Introduction -:
As we know, our solar system is near the shape of an ellipse, having the sun on its one foci. The point on the major axis which is closest to the sun is known as “Perihelion” whereas the point which is farthest from the sun is called “Aphelion”. This solar system has a lot of mysteries, one of them is the shift in perihelion of the Mercury’s orbit.
The observed precession of Mercury’s orbit = 5600 seconds of arc / century
Here, the main question is why there is precession in the perihelion of Mercury’s orbit. This question will be answered by two different approaches.
Newton’s Approach -:
According to Newton, every planet attracts every other planet in the solar system. Similarly, Mercury is attracted by the sun as well as all the planets in the solar system. Here, in the diagrams :
Fs -: Force by which the sun attracts the mercury
Fp -: Sum of all the forces by which every planet attracts the mercury
Here, two cases arrives -:
Case 1-: When mercury is at “Perihelion” (point nearest the Sun), then the force by which the Sun attracts the Mercury is greater than the sum of forces exerted by other planets on mercury. Due to this, mercury won’t change its path and stays in its orbit.
Case 2-: When mercury is placed at Aphelion (point farthest from the Sun), then the force exerted by Sun on Mercury is less as compared to the net sum of all forces exerted by other planets on it. As a consequence of it, mercury changes its orbit, which causes a shift or precession in its Perihelion.
Error -: When the precession in the perihelion of mercury’s orbit is calculated as per Newton’s explanation, then it has predicted a precession of 5557 seconds of arc/century, which is different from the observed precession. Therefore, there is an error of 43 seconds of arc/century in the Newtonian calculation. This was resolved with the help of Einstein’s general theory of relativity.
Einstein’s Approach -:
By applying the general theory of relativity, the precession in the perihelion of mercury’s orbit can be calculated. As we know, that according to Einstein, the curvature of space-time is called “gravity”. Everybody that has mass is able to wrap or curve the space. The more the mass of the body, the more is the curve in the space. However, due to the wrapping of space, every time when mercury completes its orbit, the trajectory of its motion gets changed, which leads to the precession in its perihelion. As mercury is the closest planet to the Sun, therefore, the perihelion shift is more visible.
Calculations-:
Now by using the theory of relativity, we can calculate the exact value of the precession of perihelion in Mercury’s orbit. The calculations are given below:
