Ask Ethan No. 43: Decreasing Gravity Orbits

I would prefer sharp criticism from an intelligent person than the mindless approval of the crowd
Johannes Kepler, 1601

RealClearScience Editor asks:

Does the fact of a decrease in orbits (for example, for binary stars) mean that something is wrong with the laws of Newton and Kepler? Does the theory of relativity explain this process?

Let's go back to the beginning and go through history, starting with the laws of Newton and Kepler.



If we take the sun as a fixed reference point, we can track the astronomical movement of all celestial bodies - planets, asteroids and comets - around the sun. Using the data of experiments available 400 years ago, Kepler calculated that the planets do not move in a circle with the Sun in the center, but along an elliptical path with the Sun located in one of its foci. More than 50 years after this, Newton derived the law of gravity, thanks to which such orbits were obtained - Newton's law of gravity.



This law does not apply only to planets orbiting the Sun, or objects falling to the Earth. It is universal and acts on all objects in the Universe that have mass.

That is, if at some point you knew the position and masses of all the objects of the Universe, you could deterministically predict the evolution of everything under the influence of gravity at any future moment in time. This is the power of Newton's laws.



But we do not need to simulate the entire Universe. For this, firstly, we would need a computer with power from the whole Universe. Instead of counting all the movements of all subatomic particles, we just need to make a simplified model.

What if we take a very simple system - the solar system only with planets and the sun, and apply Newton’s laws to it? We


ignore the asteroid belt and Pluto.

It could be decided that with these nine masses separated by huge distances, we get eight ellipses moving around the stationary Sun.

That is exactly what will happen if we accept the following:

• all planets and the sun are regarded as material points
• the orbit of each planet is determined only by its interaction with the Sun
• Newton’s laws are absolute, there are no such things as Lorentz invariance (i.e. the laws of physics do not care about speed)

In the real world, these statements are false.



Planets and the Sun are not material points. The distances separating them are huge in comparison with their sizes, but their sizes vary from huge (diameter of Mercury - 4879 km) to incredible (diameter of the Sun - 1391684 km). Their masses are distributed unevenly, in the core they are more dense, on the edge - less. Each body in the solar system rotates with a certain angular momentum.



Other planets also have a big impact, especially over time. None of the planets moves along an ideal ellipse, and the Sun does not stand still. The gravitational forces with which bodies act on each other constantly change their orbits, and it turns out that Kepler’s calculations can be accepted only as their approximation.

In fact, planets do not move in closed ellipses, and a small amount of orbital energy is lost over time, especially if more complex phenomena, such as collisions with other particles, are taken into account.

This was first noted before the invention of the theory of relativity - by Oliver Heaviside in 1893.



Suppose you have a central mass that creates a gravitational field. In addition, it somehow moves (the Sun is not stationary), so the gravitational field changes. And yet you have another massive particle moving in this field. What will happen?

It’s okay if you don’t know. At about the same time, scientists were sorting out the task of what happens when a charged particle moves in an electric field. They represented the atom as a positively charged nucleus around which a negatively charged electron moves.



A fast-moving particle emits electromagnetic radiation that carries away energy. So, the orbit should decrease over time, so the matter cannot be stable! Rutherford discovered this problem associated with electromagnetism, and no one could solve it until they invented quantum mechanics.

In the case of gravity, we are confronted with the limited predictive ability of Newton's laws. Since Newtonian gravity does not take into account the speed of motion, it does not say anything about gravitational radiation during acceleration (for example, when the direction of motion changes) when moving in a gravitational field. This is a flaw in a theory in which Lorentz invariance is absent.

But just as there is electromagnetism, there must be gravitomagnetism - since gravity is Lorentz invariant. You may have heard about the Gravity Probe B experiment , but in fact there is a way to measure gravitomagnetism even more accurately.



By measuring the distance to the moon with lasers, which has been available for 45 years, we not only confirmed the effect of gravitomagnetism, which is also responsible for reducing orbits, but also found that it is consistent with the theory of relativity by 99.9%.

For the Earth it will take a time of the order of 10 ¹⁵⁰ years for it to fall on the Sun - this is more than the lifetime of the Solar system. But for a double pulsar, it will end in just a few hundred million years, due to the gravitational radiation effect alone.



Therefore, in Newton's laws there is a nuance explaining the deviation of the orbits from closed ideal ellipses, but if you want to accurately predict the decrease in orbits, you will need a Lorentz-invariant theory that preserves the laws of physics regardless of speed. And the General Theory of Relativity, after so many years, works best!