May 2016 09:50 AM PDT

How do isolated populations of animals keep from getting inbred?

Posted: 06 May 2016 07:24 AM PDT

What made me think of this was my run today. I live near a pond, and there is a small family of muskrats in it. I'd say 5 or so at most. Now, there aren't any other ponds or anything for several miles around, so I'm wondering what these populations do. Do they travel back and forth? Do they breed with siblings and parents? How do different types of animals handle this situation?

submitted by /u/RPShep
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Is it possible to write an equation for eccentric anomaly of an elliptical orbit in terms of time?

Posted: 06 May 2016 09:01 AM PDT

I know you can get the mean anomaly in terms of time for an elliptical orbit, but is it possible to get the eccentric anomaly in terms of time?

submitted by /u/Jmaster414
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As the universe continues to expand, is it "seeding" (for lack of a better term) matter behind its boundary or only expanding empty space?

Posted: 06 May 2016 07:35 AM PDT

Put differently, is all the matter there ever will be already "in play," or is some of it still being carried by the expansion wave of the universe?

Edit: to be clear, I'm talking about something like debris riding a shockwave, not spontaneous creation of matter

submitted by /u/dunaan
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Packing: Rolling vs Folding. Is there even a difference?

Posted: 06 May 2016 02:22 AM PDT

I'm packing in a few hours and I should have asked this in advance.

Anyway, does it even make a difference? I'm thinking that however you fold the cloth, the size it takes will be about the same. And people are just exaggerating.

I guess the question is more like, which method compresses the cloth better without the use of a sealed container and a vacuum?

I believe that's the real question since people who are debating about which method to use are concerned about fitting more stuff.

Also ignore the difference in which rolling will occupy the bag more (imagine solid vs liquid in a container). I say to ignore because even with folding you can use your socks to fill in the gaps. Or just roll some to fill the gaps.

submitted by /u/PullIntestinesFrmAss
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Is the amount of oxygen in the air in/arround a big city noticable lower than in small cities or rural areas?

Posted: 06 May 2016 07:59 AM PDT

When I hear a sonic boom, am I hearing all the sound generated by the speeding projectile over a certain distance all in one go?

Posted: 06 May 2016 05:22 AM PDT

This is how I interpret this diagram of a mach cone if we place ourselves at the red dot, but I haven't yet (after some brief internet searching) found anywhere that explains it this way.

Mach cone

submitted by /u/BedSideCabinet
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Heard that we tend to like people who look like ourselves more. Is it about how we actually look, or how we think we look?

Posted: 06 May 2016 02:47 AM PDT

What's the difference between d^2 x(t)/dt^2 = -x(t), and idx/dt=-x(t)?

Posted: 06 May 2016 05:57 AM PDT

In this specific case, it's only true when d2 x(t)/dt2 =idx/dt, but is there a more general connection? The two equations give the same solution set.

submitted by /u/Urist_was_taken
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Why doesn't the black hole at the center of the galaxy cosumes the galaxy itself?

Posted: 06 May 2016 03:47 AM PDT

Why are large primes so desirable and hard to calculate?

Posted: 06 May 2016 04:28 AM PDT

Follow-Up: Why can't a formula like (10n ) +1 be used to find a prime of the desired length?

submitted by /u/Kaingon
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