Why Doesn't Earth Stop Turning?

[scientifico]

Hello, according to the classic physics a body subjected to an acceleration must dispers energy, the Earth is subjected to a centripetal and centrifugal force so why it doesn't stop to turn ?

 

[mikeph]

I'm not sure what exact law of classical physics you're referring to but it doesn't sound correct.

On a similar subject, centripetal/centrifugal 'forces' are not physically real forces like electromagnetism or gravity. The former is actually a condition for circular motion, and the latter is the result when you analyse a problem in a rotating coordinate system.

 

[scientifico]

probably i got the law in a wrong way, i have read that according to classical physics an electron emits energy in form of radiations because of it's acceleration and should fall into the nucleus

 

[mikeph]

Ah, yes, it is true that an accelerating charge will emit electromagnetic radiation and lose energy in the process (a result from electrodynamics). It's a result you can derive from Maxwell's equations.

I'm not sure how this applies to a planet which is, after all, rotating and made up of charged particles (though the planet as a whole is more or less electrically neutral). Perhaps the effect cancels, or the accelerations are far too minute to produce a measurable effect?

Someone else will hopefully have a better answer!

 

[mfb]

The Earth is extremely close to neutral, all charges are accelerated in a similar way, so we do not emit (significant) electromagnetic radiation based on our orbit around the sun.

Earth has a gravitational charge (=a mass), and emits gravitational waves. However, Earth is slow relative to the speed of light and gravity is weak, so the lost power is tiny: just ~200W. If there would be no other effects on the orbit, the radius of Earth would decrease by about 1 femtometer per day. About 2 millimeters in the whole lifetime of the solar system.

 

[scientifico]

does emission of gravitational waves involve loss of matter ?

 

[mfb]

If you try to see the whole solar system as one object, you could say that its mass gets reduced.
However, if you consider masses in the solar system: No. It involves a loss of energy.

 

[mikeph]

Is this loss of energy manifested as a reduction in the angular velocity of the planet? (edit- or at least a reduction in angular momentum if the radius decreases- but how does the radius decrease?)

And if so... how is angular momentum conserved? How can gravitational waves compensate for this loss of angular momentum if they're directed radially outwards?

 

[scientifico]

However, if you consider masses in the solar system: No. It involves a loss of energy.

So why the Earth radius shoud decrease 1 femtometer per day ?

 

[mfb]

The Earth loses orbital energy.

@MikeyW: No, it is independent of the rotation of earth, the 200 W come from its orbit around the sun.

How can gravitational waves compensate for this loss of angular momentum if they're directed radially outwards?

They do not have a perfect radial symmetry.

 

[scientifico]

why if it just loses energy it loses matter too ?

 

[mfb]

Why should it lose matter?

 

[scientifico]

because the redius decrease... or maybe the matter doesn't lose and the radius became more compact

 

[mfb]

?

The orbital radius of Earth decreases - the Earth comes closer to the sun. Why do you expect any influence on its mass?

 

[scientifico]

Oh, i tought it was the Earth radius :)