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## Main Question or Discussion Point

i am a physics enthusiast studying general relativity on my own with the book: "Exploring Black Holes: Introduction to General Relativity" by Edwin F. Taylor and John Archibald Wheeler. I am having the hardest time with the fourth chapter of the book and especially the 4th question in that chapter (i seem to have a thing with 4's). I have no knowledge of tensors, but that is not required for the book. The answer that i get for the first part of the problem is confusing and i want to verify that what i have as an answer is either right or wrong and then proceed from there.

the problem states:

Under what circumstances are circular orbits predicted by Newton indistinguishable from circular orbits predicted by Einstein?

A. Find the Newtonian expression similar to:r=((L/m)^2/2)[1+/-(1-(12M^2)/((L/m)^2))^(1/2)] for the radius of a stable circular orbit, starting with V(r)/m=-M/r+(L/m)^2/(2r^2).

B. Recast for the general relativistic prediction of r for stable orbits in the form:r=rnewt(1+q)

Where r¬Newt is the radius of the orbit predicted by Newton and q is a small quantity. This expression neglects differences between the Newtonian and relativistic values of L/m (angular momentum) when expressed in the same units. Use the approximation:

(1+d)^n ≈1+nd provided |d|<<1 and |nd|<<1.

To derive a simple algebraic expression for q in terms of M and rNewt.

as a little aside how do you type equations into this the equation editor i have apparently does not work for html.

thank you.

the problem states:

Under what circumstances are circular orbits predicted by Newton indistinguishable from circular orbits predicted by Einstein?

A. Find the Newtonian expression similar to:r=((L/m)^2/2)[1+/-(1-(12M^2)/((L/m)^2))^(1/2)] for the radius of a stable circular orbit, starting with V(r)/m=-M/r+(L/m)^2/(2r^2).

B. Recast for the general relativistic prediction of r for stable orbits in the form:r=rnewt(1+q)

Where r¬Newt is the radius of the orbit predicted by Newton and q is a small quantity. This expression neglects differences between the Newtonian and relativistic values of L/m (angular momentum) when expressed in the same units. Use the approximation:

(1+d)^n ≈1+nd provided |d|<<1 and |nd|<<1.

To derive a simple algebraic expression for q in terms of M and rNewt.

as a little aside how do you type equations into this the equation editor i have apparently does not work for html.

thank you.