Talk:Poynting-Robertson effect

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[edit] Radiation pressure

I think 3-6 µm is more than an order of magnitude too large for particles to get blown away from sun due to radiation pressure, the particle size should be around 300 nm. Gravitational acceleration at distance R is G*M_Sun/R^2, which is about 0.0059 m/s^2 at earth's distance. Solar radiation at earth's distance is 1367 W/m^2, the resulting pressure is (if all of the light is absorbed) 1367 W/m^2 / c = about 4.56*10^-6 Pa. The force on a spherical particle of radius r is r^2*PI*pressure; the acceleration is 3*Force/(4*PI*r^3*rho) with rho being the density of the particle. Depending on the density you get something between 100 and 200 nm for r if you assume that gravity and radiation pressure just cancel each other. 193.171.121.30 20:13, 25 Jun 2005 (UTC)

Particles as small as you describe (100-300 nm) are blown away immediately, since, as you point out, they are essentially in free fall --they ignore the Sun and keep going in a straight line, away. Larger particles (up to 3-6 µm) suffer a more gradual expulsion, since the radiation pressure doesn't quite cancel out the Sun's gravity.

Urhixidur 01:09, 2005 Jun 26 (UTC)

You're right, the particle is already in motion (e. g. when it is created in a collision) and only needs to have escape velocity at the effectively lowered solar gravity (replace G*M_Sun by G*M_Sun - 3*S*Re^2/(4*rho*r*c), where S is the solar constant at earth's distance (1367 W/m²), Re is earth's distance from sun, rho is the particle density, r the particle radius and c the speed of light). If we assume the particle initially has got the velocity of a circular orbit without effective gravity reduction at the initial distance, we can derive a formula for the particle radius which gives us just escape velocity: r = 3*S*Re^2/(2*rho*G*M_Sun*c). At a density of 3000 kg/m³ critical particle size is about 800 nm (radius about 400 nm). We get particle sizes in the 3-6 µm range if we assume low-density particles (e. g. water ice) and higher reflectivity (so far I assumed black body particles). 193.171.121.30 1 July 2005 11:58 (UTC)

[edit] Re-radiation

The "solar system perspective" explanation is flawed. The re-radiation does not contribute to the Poynting-Robertson effest. This is most easily seen by removing the sun's radiation: A glowing lightbulb flying through space would have to slow down on its own by this radiation effect (which it obviously does not). In the solar system perspective, the effect is still that the sun's radiation absorbed by the particle does not carry an impulse in the particle's direction of movement; thus, by absorption, the particle's mass, but not its impulse (in that direction) is increased: It is slowed.
Unfortunately, this mistake managed to find its way into parts of the literature, probably based on the Poynting article cited, which predates relativity theory and is ether-based. Robertson seems to have seen this problem, but I'm not sure whether he concerns himself with the solar system perspective at all. I'm no physicist myself and therefore don't know all the literature; could someone more qualified than me rewrite that section and cite an adequate reference? Yours, Huon 12:44, 3 June 2006 (UTC)

I corrected the article and I'm a physicist. But English is not my native language. Therefore someone should check the article. If there is dought about the physical content, please contact me: you will find my e-mail address on my homepage http://rschr.de . User:rschr.de 2006-07-14 15:47 UTC

It should be pointed out that it is the re-radiation of the photon which causes a drop in the angular momentum. The dust particle's motion doesn't change, because the drop in ang. momentum is caused by the drop in mass of the dust particle. L=m vXr. L goes down, m goes down, but vXr stay the same. Photons on radial trajectories do not carry angular momentum. Hence the absorption of the photon does not change the angular momentum of the dust particle. However, the dust drops into a lower orbit, in order to compensate for the increase in mass of the particle. L=m vXr stays the same, but m goes up, so vXr must go down. Unexpect 17:04, 6 December 2006 (UTC)

Hi rschr.de, I've kept the words general relativity, but re-included the other changes made post-Dec 6. The pre-Dec 6 version contains an imprecise detail or two which must be corrected. If you'd like to correct them in a different way than I have done, that is also fine. The most important flaw,in my mind, was the implication that absorption of the photons changes the angular momentum. Indeed the orbit decays due to the absorption of photons, but this is only so that angular momentum is conserved! Ultimately the dust grain loses angular momentum, but that is because it is radiating away angular momentum. This is correctly pointed out in textbooks such as Rybicki&Lightman. (Note that the orbital motion of the dust grain is unchanged by this 're-radiation', as has been pointed out by you, I think) Unexpect 23:40, 10 December 2006 (UTC)

[edit] Miselading arguments in this discussion

Hi, I have been carefully studying the PR drag and I would like to add a few words on this discussion. Let me point them out as numbered statements which may help to further discussion :

1.- The main contribution of the PR drag is the special relativistic light aberration effect. Let us assume that in a given reference system, there is a constant radiation field perpendicular to the motion of a particle; then in the comobile reference system of the particle, the radiation will be tilted a small angle, as it happens when you go by car and it is raining (form the driver's point of view, the rain comes to his front glass). In this picture, it is easy to see that the radiation field effectively breaks the particle. The same is applicable for short timescales to an orbiting dust grain. Since the PR drag is small, one can assume that it quasistatically brakes de particle, changing slowly its angular momentum dL/dt = m r x dv/dt

2.- Absorption/radiation is not required. Even if the light is simply reflected, the PR will take place. Again, imagine you drive a car and icy drops fall on the car. They exchange momentum with your car glasses even if they are bounced by the glass. In fact, reflection exchanges more momentum than absorption. The increase in mass is negligible in this scale, and the PR effect has nothing to do with this. The expression of the PR effect should include a multiplicative factor of the form (1+k), where k is the "albedo" constant (say, the fraction of radiation that is reflected with respect to the incident one).

3.- If there is absoption, there will be some isotropic radiation, but only on the instantaneously comoving reference system of the particle. As seen from the Solar System reference system, you have a time dependent radiation field form the particle which certainly dissipates angular momentum. This will, for sure, cause a loose of angular momentum. At this point i am not sure, but i have the feeling that it works at a higher v/c order (PR drag is a v/c^1 effect), thus producing negligible effects. This should be computed accurately since it depends (for example) on the albedo constant k.

I will check more carefully the literature. It may happen that the original Poynting papers gave a wrong description of the effect (they assumed there was eather!!!), but qualitatively correct answers. Most likely, a more modern review on the topic should be used and cited.

Astre 23:34, 17 Octubre 2007 (UTC)

While I'm in no way certain right now, I believe Poynting's result is quantitatively off by a factor 2 or so, but Robertson's is correct. Concerning the angular momentum: In the Solar System reference system, the radiation field dissipates angular momentum, but it also dissipates mass, and the effects cancel each other out and don't contribute to PR drag. As Rschr said above, turn off the sun, and a lightbulb flying through space doesn't slow down even though it has a similar time-dependent radiation field. By the way, since Poynting was able to discover the effect before using relativity, it can't be primarily relativity-based as you claim under 1.- Yours, Huon 23:40, 17 October 2007 (UTC)