Quick Question(?) Orbit around a Stellar Mass Black Hole

[JoeSchmuckatelli]

Would the orbit of a captured satellite (planet) around a stellar mass black hole be any different from the orbit of a planet around a star of the same mass?

 

i.e. if you were to magically replace our sun with a black hole of the same mass, would that change Earth's orbit in any meaningful way?  

 

* I used the phrase "captured planet" as I assume the formation of a black hole would destroy the original satellites of the star collapsing into a BH... but I guess the real question is what I typed into the 'i.e.'  - wondering if things like the distance matter, etc.  (I know that the sun's mass determines earth's orbital velocity at our current distance from the sun... just wondering if it matters whether the central mass is a star or BH)

 

(shrug/head scratch)

Edited April 13, 2020 by JoeSchmuckatelli

[Bill Phil]

Not substantially. 

There might be some GR affects from it and of course the side affects of losing the light of the Sun - but the actual trajectory won’t change too much.

[sevenperforce]

Once you get really close (e.g., orbits deep within the radius of the former sun), things get wonky, but the gravitational field of the Sun at any appreciable distance IS the gravitational field of a stellar-mass BH.

Same with Earth. If Earth suddenly collapsed into a black hole, it would be about the size of a dime, but the moon and the ISS would continue to orbit unchanged.

[cubinator]

No change. It would be dark, and the warping effect would be visible through a small telescope, but Earth's orbit would hardly change.

[Shpaget]

46 minutes ago, cubinator said:

the warping effect would be visible through a small telescope

To be fair, it's visible even with the Sun in optimal working condition.

https://en.wikipedia.org/wiki/Eddington_experiment

[cubinator]

18 minutes ago, Shpaget said:

To be fair, it's visible even with the Sun in optimal working condition.

https://en.wikipedia.org/wiki/Eddington_experiment

But that could only be observed during a rare event, and comparing it to the view from months away. A black hole at this distance would let you know it in one look.

[Bill Phil]

3 hours ago, sevenperforce said:

Once you get really close (e.g., orbits deep within the radius of the former sun), things get wonky, but the gravitational field of the Sun at any appreciable distance IS the gravitational field of a stellar-mass BH.

Same with Earth. If Earth suddenly collapsed into a black hole, it would be about the size of a dime, but the moon and the ISS would continue to orbit unchanged.

Well the oblateness of the Earth would no longer perturb the ISS (and other satellites). So precession would no longer be present in low orbits.

[ThatGuyWithALongUsername]

On 4/13/2020 at 3:40 PM, Bill Phil said:

Well the oblateness of the Earth would no longer perturb the ISS (and other satellites). So precession would no longer be present in low orbits.

...except, of course, those orbits wouldn't be low anymore.

 

If you want a REAL low orbit then you're gonna have other problems as mentioned above.

[Bill Phil]

1 minute ago, ThatGuyWithALongUsername said:

...except, of course, those orbits wouldn't be low anymore.

 

If you want a REAL low orbit then you're gonna have other problems as mentioned above.

Yes, of course. 

[kerbiloid]

Just keep your eyes on the stars. While they stay same, you're enough far from the blackhole to do navigation as usual.

Once they start dimming, shifting, changing their color, this means you're inside 2..3 BH radii from the BH and should be careful or better get away, because the radiation also gets stronger.

[Nightside]

7 hours ago, kerbiloid said:

Just keep your eyes on the stars. While they stay same, you're enough far from the blackhole to do navigation as usual.

Once they start dimming, shifting, changing their color, this means you're inside 2..3 BH radii from the BH and should be careful or better get away, because the radiation also gets stronger.

Just remember the old space chanty and you will make it back to port:

Starlight goes straight, spacers elate;

starlight gets bent, spacers lament.

Edited April 15, 2020 by Nightside

[sevenperforce]

7 hours ago, kerbiloid said:

Just keep your eyes on the stars. While they stay same, you're enough far from the blackhole to do navigation as usual.

Once they start dimming, shifting, changing their color, this means you're inside 2..3 BH radii from the BH and should be careful or better get away, because the radiation also gets stronger.

Of course the sun's Schwarzschild radius is 3 km so if you are less than 9 km from a stellar-mass BH you will already have problems.

Edited April 15, 2020 by sevenperforce

[p1t1o]

Wouldnt it be possible to take precise measurements of the tidal forces acting on the ship, to tell how deep into a gravity well you were?

Combined with a direct observation of your orbital period, you ought to be able to tell the mass of the BH you are orbiting and how far away you are.

That sound right?

[sevenperforce]

7 minutes ago, p1t1o said:

Wouldnt it be possible to take precise measurements of the tidal forces acting on the ship, to tell how deep into a gravity well you were?

Yeah, a simple spring with weights at each end ought to be able to do the trick. Measure length with the spring perpendicular to the BH's normal vector, then turn parallel to normal and record the new length. If you know the spring constant you can solve.

7 minutes ago, p1t1o said:

Combined with a direct observation of your orbital period, you ought to be able to tell the mass of the BH you are orbiting and how far away you are.

That sound right?

Direct observation of your orbital period may be tricky due to probable apsidal precession, particularly if your periapsis is low (the lower the periapsis, the more angry the time goblins become and the more precession you get). If your tidal-measurement spring is sufficiently sensitive, you can measure the change in tidal force as you rotate around the BH and thus determine both your apsis and periapsis so you can calculate your orbital period that way, no direct observation required.

 

[kerbiloid]

51 minutes ago, p1t1o said:

Wouldnt it be possible to take precise measurements of the tidal forces acting on the ship, to tell how deep into a gravity well you were?

An experienced star skipper can estimate the direction of gravity with a drooled finger to the wind. He feels in which direction it tends to drop.

[sevenperforce]

Just now, kerbiloid said:

An experienced star skipper can estimate the direction of gravity with a drooled finger to the wind. He feels in which direction it tends to drop.

Wouldn't a truly experienced starmariner be able to tell the depth of the gravity well by holding up two drooled fingers, thus determining both the gradient and the normal vector?

[p1t1o]

2 hours ago, kerbiloid said:

An experienced star skipper can estimate the direction of gravity with a drooled finger to the wind. He feels in which direction it tends to drop.

Pffft, everyone knows that the North star is always up-well.

 

[cubinator]

4 hours ago, p1t1o said:

Pffft, everyone knows that the North star is always up-well.

 

Along with every other star, if you're deep enough.

[K^2]

10 hours ago, p1t1o said:

Wouldnt it be possible to take precise measurements of the tidal forces acting on the ship, to tell how deep into a gravity well you were?

Sure. There is no local experiment that can tell you if you're in a gravitational field, but tidal measurements are inherently non-local. Although, I'm not sure you need to go to these lengths. You can measure relative position in space to within a few kilometers using pulsars pretty much anywhere humanity likely to ever get, and if you know your orbital radius and period, you can estimate the mass of the body you're orbiting and get all the same info with way better precision than you're likely to get from tidal force measurements.

[kerbiloid]

Experienced astrogators have two radioactive atomic clocks at the opposite sides of the ship and measure the time difference.

Though, a pendulum clock has its own advantages, too.

Edited April 16, 2020 by kerbiloid