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Poynting-Robertson effect

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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 grains in a solar system to slowly spiral inward. The first description of this effect, given by Poynting in 1903, was still "luminiferous aether"-based. Later, in 1937, Robertson described the effect correctly in terms of general relativity.

Image:Poynting-Robertson effect.png From the perspective of the grain of dust circulating the Sun, the Sun's radiation appears to be coming from a slightly forward direction (aberration of light). Therefore the absorption of this radiation leads to a force with a component against the direction of movement. (The angle of this 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. Thereby the mass of the absorbed radiation is accelerated in orbital direction, causing a force against the grain's orbital motion.

The force against the direction of the dust grain's orbital motion leads to a change of the grain's angular momentum, which causes the decrease of the grain's orbital radius. It should be mentioned that while the dust grain thus spirals slowly into the Sun's direction, its orbital speed increases continuously.

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 W is the power of the incoming radiation, v is the grain's velocity, c is the speed of light, r the object's radius, G is the universal gravitational constant, Ms the Sun's mass, Ls is the solar luminosity and R 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 R2 whereas the Poynting-Robertson force varies as one over R2.5, 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.

Dust particles sized a few micrometers need a few thousand years to get from 1 AU distance to distances where they evaporate.

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 0.5 µm in diameter [1]. If the particles are already in motion at their creation, radiation pressure does not need to cancel gravity completely to move the particles out of the solar system, so the critical size becomes a bit larger. 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 produces any significant change in their motion.

The erroneous statement that the isotropic thermal re-emission of the absorbed sunlight affects the motion of the dust grain unfortunately managed to find its way into parts of the literature. Probably it is based on the Poynting article cited, which predates relativity theory and is "luminiferous aether"-based. It violates Einstein's equivalence principle. As to the Poynting-Robertson effect the isotropic thermal re-emission is of importance only insofar as it keeps the dust grain's mass constant, for it is - in the mean - of the same magnitude as the absorbed radiation.

[edit] References

  • Poynting, J. H. (1903). "Radiation in the Solar System: its Effect on Temperature and its Pressure on Small Bodies". Philosophical Transactions of the Royal Society of London, Series A 202: 525-552.

es:Efecto Poynting-Robertson fr:Effet Poynting-Robertson it:Effetto Poynting-Robertson pl:Efekt Poyntinga-Robertsona ru:Эффект Пойнтинга — Робертсона fi:Poyntingin–Robertsonin ilmiö

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