# I need help with an exercise about Energy and Schwarzschild Black Holes

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?

## Answers and Replies

PeterDonis
Mentor
2020 Award
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.

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 dont know how to write equations properly, the equation is fine, it's just that im 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
Mentor
2020 Award
the equation is fine

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

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

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

PeterDonis
Mentor
2020 Award
I will upload the answer

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

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

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

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

PeterDonis
Mentor
2020 Award
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.

• berkeman