http://en.wikipedia.org/wiki/Gravitational_wave#Orbital_decay_from_gravitational_radiationLapidus said:Why do not planets orbiting the sun generate gravitational waves and (slowly) collapse into the sun?
Bad example in your title. Electrons do not fall into the nucleus and an atom does not emit EM waves due to an electron moving around the nucleus. Atoms emit radiation in discrete amounts (photons) when an electron energy state changes.Lapidus said:How is electromagnetism different from gravity in that accelerated objects radiate EM waves when accelerated in an electric field but no gravitational waves are generated when objects are accelerated in a gravity field?
Why do not planets orbiting the sun generate gravitational waves and (slowly) collapse into the sun?
Lapidus said:No offense, Matthew, but you do see the word classical in front of my question?
The question whether a uniformly accelerating charge radiates still seems to be open. Feynman concluded that it depended on the third time derivative of position (non-uniform acceleration).Nugatory said:Everyone agrees that with no energy loss there are stable orbits in a ##1/r## potential produced by a ##1/r^2## force. But from there...
Classically: Electrons would fall into the nucleus because they would lose energy via electromagnetic radiation.
Even the theory on this is not developed, so I don't think we can say that gravitons are necessarily emitted by Earth as it orbits the sun. But I would agree that we can say that even if gravitational radiation occurred, it would be such a small amount that it would be virtually undetectable.Planets do not fall into the sun because there is no such thing as gravitational radiation, so they don't lose energy as they orbit.
Non-classically: Electrons do not radiate away energy and fall into the nucleus because of energy quantization. Planets do radiate away energy in the form of gravitational radiation, but they don't fall into the sun (in any reasonable amount of time) because the amount of energy radiated away by a planet-sized mass in a planet-like orbit is near as no never mind negligible.
Lapidus said:But what about conservation of angular momentum?! Are the two neutron stars moving faster around each other, the closer they get?
Lapidus said:When I am orbiting a body, then a force is applied on me and I am accelerating. But then why is that orbiting motion conserved and can go on forever?
Electrons do not fall into the nucleus of an atom because of the principles of quantum mechanics. According to the laws of quantum mechanics, electrons exist in specific energy levels around the nucleus and do not follow a predictable path like planets do around the sun.
The electrons are held in their specific energy levels by the electromagnetic force. This force is created by the attraction between the negatively charged electrons and the positively charged nucleus.
The stability of an atom is maintained by the balance between the attractive force of the nucleus and the repulsive force between the electrons. If this balance is disrupted, the atom can become unstable and undergo chemical reactions.
No, electrons cannot fall into the nucleus of an atom. According to the Heisenberg Uncertainty Principle, the exact position and momentum of an electron cannot be known simultaneously. This means that the electron's position around the nucleus is never predictable and it cannot fall into the nucleus.
There are some exceptions to this principle, such as in the case of radioactive atoms or highly energetic particles. In these cases, the balance between the attractive and repulsive forces can be disrupted, causing the electrons to fall into the nucleus and undergo nuclear reactions. However, this is not a common occurrence in stable atoms.