so in Walters lecture we learned that escape velocity, v = (GMs/Rs) to the 1/2 power or sq rt
If we assume a black hole has so much gravity that it does not allow light to escape, then v = 3 x10^8 m/s
G = 6.67 x 10^-11 and the mass of the sun 1.99 x 10^30 kg and there we go.
rearrange to solve for the radius our crunched sun would have to be:
Rs = GMs/v^2 And I get about 1,474 m or 1.47 km
So the sun would have to have a radius of about nine tenths of a mile while maintaining a mass of 1.99 x10^30 kg
Who volunteers to squish it?
This of course is based on the definition of a black hole given above.
Please check my numbers or elaborate.
I agree. Sort of makes me wonder though about time dilation. Does the matter in that spinning star move slower through time if it gets spinning fast enough?
I know the theory of relativity applies for linear motion, but wonder about stuff that spins really fast. (not my area of expertise, I just think it is fun to learn about)
Sorry, today is expense voucher day. had to work through lunch hour, so I am taking a super late lunch.
Read the answer, thanks for the interesting question.
You used the low-orbit velocity and not the escape velocity pgardn, so the Schwarzchilld radius (found from that same argument) is 3km for a solar mass black hole.
In MKS units:
R = 2GM/c^2 = 2*7*10^(-11)*2*10^(30)/(3*10^8)^2 = (2*7*2)*10^(-11)*10^(30)/(9*10^(16)) = 30 *10^(-11)*10^(30)/10^(17) = 30*10^2 = 3000 (meters, since MKS units),
where I fudged things by calling 28=30 and 9=10 to make the math easier. So R = 3000 meters = 3km
I used the the idea that escape velocity for my hypothetical black hole would be the speed of light. That was the equation he gave for escape velocity I thought? So what should I have done differently? I'm not really a physics guy and definitely not an astronomy type. How dare this schwazer character mess up my thoughts.
oh thanks I see the above, I missed a 2... I need to go back and see why.
If you saw something falling into a black hole from a viewpoint outside, I think you would see it stuck at the event horizon forever. But really you wouldn't be able to see it because gravitational redshift would lower every photon's energy to arbitrarily close to zero just outside the Schwarzchild radius anyways, I think (recall the energy of a photon is ENERGY = PLANCK_CONSTANT * FREQUENCY, and gravitational redshift stretches out the wavelength, thus lowering the frequency). I mean, it would be so faint. But I know very very little general relativity, so DMC (who I could swear I saw was a physicist) could probably come in and clear things up way more, and maybe correct any errors I may have made.
Last edited by baseline bum; 04-01-2014 at 03:57 PM.
Oh , I just wrote the equation wrong. Using cconservation of energy 1/2mv^2 for K and I just left out the 2...
Always have others check your work.
Escape velocity is the speed you need to get to infinity with zero kinetic energy. Any faster and you get to infinity with a little extra kinetic energy. So since potential is U=0 at a distance r=infinity, setting K=0 the total energy would be E=K+U=0. Since energy is conserved and since you're escaping from radius R at speed v, your energy there, E=K+U = 1/2 m v^2 - GMm/R (your mass is m) must also be zero. Thus you get v^2 = 2GM/R (your mass m cancels) for the escape velocity.
The v = (GM/R)^(1/2) is the speed you need so that you go just far enough forward to balance out how much you fall towards the Sun, keeping in a circular orbit just above the surface. Its when the centripetal acceleration v^2/r is given by, and thus equal to, the gravitational acceleration GM/r^2.
This is where I get lost. Fudging for things really fast and things really small. I don't fully get relativity and definitely not quantum stuff. I have looked at the math for the easy quantum stuff and get lost.
Yes, and, I had no idea I put up the the low earth orbit equation, it was an accident, I just left the 1/2 out using the conservation of energy. In other words I just left out a 2 from what Walter had written in the lecture. But I see the other as well, but it was accidental. You used mv^2/r, yesssssss. The m cancels if equal to newtons law of gravitation. You thought about it just using acceleration, same idea.
But yes, science works es... When others check your work.
and we could even use the conservation of angular momentum for the noncircular orbits... I'm gonna do something in my pants. This is too much good for one man.
Last edited by pgardn; 04-01-2014 at 04:11 PM.
I'm kind of lost myself why that classical equation should even apply, but I don't know much more than the equivalence principle when it comes to GR. If you know some PDE a lot of the weirdness in quantum starts making a bit of sense, provided you first accept the postulated Schrodinger's equation and the Born interpretation of the wavefunction.
I am so lost reading this page lol.
E and M, waves and such, much more difficult for me. I have a much tougher time learning new things while busy, and not in my teens or twentys anymore. This stuff needs to be learned within a certain time frame imo. Biology and Chemistry can be learned older. Physics needs younger pliable minds imo. I'm a biochemistry type with decent understanding of mechanics.
It's kind of funny; that equation r = 2GM/c^2 ~ M for the Schwarzchild radius shows a supermassive black hole, such as the one at the center of the Milky Way, might not be very dense. Since M ~ p r^3 ~ p M^3, where p is density, we have p ~ 1/M^2. Thus density of the space inside the event horizon falls off as the inverse square of the mass. Wonder if that means the supermasive black hole isn't too dense or if it means that there is a lot of empty space between a supermassive black hole and its event horizon. Man, I have to pick up a relativity book, like Carroll maybe. Heard MTW is practically intractable as an introduction.
Last edited by baseline bum; 04-01-2014 at 07:52 PM.
Eh, I'm confusing black hole and singularity in the post above. Of course the singularity is dense.
An astist's rendition of an X-ray binary (like Cygnus X-1 talked about last night):
A better discussion:
The equation at the end comes from the conservation of energy. Initially the potential energy U = 0 since we drop it from infinintely far away and kinetic K = 0 since we drop it at zero speed. So E = 0 gives the total mechancial energy. Since it crashes onto the neutron star with potential U = - G * M * m/R and kinetic energy K=1/2*m*v^2, by the conservation of energy we have 0 = E = K + U = 1/2*m*v^2 - G*M*m/R.
After all the bull theories and worthless K=1/2*m*v^2 equations, Science still cant even explain Stonehenge
Mouse in the house, time to slap that shot into the stands.
So mouse mania thinks one can put math to the intentions of humans living long ago.
You just don't get it, and sadly you probably never will see the beauty.
Go back and put those headphones on and let the music of a chimp playing chopsticks bring you to tears.
First off if you don't get why math is so important to prove the universe had a designer then maybe it's you that should think twice about debating a subject you have no knowledge in even using Google.
Second: I can listen to music debate at the MIT websites and still respond to your lame ass replies, its called mul asking...
something you only do when your masturbating and clicking the mouse.
if i misunderstood evolution as much as you did, i'll be honest, i probably wouldn't buy into it either
let me help try and simplify things...
There is "micro" Evolution that is when you get two dogs to and create a new breed of dog it's from i'ts own "kind" Dogs......so "Micro" Evolution "does" exist.
But when you try and get a cat from a dog that is called "Macro" Evolution and its has not been proven yet.
That is why all the confusion and unnecessary drama you read in these topics, people just don't research anymore.
The textbooks say we all "Evolved" from a fish.... and that is a Lie.
these were a joy to watch. i've never taken astrophysics, but obviously had an elementary understand of it while going through basic physics series. i've taken physical chemistry too, but its not as exciting as astro seems to be
And with all that knowledge can you cure the common cold?
The truth is Science is still learning about the Universe and needs to cure Diabetes before it looks for another drop of water on Mars.
amen to that
damn pgardn and baselinebum are geniuses?
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