# Mercury's orbit according to Classical VS Modern Physics

• Daniel Sarioglu
In summary, the conversation discusses a high-school student's paper on Mercury's orbit, specifically using Newton and Kepler's equations to compare the predicted trajectory with the actual one. The student is unsure about which variables are dependent on modern conceptions and whether they should calculate the masses and angular velocity themselves. The conversation also touches on the difference between Newtonian mechanics and general relativity in predicting Mercury's orbit, and where to find data on the "epoch" in relativity. It is mentioned that taking into account the motion of the Sun is necessary for accurate predictions of Mercury's orbit.
Daniel Sarioglu
Hello,
I'm a high-school student and I was assigned to do this kind of a paper as a senior (one of the requirements of graduating is a short monograph on a subject of interest.)
My topic includes an analysis of Mercury's orbit using Newton and Kepler's equations and comparing the predicted trajectory vs the correct one. Just to clarify, my intentions are not to delve into relativity to predict the "correct trajectory," but to compare my calculations according to Newtonian Physics and the orbital parameters (i.e major axis, minor axis, distance between foci of ellipse, etc...) found in online sources like NASA or sth -which I suppose corresponds to the trajectory described by relativity.
My problem lies in not knowing which variables are dependent of modern "non Newtonian" conceptions and therefore would have to find myself. For example, deriving from the inverse square law and the polar equation for an ellipse, I got the following:

$\begin{equation*} L_e = \frac{L_P^2}{Gm_Sm_P^2} \end{equation*}$

Being ##L_e## the semi latus rectum of the elipse, ##L_P##, the angular momentum of the planet, ##G## the gravitational constant, and ##m_S## and ##m_P## the masses of the Sun and the planet correspondingly.

I'm not too sure whether I can get a "Newtonian" measurement if I were to pluck in the data found online for the masses and the angular momentum into the equation. Should I instead calculate the masses and the angular velocity myself? If so, how would one proceed?

This is difficult.

In Newtonian mechanics, if you have two point-masses orbiting each other you get an ellipse. In general relativity, you do not. But the solar system is not a set of two point-masses. The point of Mercury's perihelion rotates around the Sun by 5.75 arcseconds per year, this corresponds to one full rotation every 220,000 years - a very small effect. And more than 90% of this comes from the gravitational attraction from other planets - which is present in Newtonian mechanics as well.

What NASA and so on are typically publishing is "if the planet would follow a perfect Newtonian ellipse based on its position and speed at time X, how would these parameters look like?" This time is called the epoch. If you want to see an effect of general relativity, you'll need the orbital parameters for different epochs to compare them.

Thanks,
Another couple of questions:
Where could I get the data corresponding to relativity's "epoch" as you say?
And should I assume the planet is orbiting the Sun's mass without the Sun being slightly affected by the gravitational pull form the rest of the solar system, could the orbit predicted by Newton and Relativity be differentiated or does the difference lie in the fact that the Sun is also slightly moving?

Daniel Sarioglu said:
Where could I get the data corresponding to relativity's "epoch" as you say?
In databases such as HORIZONS.
Daniel Sarioglu said:
And should I assume the planet is orbiting the Sun's mass without the Sun being slightly affected by the gravitational pull form the rest of the solar system, could the orbit predicted by Newton and Relativity be differentiated or does the difference lie in the fact that the Sun is also slightly moving?
Neglecting the motion of the Sun provides a reasonable estimate in some cases (e.g. analytic estimates for the perihelion precession), but if you want accurate predictions for the orbits you'll probably have to take it into account.

## 1) What is the difference between Classical and Modern Physics?

Classical Physics is a branch of physics that was developed in the 17th and 18th centuries and is based on the laws of motion and gravity described by Sir Isaac Newton. It is a macroscopic approach that is used to explain the behavior of large objects. Modern Physics, on the other hand, encompasses the theories of relativity and quantum mechanics, which were developed in the 20th century to explain the behavior of particles at a microscopic level.

## 2) How does Classical Physics explain Mercury's orbit?

According to Classical Physics, Mercury's orbit can be explained by Newton's law of gravitation, which states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that the closer Mercury is to the sun, the stronger the force of gravity, causing it to move faster in its orbit.

## 3) What does Modern Physics say about Mercury's orbit?

Modern Physics explains Mercury's orbit using Einstein's theory of general relativity, which takes into account the curvature of spacetime caused by massive objects. This theory predicts that the orbit of Mercury is not a perfect ellipse, but rather a slightly distorted shape due to the sun's mass causing spacetime to curve around it.

## 4) Which theory is more accurate in predicting Mercury's orbit?

Modern Physics, specifically Einstein's theory of general relativity, has been proven to be more accurate in predicting Mercury's orbit. Classical Physics is still useful for understanding the behavior of larger objects, but it does not take into account the effects of relativity and cannot fully explain the anomalies in Mercury's orbit.

## 5) What implications do these theories have for our understanding of the universe?

The theories of Classical and Modern Physics have greatly expanded our understanding of the universe and how it works. They have allowed us to make predictions about the behavior of objects in space and have led to the development of technologies such as GPS that rely on these theories. Additionally, Modern Physics has led to groundbreaking discoveries such as the theory of the Big Bang and the existence of black holes.

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