- #1

JTorn

- 6

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- 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?

"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?