Does the earth also follow an undulating orbit like an electron around an atomic nucleus?

Answer

Dear William,

No, while it’s a logical comment to make, it isn’t. This is for several reasons, one of which is that you have a highly simplified atomic model in mind.

Earth’s orbit is completely controlled by gravity. Because this is a very weak force, you can initially ignore the influence of all other objects in our solar system to estimate the Earth’s orbit around the sun. You then only have to solve the 2-body problem. When two objects have the same weight, they will move nicely evenly in ellipses around their common center of gravity (see first animation in the link above). Now the sun and the earth are far from equal in mass so we get a situation that is rather similar to the second animation in the link above. Here you can see the two bodies nicely making a circular orbit with the heaviest object close to the center of mass (red cross). In the case of the Earth and the Sun, the mass difference is so great that the red cross almost coincides with the center of the heaviest object (the Sun) so that the Earth appears to move in a circle around the Sun, although it is actually a common (This is also the way astronomers use to detect planets around distant stars, if the star wobbles a little bit, it means it is moving around a common center of gravity with another mass that is much lighter: a planet).

I have always said that the orbit is circular. That’s actually not the case. The general form of a solution to a 2-body problem is a “conic section”. These include: hyperbolas, parabolas, ellipses and circles, with only the latter two giving an orbit that stays close to the sun. Which conic you have depends on the position and speed of your object (ie the angle at your conic). There is only 1 that yields a circle, and many that yield ellipses. For this reason, the orbit of the Earth(and the other planets) is not exactly circular but it is elliptical (deviation of a few %). Now what do we do with the influence of all other masses in our solar system? You can include this in the calculation. However, it is impossible to solve the n-body problem in general for n>3. What you can do is solve the whole thing numerically: on the basis of the masses, positions and speeds of the planets, moons, comets, etc. in our solar system calculate the laws of Newton using a computer. The obtained orbits will then deviate slightly from the previously calculated ellipse orbits.

The orbit of an electron is a completely different story. At this scale, gravity does not play a role, but it is the electromagnetic interaction that rules: Coulomb forces, which you are probably familiar with from physics lessons. Here too you can solve a 2-body problem (the interaction force has a slightly different shape because here it is the charges that determine the magnitude of the force). Again you expect conic sections as a solution here. And this was also what has been proposed in ancient atomic models (eg Nagaoka’s Saturn model and Rutherford and Bohr’s models). However, there is a small problem here (something that Nagaoka also knew, for example, and prevented him from defending his own model with all his might), since we are dealing with charged particles we also have to take into account what charges do during a Motion: When a charged particle accelerates it will radiate and lose energy. Because of this, you would expect these particles to crash on the atomic nucleus. In Bohr’s model, this problem is solved by assuming that charges are quantized and thus there can be no continuous loss of energy, only energy loss in steps (which explains the line spectra of pure materials). This has the side-effect that you will no longer see the orbits as perfectly circular, but as a sine wave superimposed on this circular orbit. . If you want a more accurate description of an electron around a nucleus, you enter the world of quantum mechanics. In this (more correct) model, there are no more defined orbits for the electrons, but they move in orbitals, where we can only tell that an electron is in a certain place with a certain probability.

So there are multiple reasons why the earth and an electron have different orbits.

* There is no electromagnetic energy loss at the earth (which has to be quantized and gives the wavy orbit in Bohr’s atomic model)

* Electrons don’t actually move on orbits as Bohr suggested, but they do move in quantum mechanical diffuse orbitals that only indicate the probability of finding.