[ocalhoun (OP)]

Okay, so I'm having a little debate with a person on another forum about black holes.
I think that the gravitational force felt by something orbiting the original star (Supposing it survived the supernova) would remain the same because the mass of the star doesn't change significantly when it becomes a black hole.
He thinks that when the star becomes a black hole, the gravitational force increases, and this increase would affect orbiting objects, probably causing the orbits of these objects to decay.
I think this is somewhat true, but the only difference in the gravitational field would happen within the original radius of the star.

For the sake of expediency, we're using our own solar system as an example, and ignoring the fact that the sun would have to be much more massive, then go through a few more phases before it became a black hole.

[syhprum]

I think the planets would remain in orbit but orbits would be modified as suggested in this URL http://www.fourmilab.ch/gravitation/orbits/

[another_someone]

In general terms, you are correct, and he is wrong.

The only caveat is that because a black hole is smaller than an ordinary star, so you can get closer in, and when you get very close you feel a greater gravitational pull; but at any given distance (one that is larger than the size of the ordinary star) from the centre of a star, you will feel exactly the same gravitational pull whether the star is a black hole or an ordinary star.

[another_someone]

I think the planets would remain in orbit but orbits would be modified as suggested in this URL http://www.fourmilab.ch/gravitation/orbits/

As far as I can ascertain, the site related to objects that orbit very close to the event horizon.  Since the event horizon has to be smaller than the size of the star that collapsed to form the black hole, so no existing planet would be in any of the described orbits, although it is possible that something that would have crashed into the surface of the original star would now be captured in such a peculiar orbit.

That is my understanding of what the site says, but I am willing to be corrected if someone can show otherwise.

[syhprum]

I agree when the appropriate parameters had been put into the formula in the the URL that I reccomended the differences would be tiny

[another_someone]

I agree when the appropriate parameters had been put into the formula in the the URL that I reccomended the differences would be tiny

But are these differences that are between an ordinary star and a black hole, or between General Relativity and Newtonian mechanics (that difference is observable in the orbit of Mercury, and was what Einstein used to prove GR was superior to Newtonian gravity).

[syhprum]

I think this is only the difference between Newton and Einstein, it is only that the intense gravity gradient of a black hole makes the effect more apparent

[syhprum]

I must come back to the question of rotation, if rotation is of any relevance we have now replaced our Sun rotating at about once every 28 days with a black hole rotating in milli seconds if not micro seconds (who knows?) does this affect the planets if so to what degree?.
I recant whether we should use Newton or Einstein it is not affected by this transition to a black hole we should have used Einstein all the time

[Soul Surfer]

Assuming that the sun's mass did not change as the black hole formed there would be absolutely no change to any of the solar system orbits and the resultant black hole would be about a mile across

[another_someone]

I must come back to the question of rotation, if rotation is of any relevance we have now replaced our Sun rotating at about once every 28 days with a black hole rotating in milli seconds if not micro seconds (who knows?) does this affect the planets if so to what degree?.
I recant whether we should use Newton or Einstein it is not affected by this transition to a black hole we should have used Einstein all the time

Probably of greater impact would be the loss of solar weather, loss of solar radiation, etc.

[Soul Surfer]

Any effects would only be felt very close to the event horizon where orbital velocities were significant with respect to the velocity of light

[syhprum]

My maths are not very good! suppose a star with a mass of 10 solar mass rotating in about 28 days (.0000004 Hz) and a radius 3*10^6 Km collapsed to a black hole with an event horizon of radius of 1 Km ,and all rotational energy is conserved ( I hope these values are realistic ) what would be the rotational speed and the 'surface' speed.
One would have to make the assumption that it rotates as a homogeneous body, is this realistic ?

[lightarrow]

To answer this question you have to compute the moment of inertia I of the sun.
Assuming it's an homogeneus sphere, its moment of inertia is I =2/5 M•R²; M is the mass and R the radius
(see: http://en.wikipedia.org/wiki/Moment_of_Inertia--Cone). Then you apply the law of angular momentum conservation:
K = I•ω, where ω is the angular velocity: ω = V/R = 2πν = 2π/T; where V is the tangential speed at distance R (your "surface" speed), ν is the rotation frequency and T the period of rotation. K must remain the same after the contraction. So:

2/5 M•R₁²•2π/T₁ = 2/5 M•R₂²•V₂/R₂ = 2/5 M•R₂•V₂

where the index 1 refers to the star befor contraction and 2 after contraction.
From this equation, knowing all the other variables, you can find V₂:

V₂ = 2π•R₁²/T₁•R₂.

Of course all these formulas are non-relativistic, which is not the case you are asking.

[syhprum]

My arithmetic may be wrong but it seems to me that every thing cancels out so that the rotational period is reduced by the same ratio as the radius is reduced this works out OK if I take a star of 10^6 Km radius rotating at once every 28 days and have it collapse to a neutron star of radius 10Km the rotation period would be 41 milli seconds This seems about right, the surface speed would be a reasonable 1530Km per second.

[lightarrow]

My arithmetic may be wrong but it seems to me that every thing cancels out so that the rotational period is reduced by the same ratio as the radius is reduced this works out OK if I take a star of 10^6 Km radius rotating at once every 28 days and have it collapse to a neutron star of radius 10Km the rotation period would be 41 milli seconds This seems about right, the surface speed would be a reasonable 1530Km per second.

Arithmetic is not physics. You have to use Angular Momentum Conservation law.

[lightarrow]

My arithmetic may be wrong but it seems to me that every thing cancels out so that the rotational period is reduced by the same ratio as the radius is reduced this works out OK if I take a star of 10^6 Km radius rotating at once every 28 days and have it collapse to a neutron star of radius 10Km the rotation period would be 41 milli seconds This seems about right, the surface speed would be a reasonable 1530Km per second.

It is the tangential speed V which is inversely proportional to the radius R, as you can see from the formula I wrote:

V2 = 2π•R₁²/T₁•R₂ = R₁²•ω₁/R₂ = R₁²•V₁/R₁•R₂ = V₁•R₁/R₂.

All this however is true, not only for non-relativistic speeds but also assuming the same shape of the body before and after the contraction, as I said; in this way, many things cancels out in the formulas. In general, you should know the inertia moment "I" of the body before and after the contraction.

[lightarrow]

About what happend if the sun would suddenly become a black hole, I don't think planets would be sucked in, but I think probably a strong gravitational wave would be released from the sun, affecting the planets in some way (still not known from me).

[another_someone]

About what happend if the sun would suddenly become a black hole, I don't think planets would be sucked in, but I think probably a strong gravitational wave would be released from the sun, affecting the planets in some way (still not known from me).

Don't know about gravity waves, but I'd imagine you'd get a shock wave as the Sun first went supernova as its core collapsed.

In fact, far from being sucked in, I'd expect the supernova explosion to blast the planets out of orbit (assuming they even remain intact).

[syhprum]

I will have a rethink later on and try and put my calculation into a more formally correct form, I am having rather a battle with my computer at the moment trying to get the FAX working properly

[lightarrow]

Don't know about gravity waves, but I'd imagine you'd get a shock wave as the Sun first went supernova as its core collapsed.

Ah yes, of course. I assumed we were considering what happened if the sun (if it had enough mass for it) only contracted to form a black hole.