Editing Poynting–Robertson effect (section)

== Relation to other forces ==

The Poynting–Robertson effect is more pronounced for smaller objects. Gravitational force varies with mass, which is <math>\propto r^3</math> (where <math>r</math> is the radius of the dust), while the power it receives and radiates varies with surface area (<math>\propto r^2</math>). So for large objects the effect is negligible.

The effect is also stronger closer to the Sun. Gravity varies as <math>R^{-2}</math> (where ''R'' is the radius of the orbit), whereas the Poynting–Robertson force varies as <math>R^{-2.5}</math>, so the effect also gets relatively stronger as the object approaches the Sun. This tends to reduce the [[eccentricity (orbit)|eccentricity]] of the object's orbit in addition to dragging it in.

In addition, as the size of the particle increases, the surface temperature is no longer approximately constant, and the radiation pressure is no longer isotropic in the particle's reference frame. If the particle rotates slowly, the radiation pressure may contribute to the change in angular momentum, either positively or negatively.

Radiation pressure affects the effective force of gravity on the particle: it is felt more strongly by smaller particles, and blows very small particles away from the Sun. It is characterized by the dimensionless dust parameter <math>\beta</math>, the ratio of the force due to radiation pressure to the force of gravity on the particle:
: <math>\beta \equiv \frac{F_\text{r}}{F_\text{g}} = \frac{3LQ_\text{PR}}{16\pi GMc \rho s },</math>
where <math>Q_\text{PR} </math> is the [[Mie scattering]] coefficient, <math>\rho</math> is the density, and <math>s</math> is the size (the radius) of the dust grain.<ref>{{cite journal |last1=Burns |last2=Lamy |last3=Soter |year=1979 |title=Radiation Forces on Small Particles in the Solar System |journal=[[Icarus (journal)|Icarus]] |volume=40 |issue=1 |pages=1–48 |doi=10.1016/0019-1035(79)90050-2 |bibcode=1979Icar...40....1B}}</ref>

=== Impact of the effect on dust orbits ===

Particles with <math>\beta \geq 0.5</math> have radiation pressure at least half as strong as gravity and will pass out of the Solar System on hyperbolic orbits if their initial velocities were Keplerian.<ref name="wyatt">{{Cite web | url = http://www.ast.cam.ac.uk/~wyatt/wyat06b.pdf | title = Theoretical Modeling of Debris Disk Structure | first = Mark | last = Wyatt | publisher = University of Cambridge | date = 2006 | access-date = 2014-07-16 | archive-date = 2014-07-27 | archive-url = https://web.archive.org/web/20140727004344/http://www.ast.cam.ac.uk/~wyatt/wyat06b.pdf | url-status = live }}</ref> 
For rocky dust particles, this corresponds to a diameter of less than 1&nbsp;[[μm]].<ref>{{Cite encyclopedia |title=Interplanetary dust particle (IDP) |encyclopedia=[[Britannica Online]] |url=https://www.britannica.com/topic/interplanetary-dust-particle |access-date=2017-02-17 |last=Flynn |first=George J. |date=2005-06-16 |archive-date=2017-02-17 |archive-url=https://web.archive.org/web/20170217224342/https://www.britannica.com/topic/interplanetary-dust-particle |url-status=live }}</ref>

Particles with <math>0.1 < \beta < 0.5</math> may spiral inwards or outwards, depending on their size and initial velocity vector; they tend to stay in eccentric orbits.

Particles with <math>\beta \approx 0.1</math> take around 10,000 years to spiral into the Sun from a [[circular orbit]] at 1&nbsp;[[Astronomical unit|AU]]. In this regime, inspiraling time and particle diameter are both roughly <math>\propto 1/\beta</math>.<ref name="inspiral">{{Cite journal |last1=Klačka |first1=J. |last2=Kocifaj |first2=M. |title=Times of inspiralling for interplanetary dust grains |journal=[[Monthly Notices of the Royal Astronomical Society]]|location=Oxford |date=27 October 2008 |volume=390 |issue=4 |pages=1491–1495 |quote=Sec. 4, Numerical results |doi=10.1111/j.1365-2966.2008.13801.x|bibcode=2008MNRAS.390.1491K |doi-access=free }}</ref>

If the initial grain velocity was not Keplerian, then circular or any confined orbit is possible for <math>\beta < 1</math>.

It has been theorized that the slowing down of the rotation of Sun's outer layer may be caused by a similar effect.<ref>{{Cite news |url=http://www.hawaii.edu/news/2016/12/12/giving-the-sun-a-brake/ |title=Giving the Sun a brake |date=2016-12-12 |newspaper=University of Hawai{{okina}}i System News |access-date=2017-02-17 |language=en-US |archive-date=2022-06-01 |archive-url=https://web.archive.org/web/20220601203813/http://www.hawaii.edu/news/2016/12/12/giving-the-sun-a-brake/ |url-status=live}}</ref><ref>{{cite journal | arxiv = 1612.00873 | title = Poynting-Robertson-like Drag at the Sun's Surface | first1 = Ian | last1 = Cunnyngham | first2 = Marcelo | last2 = Emilio | first3 = Jeff | last3 = Kuhn | first4 = Isabelle | last4 = Scholl | first5 = Rock | last5 = Bush | year = 2017 | journal = [[Physical Review Letters]] | volume = 118 | issue = 5 | page = 051102 | doi = 10.1103/PhysRevLett.118.051102 | pmid = 28211737 | bibcode = 2017PhRvL.118e1102C | s2cid = 206285189 }}</ref><ref>{{Cite journal |last=Wright |first=Katherine |date=2017-02-03 |title=Focus: Photons Brake the Sun |url=https://physics.aps.org/articles/v10/13 |journal=Physics |language=en-US |volume=10 |page=13 |doi=10.1103/Physics.10.13 |access-date=2017-02-17 |archive-date=2017-02-17 |archive-url=https://web.archive.org/web/20170217223800/https://physics.aps.org/articles/v10/13 |url-status=live|url-access=subscription }}</ref>