While you had right, it was necessary to integrate it numerically, using mathematica or something like that.
The distance between two orbits, 2M to 6M is7.2M!
x=r/M
x_1= 2 x_2= 3
d_1 = M\int_2^3{(1-x/M)}^{-1/2}dx
d_1= 3.05M d_2= 1.54M d_3= 2.60M
d_{tot}= 7.2M
We...
Ok, thank you very much, indeed I hoped a solution more elegant that the integration beast and nasty, but if it's impossible, I will do that. Thanks for all Kdv :)
Yes it's geometrized units, I don't use the technical terme sorry.
I understand that my distance is (for d1)
d_{1} = \int_{2M}^{3M} (1 - \frac{2M}{r})^{-1/2} dr
with no intergration of dt and d\Omega
But the integration is difficult not?
I've no idea to resolve this...
[SOLVED] Distance between 2 orbits of a black hole
Homework Statement
Hello.
I am currently working on the black holes in the Schwarzschild metric, an exercise course asks me to calculate the physical distance between different orbits.
d_{1} = distance betwenn 2M and 3M
d_{2} = distance...