Poynting-Robertson effect
|
|
The Poynting-Robertson effect, also known as Poynting-Robertson drag, named after John Henry Poynting and Howard Percy Robertson, is a process by which solar radiation causes dust particles in a solar system to slowly spiral inward. The effect is due to the orbital motion of the dust grains causing the radial push of the solar radiation to be offset slightly, slowing its orbit. The effect can be interpreted in two ways, depending on the reference frame chosen.
From the perspective of the grain of dust, the Sun's radiation appears to be coming from slightly forward of the direct line to the centre of its orbit because the dust is moving perpendicular to the radiation's movement. This angle of aberration is extremely small since the radiation is moving at the speed of light and the dust grain is moving many orders of magnitude slower than that.
From the perspective of the solar system as a whole, the dust grain absorbs sunlight entirely in a radial direction. However, the dust grain's motion relative to the Sun causes it to re-emit that energy unevenly (more forward than aft), causing an equivalent change in angular momentum (a sort of recoil).
The Poynting-Robertson force is equal to:
- <math>F_{PR} = \frac{Wv}{c^2} = \frac{r^2}{4 c^2}\sqrt{\frac{G M_s L_s^2}{R^5}}<math>
where <math>W<math> is the power radiated from the particle (equal to the incoming radiation), <math>v<math> is the particle's velocity, <math>c<math> is the speed of light, <math>r<math> the object's radius, <math>G<math> is the universal gravitational constant, <math>M_s<math> the Sun's mass, <math>L_s<math> is the solar luminosity and <math>R<math> the object's orbital radius.
Since the gravitational force goes as the cube of the object's radius (being a function of its volume) whilst the power it receives and radiates goes as the square of that same radius (being a function of its surface), the Poynting-Robertson effect is more pronounced for smaller objects. Also, since the Sun's gravity varies as one over <math>R^2<math> whereas the Poynting-Robertson force varies as one over <math>R^{2.5}<math>, the latter gets relatively stronger as the object approaches the Sun, which tends to reduce the eccentricity of the object's orbit in addition to dragging it in.
There is a critical size at which small objects are so affected by radiation pressure that the latter actually cancels the Sun's gravitation altogether. For rocky particles, this size is about 3-6 µm in diametre. The Poynting-Robertson effect still affects these small particles, but they will be blown out of the solar system by the Sun's light before the Poynting-Robertson force works any significant change in their motion.
Poynting conceived of the force in the then-dominant "luminiferous aether" view of the propagation of light; Robertson is the one who redid the demonstration from a relativistic standpoint and confirmed the result.
References
- 1 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1903MNRAS..64A...1P&db_key=AST&high=40b75ae47027409) Poynting, J. H., (Nov 1903). Radiation in the solar system: its effect on temperature and its pressure on small bodies, Monthly Notices of the Royal Astronomical Society, Vol. 64, Appendix, pp. 1-5
- 2 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1937MNRAS..97..423R&db_key=AST&high=40b75ae47028044) Robertson, H. P., (April 1937). Dynamical effects of radiation in the solar system, Monthly Notices of the Royal Astronomical Society, Vol. 97, pp. 423-437