Re: Electromagnetic radiation of planets

On Wed, 27 Feb 2007, proton wrote:

An electric charge being accelerated radiates energy. This includes
all protons and electrons forming any physical body, for example a
planet. Since a planet is constantly being accelerated in its orbit
around the Sun, shouldn't it constantly radiate electromagnetic
energy? If so, how can the orbits be stable? Why don't planets spiral
into the Sun as they lose energy through radiation? Has this radiation
been detected? Or is there anything wrong with my assumptions?

How much energy is radiated?

The acceleration of the Earth has a magnitude of about 0.006 m/s^2, and
a figure commonly given for the charge of the Earth is 500kC (perhaps a
serious overestimate - see H. Dolezalek, Meteorol. Atmos. Phys. 38, 240
(1988)). The Larmor formula for radiated power is

P = q^2 a^2 / ( 6 pi epsilon_0 c^3 )

giving P = 2 nW, which would take a long time to have much impact on the
approximately 3x10^33 J of kinetic energy.

How does this compare to the force due to Poynting-Robertson effect? The
drag force is equal to f v/c for a circular orbit, with f being the
radiation pressure. The power incident on the Earth is about 2x10^14 W, so
the radiation pressure is about 700kN, for a drag of 70N. The radiation
damping force due to a radiated power of 2nW is P/v, or about
7x10^(-14) N, negligible compared to other forces.

Of course, then there is the controversy as to whether uniformly
accelerated charges radiate or not, but the acceleration of a planet in a
circular orbit is not constant, so ...

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.

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