13 ms·

Astronomers Have Found a Star Orbiting a Black Hole at 1% the Speed of Light

232 points by curtis 10y ago

JumpCrisscross 10y ago
How much temporal dilation would a relativistic orbit about a frame-dragging massive object create? Would the black hole or other objects orbiting it look weird (relatively--hehe--speaking).
- theemathas 10y ago
  Using 1% of speed of light, it will slow down by 0.005% (That's much less than I expected)
  - sliken 10y ago
    Yes, but doesn't that ignore the gravitational acceleration? Time dilation isn't just speed, it's also acceleration. Even if you could hover very near the event horizon the time dilation would be severe.
    - amelius 10y ago
      As far as I know, there's only speed in the formula of time dilation, not acceleration. See also [1]. [1] http://www.edu-observatory.org/physics-faq/Relativity/SR/clock.html http://www.edu-observatory.org/physics-faq/Relativity/SR/clo...
      - xelxebar 10y ago
        Special relativity gives you dilation from velocity. General relativity gives you dilation from acceleration.
        pdonis 10y ago
        > General relativity gives you dilation from acceleration. Not from acceleration, from depth in a gravitational potential well. See my other posts upthread.
      - Filligree 10y ago
        That's for special relativity, which is only valid if you're not accelerating. This star is, so we'd need general relativity... I don't know what that formula looks like.
        valarauca1 10y ago
        Seeing as the star is in close proximity to a blackhole it would likely be similar to the Kerr-Metric [1] (as we _should_ assume the black hole as some spin). The white star has non-trivial mass of its own which greatly complicates the curvature of the local space-time region and render the Kerr-Metric equations lacking. GR is really complicated FYI. [1] https://en.wikipedia.org/wiki/Kerr_metric https://en.wikipedia.org/wiki/Kerr_metric
        pdonis 10y ago
        > it would likely be similar to the Kerr-Metric Unless the hole is rotating extremely rapidly (which I don't see mentioned), the difference between the Kerr metric and the Schwarzschild metric (which is what I used for the formula I posted upthread) is too small to matter unless you are really close to the hole's horizon.
        jpmattia 10y ago
        You got me curious, and I wanted to put numbers around this. It's worth noting that the actual paper claims only this is a black hole candidate, and is not certain it's a black hole (despite the Science alert headline). The paper guesses that the black hole is ~ 1 solar mass, so the Schwarzschild radius would be about 3 km. The distance is about 2.5x the earth-moon, which is about 10^6 km. btw, paper here: https://arxiv.org/pdf/1702.02167.pdf https://arxiv.org/pdf/1702.02167.pdf
        pdonis 10y ago
        The formula for an object at radius r in the field of a non-rotating gravitating mass M is: sqrt(1 - 2M/r - v^2) instead of sqrt(1 - v^2) (where I am using units where G = c = 1). For an object in a free-fall circular orbit, v^2 = M/r, so the above formula can be simplified to sqrt(1 - 3M/r)
    - valarauca1 10y ago
      Yes, but doesn't that ignore the gravitational acceleration Gravitational acceleration doesn't exist (in GR). All bodies are stationary in GR and observe other things moving in reference to themselves. What we perceive as gravitational acceleration is just objects traveling in straight lines (at constant speeds) though 4D space-time. Circular orbits are just straight lines of constant velocity bent around by the local curvature of space-time (which can be caused by a local density of mass-energy). The idea of acceleration assumes a force is acting on a body. Gravity isn't a force in General Relativity. It is the shape of the universe.
      - pdonis 10y ago
        > Gravitational acceleration doesn't exist (in GR). A better way of stating this would be that objects moving solely under gravity have zero acceleration in GR, because in GR, acceleration means proper acceleration--what is measured by an accelerometer. Objects moving solely under gravity are in free fall. > All bodies are stationary in GR and observe other things moving in reference to themselves. This isn't correct. There is no requirement that an observer in GR must use coordinates in which they are at rest.
    - pdonis 10y ago
      > Time dilation isn't just speed, it's also acceleration. That's not correct. Gravitational time dilation isn't a function of acceleration, it's a function of gravitational potential, i.e., how deep you are in the potential well of the source. (Also, an object that is in a free-fall orbit has zero acceleration in GR, since in GR acceleration is proper acceleration--what is measured by an accelerometer.)
  - jessriedel 10y ago
    If anyone is curious, the reason is that many/most special relativistic effects are proportional to gamma = 1/sqrt(1-v^2/c^2), with gamma = 1 being non-relativistic. Even at v=20% of c, gamma is only 1.02 (a mere 2% effect). http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=Plot%5B1%2FSqrt(1-v%5E2),%7Bv,0,1%7D%5D http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=Plot%5B1...
    - cuspycode 10y ago
      General relativity also accounts for gravitational/accelerational effects, in addition to the speed-related effects. For example, in the Schwarzschild metric[1], effects such as time dilation are on the order of 1-phi/c^2 where phi=GM/r. Or expressed in terms of "g-force": phi=gr. [1] https://en.wikipedia.org/wiki/Schwarzschild_metric https://en.wikipedia.org/wiki/Schwarzschild_metric
- TorKlingberg 10y ago
  As a rule of thumb, relativistic effects are very small below 5-10% of the speed of light. You may still need to calculate them if you want very high precision, like for GPS.
  - splike 10y ago
    There is the relativistic effects of gravity to consider in this case too
    - M_Grey 10y ago
      Right, but for that orbit to be so slow, it must be a very distant orbit.
- overcast 10y ago
  It's not really until you get up near 90% of the speed of light, where dilation starts getting insane. That's when the curve starts to sharply jump straight up.
du_bing 10y ago
Once I read on a book, that there may be a star so huge that it orbits a black hole at half of the speed of light, i.e., 150,000 km/s. Is this possible?
- thriftwy 10y ago
  I think that star size is irrelevant here - any massive object will need to have the same speed to hold a given orbit. It's black hole mass and star's proximity to black hole that are in this equation. Assuming star is much lighter than the black hole, or course.
  - hinkley 10y ago
    But it's possible to have a star that is heavier than a black hole. Say you had a binary star system of two supermassive stars. The smaller one goes nova because it runs out of fuel first. The core starts to collapse, meanwhile the twin is scooping up the ejecta, and the star and the black hole start getting closer together...
    - kerryfalk 10y ago
      Wait. What? A star more massive than a black hole? I must be missing something here. Once something reaches the mass of a black hole, it becomes a black hole. No? How is it possible for a mass to be greater than a black hole but not a black hole? Mass over distance?
      - hxegon 10y ago
        no, there isn't some set mass that will make a black hole. A black hole is gravity overcoming the other fundamental forces. When a star dies and forms a black hole the force pushing outward from the fusion is overcome by the gravity of the star, but there isn't some threshold of size where this happens.
        saagarjha 10y ago
yodon 10y ago
I wonder if you could model this in Universe Sandbox [0]? (I live in Seattle so I've met the author Dan Dixon a few times at meetups but have no other relationship to it) [0] http://universesandbox.com/ http://universesandbox.com/
- ISL 10y ago
  I expect so -- at least one of the people on the team is a relativist. Sending her an email now...
  - BrendanD 10y ago
    Nope: http://universesandbox.com/faq/ http://universesandbox.com/faq/ Does it account for relativity? No, the physics in Universe Sandbox ² is currently only Newtonian. Why? The short answer is that you need a supercomputer to accurately simulate general relativity. Jenn, astrophysicist and Universe Sandbox ² developer, explains more in a blog post: "General relativity requires simulating the spacetime itself. That is, taking your simulation space, discretizing it to a hi-res 3-D grid and checking the effect that each and every point in that grid has on all neighboring points at every timestep. Instead of simulating N number of bodies, you are simulating a huge number of points. You start with some initial data of the shape of your spacetime and then see how it evolves according to the Einstein equations, which are 10 highly non-linear partial differential equations." We are, however, interested in adding in a few features which would address some effects of relativity. One example is setting gravity to travel at the speed of light, instead of instantaneously taking effect as it currently does. You can read more about these in Jenn's blog post: Gravitational Waves & Universe Sandbox ².
    - marxidad 10y ago
      Sounds like it would need Minecraft.
    - athom 10y ago
      Finite element analysis on the spacetime continuum? Yikes!
blowski 10y ago
For those like myself who struggle to understand these numbers, 1% of speed of light is like travelling the circumference of the Earth 75 times every second.
- e98cuenc 10y ago
  It's slower than that, it will be travelling the circumference of the Earth once in 13 seconds. Light itself can "only" go around the Earth 7 times in a second.
  - blowski 10y ago
    You're absolutely right - I did the calculation as km/s instead of m/s. So at 1% of speed of light, it would take just over 14 seconds to travel the circumference of the Earth. Travelling at 1% of speed of light, I could travel from New Orleans to California in 1 second.
    - BurningFrog 10y ago
      Which is why New Orleans to California internet signals can't take less than 10ms. In reality it was maybe 40-50ms last I checked.
- runeks 10y ago
  Converting 1% the speed of light to km/miles-per-second gives: 3000 km/s or 1860 miles/s. That's Paris to New York City in two seconds. I don't understand why they use distance-per-hour, either. It ends up being millions of miles/km, which no human has any sense of.
mkempe 10y ago
The units are oddly disconnected from the usual measurement given for the speed of light (km/s not km/h). This star travels at 3750 km/s.
pif 10y ago
By the way, 1% of the speed of light is 3000 km/s, which is "just" a hundred times the speed the Earth travels around the Sun.
- mrb 10y ago
  The Earth travels at 30 km/s around the Sun. (And the Sun at 230 km/s around the center of the Galaxy.)
  - coldtea 10y ago
    >The Earth travels at 30 km/s around the Sun. That's exactly what the parent comment just said.
    - anaximander 10y ago
      I think they're pointing out that while the speed of the earth relative to the sun is 30 km/s, its speed relative to the center of the galaxy is quite a bit faster, which may be a fairer comparison to what's being discussed in the original article.
      - thraway2016 10y ago
        They're not even remotely comparable. Tangential speed x where r=several thousand light years results in SUBSTANTIALLY less centripetal acceleration than the same tangential speed where r=a few AU.
- deleted 10y ago
  [deleted]
- liberte82 10y ago
  Somehow that suddenly makes the speed of light seem less fast.
  - ex3ndr 10y ago
chiph 10y ago
Circling the drain...
AnimalMuppet 10y ago
If I read this right, that 1% number is a guess. That is, they know it orbits in 28 minutes. They don't know the radius of the orbit. They guessed what the mass of the black hole is, and from that solved for the radius of the orbit, and therefore found the velocity - but it's all based on the guess of the black hole mass. Or did I miss something?
Winblows69 10y ago
Isn't there something else these astronomers can do that provide more immediate help to society?
skdotdan 10y ago
How did they estimate the orbit?

232 points by curtis 10y ago

How much temporal dilation would a relativistic orbit about a frame-dragging massive object create? Would the black hole or other objects orbiting it look weird (relatively--hehe--speaking).

theemathas 10y ago
Using 1% of speed of light, it will slow down by 0.005% (That's much less than I expected)
- sliken 10y ago
  Yes, but doesn't that ignore the gravitational acceleration? Time dilation isn't just speed, it's also acceleration. Even if you could hover very near the event horizon the time dilation would be severe.
  - amelius 10y ago
    As far as I know, there's only speed in the formula of time dilation, not acceleration. See also [1]. [1] http://www.edu-observatory.org/physics-faq/Relativity/SR/clock.html http://www.edu-observatory.org/physics-faq/Relativity/SR/clo...
    - xelxebar 10y ago
      Special relativity gives you dilation from velocity. General relativity gives you dilation from acceleration.
      - pdonis 10y ago
        > General relativity gives you dilation from acceleration. Not from acceleration, from depth in a gravitational potential well. See my other posts upthread.
    - Filligree 10y ago
      That's for special relativity, which is only valid if you're not accelerating. This star is, so we'd need general relativity... I don't know what that formula looks like.
      - valarauca1 10y ago
        Seeing as the star is in close proximity to a blackhole it would likely be similar to the Kerr-Metric [1] (as we _should_ assume the black hole as some spin). The white star has non-trivial mass of its own which greatly complicates the curvature of the local space-time region and render the Kerr-Metric equations lacking. GR is really complicated FYI. [1] https://en.wikipedia.org/wiki/Kerr_metric https://en.wikipedia.org/wiki/Kerr_metric
        pdonis 10y ago
        > it would likely be similar to the Kerr-Metric Unless the hole is rotating extremely rapidly (which I don't see mentioned), the difference between the Kerr metric and the Schwarzschild metric (which is what I used for the formula I posted upthread) is too small to matter unless you are really close to the hole's horizon.
        jpmattia 10y ago
        You got me curious, and I wanted to put numbers around this. It's worth noting that the actual paper claims only this is a black hole candidate, and is not certain it's a black hole (despite the Science alert headline). The paper guesses that the black hole is ~ 1 solar mass, so the Schwarzschild radius would be about 3 km. The distance is about 2.5x the earth-moon, which is about 10^6 km. btw, paper here: https://arxiv.org/pdf/1702.02167.pdf https://arxiv.org/pdf/1702.02167.pdf
      - pdonis 10y ago
        The formula for an object at radius r in the field of a non-rotating gravitating mass M is: sqrt(1 - 2M/r - v^2) instead of sqrt(1 - v^2) (where I am using units where G = c = 1). For an object in a free-fall circular orbit, v^2 = M/r, so the above formula can be simplified to sqrt(1 - 3M/r)
  - valarauca1 10y ago
    Yes, but doesn't that ignore the gravitational acceleration Gravitational acceleration doesn't exist (in GR). All bodies are stationary in GR and observe other things moving in reference to themselves. What we perceive as gravitational acceleration is just objects traveling in straight lines (at constant speeds) though 4D space-time. Circular orbits are just straight lines of constant velocity bent around by the local curvature of space-time (which can be caused by a local density of mass-energy). The idea of acceleration assumes a force is acting on a body. Gravity isn't a force in General Relativity. It is the shape of the universe.
    - pdonis 10y ago
      > Gravitational acceleration doesn't exist (in GR). A better way of stating this would be that objects moving solely under gravity have zero acceleration in GR, because in GR, acceleration means proper acceleration--what is measured by an accelerometer. Objects moving solely under gravity are in free fall. > All bodies are stationary in GR and observe other things moving in reference to themselves. This isn't correct. There is no requirement that an observer in GR must use coordinates in which they are at rest.
  - pdonis 10y ago
    > Time dilation isn't just speed, it's also acceleration. That's not correct. Gravitational time dilation isn't a function of acceleration, it's a function of gravitational potential, i.e., how deep you are in the potential well of the source. (Also, an object that is in a free-fall orbit has zero acceleration in GR, since in GR acceleration is proper acceleration--what is measured by an accelerometer.)
- jessriedel 10y ago
  If anyone is curious, the reason is that many/most special relativistic effects are proportional to gamma = 1/sqrt(1-v^2/c^2), with gamma = 1 being non-relativistic. Even at v=20% of c, gamma is only 1.02 (a mere 2% effect). http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=Plot%5B1%2FSqrt(1-v%5E2),%7Bv,0,1%7D%5D http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=Plot%5B1...
  - cuspycode 10y ago
    General relativity also accounts for gravitational/accelerational effects, in addition to the speed-related effects. For example, in the Schwarzschild metric[1], effects such as time dilation are on the order of 1-phi/c^2 where phi=GM/r. Or expressed in terms of "g-force": phi=gr. [1] https://en.wikipedia.org/wiki/Schwarzschild_metric https://en.wikipedia.org/wiki/Schwarzschild_metric
TorKlingberg 10y ago
As a rule of thumb, relativistic effects are very small below 5-10% of the speed of light. You may still need to calculate them if you want very high precision, like for GPS.
- splike 10y ago
  There is the relativistic effects of gravity to consider in this case too
  - M_Grey 10y ago
    Right, but for that orbit to be so slow, it must be a very distant orbit.
overcast 10y ago
It's not really until you get up near 90% of the speed of light, where dilation starts getting insane. That's when the curve starts to sharply jump straight up.

du_bing 10y ago

Once I read on a book, that there may be a star so huge that it orbits a black hole at half of the speed of light, i.e., 150,000 km/s. Is this possible?

thriftwy 10y ago
I think that star size is irrelevant here - any massive object will need to have the same speed to hold a given orbit. It's black hole mass and star's proximity to black hole that are in this equation. Assuming star is much lighter than the black hole, or course.
- hinkley 10y ago
  But it's possible to have a star that is heavier than a black hole. Say you had a binary star system of two supermassive stars. The smaller one goes nova because it runs out of fuel first. The core starts to collapse, meanwhile the twin is scooping up the ejecta, and the star and the black hole start getting closer together...
  - kerryfalk 10y ago
    Wait. What? A star more massive than a black hole? I must be missing something here. Once something reaches the mass of a black hole, it becomes a black hole. No? How is it possible for a mass to be greater than a black hole but not a black hole? Mass over distance?
    - hxegon 10y ago
      no, there isn't some set mass that will make a black hole. A black hole is gravity overcoming the other fundamental forces. When a star dies and forms a black hole the force pushing outward from the fusion is overcome by the gravity of the star, but there isn't some threshold of size where this happens.
      - saagarjha 10y ago

yodon 10y ago

I wonder if you could model this in Universe Sandbox [0]? (I live in Seattle so I've met the author Dan Dixon a few times at meetups but have no other relationship to it) [0] http://universesandbox.com/ http://universesandbox.com/

ISL 10y ago
I expect so -- at least one of the people on the team is a relativist. Sending her an email now...
- BrendanD 10y ago
  Nope: http://universesandbox.com/faq/ http://universesandbox.com/faq/ Does it account for relativity? No, the physics in Universe Sandbox ² is currently only Newtonian. Why? The short answer is that you need a supercomputer to accurately simulate general relativity. Jenn, astrophysicist and Universe Sandbox ² developer, explains more in a blog post: "General relativity requires simulating the spacetime itself. That is, taking your simulation space, discretizing it to a hi-res 3-D grid and checking the effect that each and every point in that grid has on all neighboring points at every timestep. Instead of simulating N number of bodies, you are simulating a huge number of points. You start with some initial data of the shape of your spacetime and then see how it evolves according to the Einstein equations, which are 10 highly non-linear partial differential equations." We are, however, interested in adding in a few features which would address some effects of relativity. One example is setting gravity to travel at the speed of light, instead of instantaneously taking effect as it currently does. You can read more about these in Jenn's blog post: Gravitational Waves & Universe Sandbox ².
  - marxidad 10y ago
    Sounds like it would need Minecraft.
  - athom 10y ago
    Finite element analysis on the spacetime continuum? Yikes!

blowski 10y ago

For those like myself who struggle to understand these numbers, 1% of speed of light is like travelling the circumference of the Earth 75 times every second.

e98cuenc 10y ago
It's slower than that, it will be travelling the circumference of the Earth once in 13 seconds. Light itself can "only" go around the Earth 7 times in a second.
- blowski 10y ago
  You're absolutely right - I did the calculation as km/s instead of m/s. So at 1% of speed of light, it would take just over 14 seconds to travel the circumference of the Earth. Travelling at 1% of speed of light, I could travel from New Orleans to California in 1 second.
  - BurningFrog 10y ago
    Which is why New Orleans to California internet signals can't take less than 10ms. In reality it was maybe 40-50ms last I checked.
runeks 10y ago
Converting 1% the speed of light to km/miles-per-second gives: 3000 km/s or 1860 miles/s. That's Paris to New York City in two seconds. I don't understand why they use distance-per-hour, either. It ends up being millions of miles/km, which no human has any sense of.

mkempe 10y ago

The units are oddly disconnected from the usual measurement given for the speed of light (km/s not km/h). This star travels at 3750 km/s.

pif 10y ago

By the way, 1% of the speed of light is 3000 km/s, which is "just" a hundred times the speed the Earth travels around the Sun.

mrb 10y ago
The Earth travels at 30 km/s around the Sun. (And the Sun at 230 km/s around the center of the Galaxy.)
- coldtea 10y ago
  >The Earth travels at 30 km/s around the Sun. That's exactly what the parent comment just said.
  - anaximander 10y ago
    I think they're pointing out that while the speed of the earth relative to the sun is 30 km/s, its speed relative to the center of the galaxy is quite a bit faster, which may be a fairer comparison to what's being discussed in the original article.
    - thraway2016 10y ago
      They're not even remotely comparable. Tangential speed x where r=several thousand light years results in SUBSTANTIALLY less centripetal acceleration than the same tangential speed where r=a few AU.
deleted 10y ago
[deleted]
liberte82 10y ago
Somehow that suddenly makes the speed of light seem less fast.
- ex3ndr 10y ago

chiph 10y ago

Circling the drain...

AnimalMuppet 10y ago

If I read this right, that 1% number is a guess. That is, they know it orbits in 28 minutes. They don't know the radius of the orbit. They guessed what the mass of the black hole is, and from that solved for the radius of the orbit, and therefore found the velocity - but it's all based on the guess of the black hole mass. Or did I miss something?

Winblows69 10y ago

Isn't there something else these astronomers can do that provide more immediate help to society?

skdotdan 10y ago

How did they estimate the orbit?