What if the Sun turned into a Black Hole?

[geordief]

No I know it can't  normally but what if it did and we could  decide on the radius of the new body?

 

If the radius was small enough would it cease to have much effect on the  movement of the planets (would they lie outside its region of gravitational influence? )

 

Is there a limit to how small a radius the "new body" could have? Does its radius depend  directly on the mass of the bodies that have  been incorporated into it  in the first place? Does its radius remain the same provided there are no more additions of massive bodies?

 

[swansont]

33 minutes ago, geordief said:

No I know it can't  normally but what if it did and we could  decide on the radius of the new body?

 

If the radius was small enough would it cease to have much effect on the  movement of the planets (would they lie outside its region of gravitational influence? )

 

Is there a limit to how small a radius the "new body" could have? Does its radius depend  directly on the mass of the bodies that have  been incorporated into it  in the first place? Does its radius remain the same provided there are no more additions of massive bodies?

 

There would be basically no effect on the orbits of the planets. The mass is the same, and that's primarily what matters.

There might be tiny effects, such as radiation pressure changing.

 

[Strange]

36 minutes ago, geordief said:

No I know it can't  normally but what if it did and we could  decide on the radius of the new body?

It would have a radius of about 3km (assuming no change in mass).

37 minutes ago, geordief said:

If the radius was small enough would it cease to have much effect on the  movement of the planets (would they lie outside its region of gravitational influence? )

Gravity follows an inverse square law and so it has limits on distance. The size of the source has no effect, either. The planets would continue to orbit the black hole as if nothing had changed.

38 minutes ago, geordief said:

Does its radius depend  directly on the mass of the bodies that have  been incorporated into it  in the first place? Does its radius remain the same provided there are no more additions of massive bodies?

Yes, the mass is directly proportional to the radius. Set the mass to "1 solar mass" in this calculator and see the results: http://xaonon.dyndns.org/hawking/

(Note you need to change the units first and then the number)

[Phi for All]

2 minutes ago, Strange said:

The planets would continue to orbit the black hole as if nothing had changed.

... unaware of how lucky they were that, in the OP, a magic wand created the black hole instead of a supernova.

[geordief]

So ,taking the solar system as a whole it would (be almost as if all the space in the Sun except for  a 3km radius volume would have simply ceased to exist?

 

Would the volume of the Solar System  have also shrunk  by the same amount?

[Strange]

11 minutes ago, Phi for All said:

... unaware of how lucky they were that, in the OP, a magic wand created the black hole instead of a supernova.

It would get rather chilly, though.

2 minutes ago, geordief said:

So ,taking the solar system as a whole it would (be almost as if all the space in the Sun except for  a 3km radius volume would have simply ceased to exist?

No. It would just be as if the Sun had got smaller.

It would have no significant effect on the rest of the solar system. The loss of the solar wind would probably have a detectable effect on some things (tails of comets, atmospheres of planets, etc)

[geordief]

9 minutes ago, Strange said:

 

No. It would just be as if the Sun had got smaller.

It would have no significant effect on the rest of the solar system. The loss of the solar wind would probably have a detectable effect on some things (tails of comets, atmospheres of planets, etc)

Does "volume of the Solar System" have an actual meaning? If so ,what might it be  ?....you seem to be saying it would be unchanged if the Sun was transformed (with a magic wand) to a 3k radius wide body ...

Edited November 8, 2018 by geordief

[Strange]

3 minutes ago, geordief said:

Does "volume of the Solar System" have an actual meaning? If so ,what might it be  ?....you seem to be saying it would be unchanged if the Sun was transformed (with a magic wand) to a 3k radius wide body ...

Well, I would take it to mean the volume of a sphere with a radius corresponding to [whatever we consider the edge to be]. I think the edge of the solar system is sometimes defined by where the solar wind stops (the heliopause), but that would no longer apply in this case. But whatever (slightly arbitrary) boundary you choose, I don't see why it would change.

[geordief]

27 minutes ago, Strange said:

Well, I would take it to mean the volume of a sphere with a radius corresponding to [whatever we consider the edge to be]. I think the edge of the solar system is sometimes defined by where the solar wind stops (the heliopause), but that would no longer apply in this case. But whatever (slightly arbitrary) boundary you choose, I don't see why it would change.

But would it be ,in theory be possible to take a volume extending out ,say I light year from the Sun ,calculate its volume and then perform the same calculation after the Sun was migicked to its new 3km radius size?

 

It seems impossible to me  to calculate the volume in the first place as it is a moving/dynamic  quantity (the time at the edge of the volume of the sphere is not the same as the time at its centre (the Sun)

 

But maybe there are ways to do it....are there?

[Strange]

17 minutes ago, geordief said:

But would it be ,in theory be possible to take a volume extending out ,say I light year from the Sun ,calculate its volume and then perform the same calculation after the Sun was migicked to its new 3km radius size?

You could, and it would be the same. Or, at least, I can't see why it wouldn't be.

18 minutes ago, geordief said:

It seems impossible to me  to calculate the volume in the first place as it is a moving/dynamic  quantity (the time at the edge of the volume of the sphere is not the same as the time at its centre (the Sun)

I'm not sure why the time difference (which is probably quite small - we can calculate it if necessary) would make a difference to the volume. 

Say we use the orbit of Neptune (also start of the Kuiper belt) as the radius. It averages 30 AU (about 4.5 million km). So you can work out the volume of that sphere. It won't change if the sun becomes a black hole, because the orbit of Neptune won't change.

[beecee]

1 hour ago, Phi for All said:

... unaware of how lucky they were that, in the OP, a magic wand created the black hole instead of a supernova.

Or just swell up and become a red giant,  enveloping Mercury, Venus and possibly Earth too...and then poof! blow off its outer layers and leave a White Dwarf behind. 

[Phi for All]

1 minute ago, beecee said:

Or just swell up and become a red giant,  enveloping Mercury, Venus and possibly Earth too...and then poof! blow off its outer layers and leave a White Dwarf behind. 

No magic needed for that.

[geordief]

16 minutes ago, Strange said:

You could, and it would be the same. Or, at least, I can't see why it wouldn't be.

I'm not sure why the time difference (which is probably quite small - we can calculate it if necessary) would make a difference to the volume. 

Say we use the orbit of Neptune (also start of the Kuiper belt) as the radius. It averages 30 AU (about 4.5 million km). So you can work out the volume of that sphere. It won't change if the sun becomes a black hole, because the orbit of Neptune won't change.

(I feel like a contestant on QI who knows that his answer is going to set off the klaxon, but here goes)

What about the volume that has been "sucked out" of the Sun , won't that draw in the  rest of the Solar System's  volume in  so that the "perimetre"  of that volume shrinks (imperceptibly)  in proportion missing volume  ?

 

I expect I am wrong but do you see why I am thinking this?

 

[Strange]

1 minute ago, geordief said:

What about the volume that has been "sucked out" of the Sun , won't that draw in the  rest of the Solar System's  volume in  so that the "perimetre"  of that volume shrinks (imperceptibly)  in proportion missing volume  ?

That seems to assume that "volume" is a thing, like water or something. Changing the size of something doesn't change the space it is in. Water expands when it freezes (enough to burst pipes) but it doesn't "push space away".

[geordief]

1 minute ago, Strange said:

That seems to assume that "volume" is a thing, like water or something. Changing the size of something doesn't change the space it is in. Water expands when it freezes (enough to burst pipes) but it doesn't "push space away".

 

I probably need to  increase my general knowledge in this area but maybe I can understand that concentrating the density of mass in any one location frees up empty space vacated by the objects in their previous locations.(so that the overall volume is unaffected )

[Strange]

13 minutes ago, geordief said:

 

I probably need to  increase my general knowledge in this area but maybe I can understand that concentrating the density of mass in any one location frees up empty space vacated by the objects in their previous locations.(so that the overall volume is unaffected )

I'm trying to get my head round your mental model here.  

If you move something (your teacup) from position A to position B, you didn't have to move empty space from B to A. Space is just the set of dimensions/measurements where the cup exists - moving the cup, changes where we measure it to be, but doesn't change the measurements of space around it. (Ignoring the minute gravitational effect!)

Similarly, if your teacup shrank it would change the measurements of the cup but not the space it is in.

[geordief]

17 minutes ago, Strange said:

I'm trying to get my head round your mental model here.  

If you move something (your teacup) from position A to position B, you didn't have to move empty space from B to A. Space is just the set of dimensions/measurements where the cup exists - moving the cup, changes where we measure it to be, but doesn't change the measurements of space around it. (Ignoring the minute gravitational effect!)

Similarly, if your teacup shrank it would change the measurements of the cup but not the space it is in.

I am clearly fixated on the notion that mass curves spacetime (a sphere  with a radius r will have a different value of pi if it has mass at its centre -different from it would have if it didn't) and I am imagining that this redistribution of mass in the Sun converted magically into a  Black Hole  should have some comparable  effect on the surrounding volumes (pi is related to the volume ,isn't it?)

I may have made a leap too far,.(My volume is 3d and these effects -if they apply -are 4d)

 

[Strange]

13 minutes ago, geordief said:

I am clearly fixated on the notion that mass curves spacetime (a sphere  with a radius r will have a different value of pi if it has mass at its centre -different from it would have if it didn't) and I am imagining that this redistribution of mass in the Sun converted magically into a  Black Hole  should have some comparable  effect on the surrounding volumes (pi is related to the volume ,isn't it?)

While that is true, the curvature of space-time (at any given distance) will be unaffected by the size of the mass at the centre; it just depends on the mass. After all, the curvature of spacetime is what creates gravity and we know that is only dependent on mass and distance (not size). I don't think there are any extra, subtle effects in GR that change this.

[geordief]

30 minutes ago, Strange said:

While that is true, the curvature of space-time (at any given distance) will be unaffected by the size of the mass at the centre; it just depends on the mass. After all, the curvature of spacetime is what creates gravity and we know that is only dependent on mass and distance (not size). I don't think there are any extra, subtle effects in GR that change this.

Yes I think I am happy with that now.  The curvature remains the same ;so PI remains the same and so the (4d?) volume remains the same.

But in the vicinity of the Sun turned Black Hole  4d volumes would have changed alarmingly I guess. 

 

Are you still saying (if you were) that the curvature at the place that was the edge of the Sun  is the same after the Black Hole  has formed?

 

edit: on reflexion I suppose it is ---all the changes of curvature seem to me now to take place  within that region.

Edited November 8, 2018 by geordief

[Strange]

8 minutes ago, geordief said:

Are you still saying (if you were) that the curvature at the place that was the edge of the Sun  is the same after the Black Hole  has formed?

Yes. The only difference, really, is that you can get closer to the source of the gravity with a black hole.

This means that as you approach the lack hole, there will be greater gravity than the surface gravity of the sun (because closer to the mass). In GR there are extra effects like time dilation and frame dragging but (as far as I know) these will be the same at the old radius of the Sun (or further out). 

[beecee]

21 hours ago, geordief said:

Are you still saying (if you were) that the curvature at the place that was the edge of the Sun  is the same after the Black Hole  has formed?

Bingo! which as Strange has said means that one can now orbit closer to this magical BH that was the mass of the Sun, squeezed into a radius of around 3 kms. In fact speaking theoretically, one could orbit as close as 1.5 Schwarzchild radius from the centre, if one could obtain the speed of "c". 

[mistermack]

I think all of our global warming problems would go away. 

We might have to turn up the boiler a bit though. 

But on the plus side, I could drive to France without paying for the tunnel.

[swansont]

!

Moderator Note

Tangential discussion has been split

https://www.scienceforums.net/topic/116972-hijack-from-what-if-the-sun-turned-into-a-black-hole/