The explanation for why electrons don't fall into the nucleus when they run out of energy and why planets don't run out of energy and fall into the Sun lies in the principles of quantum mechanics and classical mechanics, respectively.
In the case of electrons and the Rutherford atomic model, it was later discovered through quantum mechanics that electrons do not follow classical paths like planets orbiting the Sun. Instead, electrons exist in quantized energy states around the nucleus. According to the quantum mechanical model, electrons are described by wave functions that define their probability distribution in space. These wave functions are solutions to the Schrödinger equation, which determines the allowed energy states for electrons in an atom.
Electrons occupy specific energy levels or orbitals within an atom, each with a defined energy. These orbitals have different shapes and can be thought of as regions where an electron is likely to be found. The lowest energy level, called the ground state, is closest to the nucleus. When an electron loses energy, it can transition to a lower energy level, emitting a photon in the process. However, it doesn't "fall" into the nucleus because the electron's behavior is governed by the laws of quantum mechanics, which are fundamentally different from classical mechanics.
As for the planets orbiting the Sun, their motion is explained by classical mechanics and gravity. According to Newton's laws of motion and his law of universal gravitation, the planets continuously move in elliptical orbits around the Sun. The gravitational force between the Sun and the planets keeps them in their respective orbits. The planets' kinetic energy and angular momentum balance the gravitational potential energy, resulting in a stable orbit.
The reason planets do not fall into the Sun is due to their momentum and the balance of forces. The planets have sufficient tangential velocity and momentum to counteract the force of gravity pulling them inward. The combination of their orbital velocity and the gravitational force keeps them in a stable orbit, where the centripetal force provided by gravity is balanced by their inertia.
In summary, while there are similarities between the Rutherford atomic model and the planetary model, the behavior of electrons in atoms is fundamentally different from that of planets orbiting the Sun. Quantum mechanics governs the behavior of electrons, while classical mechanics explains the motion of planets.