# Mercury's Orbital Precession Anomaly

• Bjarne
In summary, Albert Einstein proposed a second-order correction to Mercury's orbit, based on his general theory of relativity. This correction takes into account the perihelion precession of Mercury, which is 43 arc-seconds per century more than what Newtonian physics alone would predict. The equation used by Einstein to calculate this is given by \Delta \phi = 2 l \int_{r_1}^{r_2}\frac{dr}{r^2}\left(1-\frac{2GM}{r c^2}\right)^{-1/2}\left[c^2 e^2 \left(1-\frac{2GM}{r c^2}\right)^{-1} - \left(c

#### Bjarne

The perihelion of Mercury precesses by 5600 arc-seconds per century, which is 43 arc-seconds per century more than Newtonian physics alone would predict

Albert Einstein proposed a second-order correction to Mercury's orbit, based on his general theory of relativity.

Which equation had Einstein used to calculate this?

The equation one gets from the analysis is, I believe (lifted from Hartle):
$$\Delta \phi = 2 l \int_{r_1}^{r_2}\frac{dr}{r^2}\left(1-\frac{2GM}{r c^2}\right)^{-1/2}\left[c^2 e^2 \left(1-\frac{2GM}{r c^2}\right)^{-1} - \left(c^2 + \frac{l^2}{r^2}\right)\right]^{-1/2}$$
I don't have the book in front of me though so there might be small errors.
One can expand this to get a definite answer neglecting higher order corrections, but I don't have that equation in front of me.

## 1. What is Mercury's Orbital Precession Anomaly?

Mercury's Orbital Precession Anomaly refers to the phenomenon observed in Mercury's orbit where its closest approach to the sun (perihelion) shifts slightly each orbit, rather than remaining in a fixed position relative to the stars.

## 2. Why does Mercury's orbital precession occur?

This anomaly occurs due to the influence of other planets, mainly the gravitational pull of Venus and Jupiter, on Mercury's orbit. This causes a small but significant change in the shape of Mercury's orbit, leading to the observed precession.

## 3. How long does it take for Mercury's orbit to precess?

Mercury's orbit precesses at a rate of 5600 arc seconds per century, which means it takes approximately 11.86 years for the anomaly to complete one full cycle.

## 4. How was Mercury's orbital precession anomaly discovered?

The anomaly was first observed by astronomers in the 19th century, who noticed that Mercury's perihelion was not staying in a fixed position as predicted by Newton's laws of motion. It wasn't until Albert Einstein's theory of general relativity was introduced in the early 20th century that this phenomenon could be fully explained.

## 5. What are the implications of Mercury's orbital precession anomaly?

The accurate measurement and study of Mercury's orbital precession has provided strong evidence for the validity of Einstein's theory of general relativity. It also has practical applications in improving our understanding of the dynamics of the solar system and for space missions to Mercury, as it affects the spacecraft's trajectory and timing of arrival to the planet.