Mathaddict809 said:Greetings I have been trying to find the orbit of Mercury using the geodesic equations with the Schwarzschild Metric, more precisely I have been using the equations derived in "General Relativity, An Introduction for Physicists" by M.P. Hobson, etc, that is:
[tex]\left(1-\frac{2\mu}{r}\right) \frac{dt}{d\tau} =k [/tex]<br>
c^2
There are several factors that contribute to the difficulty of predicting Mercury's orbit, including its highly elliptical orbit, its close proximity to the sun, and the influence of other planets on its trajectory.
With current technology and understanding of celestial mechanics, we can predict Mercury's orbit with a high degree of accuracy. However, there will always be some margin of error due to the complex nature of the solar system.
Accurately predicting Mercury's orbit is crucial for space missions and exploration, as well as for understanding the dynamics of our solar system. It also helps us make accurate calculations for calendars and timekeeping.
Our predictions of Mercury's orbit have significantly improved with advancements in technology and our understanding of gravity and celestial mechanics. Early predictions were often off by several degrees, but now we can predict its position with high precision.
While our predictions have greatly improved, there are still some ongoing challenges and uncertainties in predicting Mercury's orbit. These include the influence of other planets, potential unknown factors affecting its orbit, and the constant changes in the sun's gravitational pull.