What other factors need to be taken into account to prove that the speed of an electron revolving around the nucleus of an atom is the same as the speed of a planet revolving around the sun? So basically what factors would cause it to be different?

 ChatGPT's response to the above question:

There are several factors that can affect the comparison of the speed of an electron revolving around the nucleus of an atom and the speed of a planet revolving around the sun:

1. Distance: The distance between the electron and nucleus in an atom is much smaller than the distance between a planet and the sun. The force of gravity decreases with distance, so the gravitational force between an electron and nucleus is much stronger than the gravitational force between a planet and the sun. Therefore, the speed of an electron is higher than the speed of a planet for a given distance.

2. Mass: The mass of an electron is much smaller than the mass of a planet. According to Newton's second law of motion, a smaller force is required to accelerate a smaller mass to a given speed compared to a larger mass. Therefore, the speed of an electron is higher than the speed of a planet for a given force.

3. Orbital shape: The orbit of an electron around the nucleus is not a perfect circle, but rather an elliptical shape. The speed of an electron changes as it moves through different parts of its orbit, so there is no single "average" speed for an electron in an atom. On the other hand, the orbit of a planet around the sun is more circular, so the speed of the planet is more consistent throughout its orbit.

4. Relativistic effects: The speed of an electron can approach the speed of light, which can cause time dilation and other relativistic effects. These effects are not significant at the speeds of planets in their orbits around the sun.

Therefore, while the speeds of an electron and a planet can be compared using similar formulas, the comparison is not entirely straightforward due to the above factors.