I with an exercise about Energy and Schwarzschild Black Holes

[JTorn]

Homework Statement

Deadline : 18 of November

Relevant Equations

SW orbital equations adn Newtonian mechanical Energy

The thing is that this is an exercise that I have to show my teacher but I don´t know how to get the answer.The exercise says:

"A body of mass m moving in the Keplerian field V = −M/r (in G = 1 units) has a total conserved energy, Etot = 1 /2( m r˙^2 + r ^2ϕ˙ ^2 )− mM/r.

Show that the Newtonian limit of the Schwarzschild orbital equations leads to this same expression; use this calculation to obtain Etot. "

I tried starting from r·^2 = E - ( 1 - 2M/r)(1-L^2/(m^2)) using L = r^2 ϕ· but I cannot get rid of some squares.

Any help?

 

[PeterDonis]

I tried starting from r·^2 = E - ( 1 - 2M/r)(1-L^2/(m^2))

You might want to check this equation; it's a good one to start from but I think you have some factors wrong.

 

[JTorn]

You might want to check this equation; it's a good one to start from but I think you have some factors wrong.

Sorry, I'm new here and i don't know how to write equations properly, the equation is fine, it's just that I am using G=c=1 units.

I have completed the exercise and I will upload the answer as soon as possible but now I'm quite busy trying to complete other exercises.

Thanks you.

 

[PeterDonis]

the equation is fine

I'm not sure it is, as you wrote it.

it's just that I am using G=c=1 units.

I know that. That's not the issue I was talking about.

 

[PeterDonis]

I will upload the answer

You shouldn't post the answer here explicitly since this is a homework forum.

 

[PeterDonis]

i don't know how to write equations properly

PF's LaTeX feature is the best way to do it:

https://www.physicsforums.com/help/latexhelp/

 

[JTorn]

[QUOTE = "PeterDonis, publicación: 6260852, miembro: 197831"]
No debe publicar la respuesta aquí explícitamente you que este es un foro de tareas.
[/ CITAR]

I'm really really sorry. I did not read the rules. Now I know them.

 

[JTorn]

Oh, I didn't know I could use Látex code here. Sorry for my ignorance and Thank you very much.

 

[PeterDonis]

You shouldn't post the answer here explicitly since this is a homework forum.

I'm really really sorry. I did not read the rules. Now I know them.

Actually it's I who need to apologize. I have checked the homework help guidelines and they do allow the person asking the question to post a solution if they find one:

Complete solutions can be provided to a questioner after the questioner has arrived at a correct solution. If the questioner has not produced a correct solution, complete solutions are not permitted, whether or not an attempt has been made.

So it's OK for you to post your solution.