Are Newton's Laws Still Valid Near Black Hole Orbits?

[PeterDonis]

when I calculate it I get (and is until rs):

$$
g = \frac{Gm}{r^2 \left( 1 - \frac{r_s}{r} \right)}
$$

I don't know how you're calculating this, but your answer is wrong. The factor $\left( 1 - \frac{r_s}{r} \right)$ should be under a square root sign.

If that is not the case, then other formula does change.

What other formula?

 

[DParlevliet]

The classic calculation of an orbit is based on: s = 0.5g.t² and y = x²/2r (circle at x ≈ 0) which is : s = v²t^2/2r
together: 0.5g.t² = v²t^2/2r, resulting in: g = v²/r

In classic the orbit formula is v² = G.m/r with gives in above: g = G.m/r²

In GR the orbit formula is v² = G.m/(r-r_s) with gives: g = G.m/r(r-r_s) = G.m/r²(1-r_s/r)

If this is not right, then one of the two classic formula on top is changing too in GR. Which one?

 

[PeterDonis]

The classic calculation of an orbit is based on

The classic calculation of an orbit in Newtonian physics. To repeat once more Newtonian physics is wrong. It's not a matter of which one of the Newtonian formulas has to change. They are all built on the wrong conceptual foundation. The correct procedure is to start over with the right conceptual foundation, that of GR, and derive the formulas for orbits (and everything else) from first principles using GR. Any GR textbook will show you how to do that. I'm pretty sure Carroll's online lecture notes on GR do it too, which is nice because they're online and free.

with gives: g = G.m/r(r-rs) = G.m/r2(1-rs/r)

No, it doesn't. The (1 - r_s / r) factor is under a square root sign, as I've posted before. You say you've calculated it, but unless I see your calculation I can't tell where it's going wrong. I suspect it's because you are continuing to assume that it's just a matter of tweaking some Newtonian formulas and you just need to know which ones. It isn't. See above.

then one of the two classic formula on top is changing too in GR. Which one?

All of them, because the entire "classic" conceptual foundation is wrong. See above.

 

[DParlevliet]

Someone else who can follow my simple math calculations?
Or must I write it in small steps?

 

[PeterDonis]

Someone else who can follow my simple math calculations?

It's not a matter of following them; of course the equations you're using are simple. They're just the wrong ones. It's not a matter of which ones "change" in GR; GR doesn't even use the conceptual foundation you're using. You can't just take your Newtonian formulas and replace them with "GR versions". You have to rework your whole approach.

Or must I write it in small steps?

No, you need to go back and start from the right conceptual foundation.

 

[Drakkith]

Someone else who can follow my simple math calculations?
Or must I write it in small steps?

As Peter has repeatedly told you, Newtonian physics is not correct here, so you need to use GR. GR is not a simple modification of the former.

 

[DParlevliet]

...You say you've calculated it, but unless I see your calculation I can't tell where it's going wrong.

That is what you wrote. That math is there. Then you are not interested or not familiar with this math

There are three formula which together give a wrong result. Then one of the formula must wrong. Unless math also changes in GR...
If you don't know the answer, please wait for someone who does instead of repeating the same clincher.

 

[Nugatory]

There are three formula which together give a wrong result. Then one of the formula must wrong.

No. All three of them are wrong or do not apply to the Schwarzschild spacetime or both.

 

[PeterDonis]

The OP's question has been answered, and the discussion has run its course. Thread closed.