Classical, electrons fall into nucleus, why not planets into sun?

[Lapidus]

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?

 

[A.T.]

Why do not planets orbiting the sun generate gravitational waves and (slowly) collapse into the sun?

http://en.wikipedia.org/wiki/Gravitational_wave#Orbital_decay_from_gravitational_radiation

 

[Lapidus]

Nice! Thanks, A.T.

 

[Andrew Mason]

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?

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.

Besides, it is not clear whether a charge radiates if it is uniformly accelerated. See, for example this exchange.

AM

 

[Lapidus]

No offense, Matthew, but you do see the word classical in front of my question?

 

[Nugatory]

No offense, Matthew, but you do see the word classical in front of my question?

Everyone agrees that with no energy loss there are classically 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. 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.

 

[Andrew Mason]

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.

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).

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.

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.

AM

 

[Lapidus]

I have a follow-up question! Or rather two.

1. Assume we have two bodies orbiting each other, say two super-massive neutron stars. They give off gravitational waves and are (slowly) spiralling into each other. But what about conservation of angular momentum?! Are the two neutron stars moving faster around each other, the closer they get?

2. I do not really understand angular momentum (and its conservation), I'm afraid. 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?

thank you!

 

[WannabeNewton]

But what about conservation of angular momentum?! Are the two neutron stars moving faster around each other, the closer they get?

Yes but some of the angular momentum is carried away by the gravitational waves.

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?

In Newtonian gravity this is simply because there is no damping force present in celestial orbits. The only force present is gravity and given a stationary central potential, in this case a stationary central gravitational potential, one can easily show that angular momentum must be conserved and energy must be conserved and from this one can calculate the trajectories of freely falling particles to find that the bound ones must be circles or ellipses which is of course the Kepler problem. The only transitions between bound trajectories are due to perturbations e.g. from collision with an asteroid of negligible size.