Talk:Poynting–Robertson effect

Equation Origin

I may be wrong but so far as I can tell the given equation on the page has no source, and from sources in my own search, papers and lectures appear to have a much lengthier/involved rendition. Is this equation correct? I'm wanting to use it in my own writing but I'm failing to verify if it is accurate and I'm not of the needed skillset to check if the other forms do simplify to the one given here. The inclusion of a derivation would be well received I'm sure.

Examples of variations to the equation: slide 11 of this At the bottom of this NASA paper

160.5.189.168 (talk) 18:21, 25 April 2019 (UTC)

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)

The expression "spiral outwards from the Sun" for the case of dominating radiation pressure is misleading/wrong. If the radiation pressure is large enough that beta is larger than 1, the equation of motion provides a simple hyperbolic trajectory (negative central mass if I neglect the second order terms of the Poynting Robertson interaction), not a spiral. The spiral only happens for the in ward motion. The equation given in the article eventually contains all the information, but it is poorly interpreted. — Preceding unsigned comment added by 134.95.50.176 (talk) 15:28, 15 April 2014 (UTC)

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)

Yes, the re-radiation argument is wrong. Consider if the particle was a black hole. From its perspective, it would continue to absorb radiation at an angle and lose velocity. However, there would be no re-radiation. Cheesefondue (talk) 05:26, 7 October 2016 (UTC)

Misleading 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)

@Astre; re 2: "simply reflected" can mean many things --- that's how solar sails work! If the mirror normal is radial, then there is no angular momentum transfer, but there is radiation pressure; if the mirror normal is tangential, then we get a large PR effect; and if the mirror normal is orbit-binormal, ... then I think there's nothing going on. Jcmckeown (talk) 23:45, 20 September 2016 (UTC)

Komar11's edits

I have reverted Komar11's edits. He mangled the references, removed the image, and completely rewrote the explanation. I believe several of his equations are wrong because the units don't match (namely dp/dt=p_incoming-p_outgoing), and I found the explanation much less clear than before. I have read one of the new references he introduced, and it didn't explain the P-R effect at all, taking it for granted. Huon (talk)

Royal Philosophical Society Archives

The Royal Philosophical Society Archives are now on-line going back to the mid 1600's. The original Poynting paper is sharp text on clear background vs the poorly-done copy-machine version. The Astronomical Society references are a bit more difficult to find.

Hpfeil (talk) 16:25, 27 October 2011 (UTC)

Explanation of the final equation please!

I found the explanations and variable descriptions really helpful, except for the final mother of an equation of motion. I think I understood some of the vectors from a book I read once, but I could be wrong.

It would be really helpful if whoever put the equation in could explain it in some way, and define what the variables are. Thanks! Cephas Atheos (talk) 13:28, 6 July 2013 (UTC)

That equation looks out of place. I don't think it has to do with the topic of the article: it doesn't seem to consider the PR effect at all, since the paper is on protoplanetary disks, where this may not be a significant factor. I've removed it and its reference here to the talk page. – SJ +

The Equations of Motion for the dust grain are expressed by

$m{\operatorname {d^{2}} {\vec {x}} \over \operatorname {d} t^{2}}=-GMm{\Big (}1-\beta {\Big )}{{\vec {x}} \over r^{3}}+GMm\beta {\Bigg \{}{-{{{\vec {x}}\cdot {\vec {v}}} \over {cr}}{{\vec {x}} \over r^{3}}-{{\vec {v}} \over {cr^{2}}}+{R_{\rm {s}}^{2} \over {cr^{4}}}{\Big (}{\vec {\omega }}\times {\vec {x}}{\Big )}}{\Bigg \}}$

where $R_{\rm {s}}$ is the stellar radius.

Radiation explanation

This explanation:

"From the perspective of the Solar System as a whole (panel (b) of the figure), the dust grain absorbs sunlight entirely in a radial direction, thus the grain's angular momentum remains unchanged. However, in absorbing photons, the dust acquires added mass via mass–energy equivalence. In order to conserve angular momentum (which is proportional to mass), the dust grain must drop into a lower orbit."

doesn't make much sense. The dust grain doesn't keep absorbing photons forever, it radiates too. The mass cannot keep increasing, and a different explanation seems necessary. — Preceding unsigned comment added by 2620:0:1000:1B02:AE16:2DFF:FE07:4F9D (talk) 23:12, 1 October 2013 (UTC)

Since corrected. – SJ +

Random cite

Showing the PR effect discussed in practice (here as a destabilizing factor that will draw meteoroids into a star if the meteoroids aren't broken down into smaller pieces by collisions first): A mechanism for interstellar panspermia, Napier 2002.

Angular momentum

Please could mention be made of where the angular momentum goes? Does the Poynting–Robertson effect, ever so slightly, cause the sun to spin faster? Or is it somehow radiated into deep space? The answer isn’t obvious to this scientific reader, and might be even less obvious to some other readers. JDAWiseman (talk) 20:59, 2 May 2018 (UTC)

Retardation

Exactly like the Sun seen by an astronomer the dust particle receives the light with an aberration effect poynting (pun intended) forward its own movement AND also submitted to a retardation effect poynting backward proportional to the remoteness of the source. Only the vectorial sum of these two causes can yield the actual direction of the light pressure. — Preceding unsigned comment added by 37.164.218.13 (talk) 11:54, 14 January 2022 (UTC)