# Precession of the perihelion - Schwarzschild metric

• tel
In summary, the individual was seeking assistance with solving a question from the Hartle's book, exercise 9.15, on the expansion of (1-2GM/c^2r) in powers of 1/c^2. They were specifically looking for help in obtaining the first term (in front of the first integral) by expanding the expression (1-2GM/rc^2) in powers of 1/c^2. Another individual suggested using the binomial theorem to expand the expression in the form (1+u)^n, where u << 1, and applying it twice. The first step would be to consider the case where n=-1 and u = 2GM/c^2 r, followed by the
tel
Hi everyone!
I was trying to solve this question following the Hartle's book (Gravity: an introduction to Einstein’s general relativity) , exercise 9.15, but I don't know how to do the expansion of (1-2GM/c^2r) in powers of 1/c^2...

I know this sounds easy, but I couldn't get the expression from item (b)

For those who don't have the book, what I want is to get this equation:

from this one:

My problem is how to get the first term (in front of the first integral), only by expanding the (1-2GM/rc^2) in powers of 1/c^2. Someone?

What you need to do is to get the expression in the form

(1+u)^n

where u << 1

This can be expanded by the binomial theorem as

1 + n u + n(n-1) u^2 + ...

It looks like you will have to do this twice. The first step would be to consider the case where n=-1 and u = 2GM/c^2 r. Then you have to apply the same idea again with n=-1/2 and a much more complicated expression for u.

Thank you!

## 1. What is the precession of the perihelion?

The precession of the perihelion is a phenomenon observed in the orbit of a planet around the sun. It refers to the gradual shift in the point where the planet is closest to the sun, known as the perihelion, over time.

## 2. What is the Schwarzschild metric?

The Schwarzschild metric is a mathematical description of the curvature of spacetime around a non-rotating, spherically symmetric mass, such as a planet or a star. It is a key component of Einstein's theory of general relativity.

## 3. How does the Schwarzschild metric explain the precession of the perihelion?

The Schwarzschild metric predicts that the presence of a massive object, like the sun, will cause the fabric of spacetime to curve. This curvature affects the orbit of a planet, causing it to precess or shift over time.

## 4. Why is the precession of the perihelion important?

The precession of the perihelion is important because it provides evidence for the validity of general relativity. It also has practical applications, such as predicting the positions of planets and spacecraft in their orbits.

## 5. How is the precession of the perihelion measured?

The precession of the perihelion is measured by comparing the predicted and observed positions of a planet's perihelion over time. This can be done using telescopes and mathematical calculations, as well as through data collected by space probes.

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