Poynting-Robertson effect
Encyclopedia
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 a dust grain in the Solar System
to slowly spiral into the sun. The drag is essentially a component of radiation pressure
tangential to the grain's motion.
Poynting gave a description of the effect in 1903 based on the "luminiferous aether
" theory, which was superseded by the theories of relativity
in 1905–1915. In 1937 Robertson described the effect in terms of general relativity
.
chosen.
From the perspective of the grain of dust circling the Sun (panel (a) of the figure), 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 aberration is extremely small since the radiation is moving at the speed of light
while the dust grain is moving many orders of magnitude slower than that.)
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.
Note that the re-emission of photons, which is isotropic in the frame of the grain (a), does not affect the dust particle's orbital motion. However, in the frame of the Solar System (b), the emission is beamed anisotropically, and hence the photons carry away angular momentum from the dust grain. It is somewhat counter-intuitive that angular momentum is lost while the orbital motion of the grain is unchanged, but this is an immediate consequence of the dust grain shedding mass during emission and that angular momentum is proportional to mass.
The Poynting–Robertson drag can be understood as an effective force opposite the direction of the dust grain's orbital motion, leading to a drop in the grain's angular momentum. It should be mentioned that while the dust grain thus spirals slowly into the Sun, its orbital speed
increases continuously.
The Poynting–Robertson force is equal to:
where v is the grain's velocity, c is the speed of light
, W is the power of the incoming radiation, r the grain's radius, G is the universal gravitational constant
, Ms the Sun
's mass, Ls is the solar luminosity and R the grain'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
whereas the Poynting–Robertson force varies as 
, the Poynting–Robertson effect also 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.
Rocky dust particles sized a few micrometers need a few thousand years to get from 1 AU
distance to distances where they evaporate.
For particles much smaller than this, radiation pressure, which makes them spiral outwards from the Sun, is stronger than the Poynting–Robertson effect that makes them spiral inward. For rocky particles about half a µm
in diameter, the radiation pressure equals gravity, and they will be always blown out of the Solar System even though the Poynting–Robertson effect still affects them. Particles of intermediate size will either spiral inwards or outwards depending on their size and their initial velocity vector.
Robertson considered dust motion in a beam of radiation emanating from a point source. Guess also considered the problem but for a spherical source of radiation and found that for particles far from the source the resultant forces are in agreement with those concluded by Robertson.
The dimensionless dust parameter
is the ratio of the force due to radiation pressure
to the force of gravity on the particle:
where
is the Mie scattering coefficient, and 
is the density and 
is the size of the dust grain.
The Equations of Motion for the dust grain are expressed by
where
is the stellar radius.
John Henry Poynting
John Henry Poynting was an English physicist. He was a professor of physics at Mason Science College from 1880 until his death....
and Howard Percy Robertson
Howard Percy Robertson
Howard Percy Robertson was an American mathematician and physicist known for contributions related to physical cosmology and the uncertainty principle...
, is a process by which solar radiation causes a dust grain in the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
to slowly spiral into the sun. The drag is essentially a component of radiation pressure
Radiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...
tangential to the grain's motion.
Poynting gave a description of the effect in 1903 based on the "luminiferous aether
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
" theory, which was superseded by the theories of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
in 1905–1915. In 1937 Robertson described the effect in terms of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
.
Explanation
The effect can be understood in two ways, depending on the reference frameReference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
chosen.
From the perspective of the grain of dust circling the Sun (panel (a) of the figure), the Sun's radiation appears to be coming from a slightly forward direction (aberration of light
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
). Therefore the absorption of this radiation leads to a force
Radiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...
with a component against the direction of movement. (The angle of aberration is extremely small since the radiation is moving at the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
while the dust grain is moving many orders of magnitude slower than that.)
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
Mass-energy equivalence
In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...
. In order to conserve angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
(which is proportional to mass), the dust grain must drop into a lower orbit.
Note that the re-emission of photons, which is isotropic in the frame of the grain (a), does not affect the dust particle's orbital motion. However, in the frame of the Solar System (b), the emission is beamed anisotropically, and hence the photons carry away angular momentum from the dust grain. It is somewhat counter-intuitive that angular momentum is lost while the orbital motion of the grain is unchanged, but this is an immediate consequence of the dust grain shedding mass during emission and that angular momentum is proportional to mass.
The Poynting–Robertson drag can be understood as an effective force opposite the direction of the dust grain's orbital motion, leading to a drop in the grain's angular momentum. It should be mentioned that while the dust grain thus spirals slowly into the Sun, its orbital speed
Orbital speed
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body...
increases continuously.
The Poynting–Robertson force is equal to:
where v is the grain's velocity, c is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, W is the power of the incoming radiation, r the grain's radius, G is the universal gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
, Ms the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
's mass, Ls is the solar luminosity and R the grain's orbital radius.
Since the gravitational force goes as the cube of the object's radius (being a function of its volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
) whilst the power it receives and radiates goes as the square of that same radius (being a function of its surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
), the Poynting–Robertson effect is more pronounced for smaller objects. Also, since the Sun's gravity varies as
whereas the Poynting–Robertson force varies as , the Poynting–Robertson effect also 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.Rocky dust particles sized a few micrometers need a few thousand years to get from 1 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
distance to distances where they evaporate.
For particles much smaller than this, radiation pressure, which makes them spiral outwards from the Sun, is stronger than the Poynting–Robertson effect that makes them spiral inward. For rocky particles about half a µm
1 E-6 m
To help compare different orders of magnitude this page lists some items with lengths between 10−6 and 10−5 m .Distances shorter than 1 µm*~0.7–300 µm — Wavelength of infrared radiation...
in diameter, the radiation pressure equals gravity, and they will be always blown out of the Solar System even though the Poynting–Robertson effect still affects them. Particles of intermediate size will either spiral inwards or outwards depending on their size and their initial velocity vector.
Robertson considered dust motion in a beam of radiation emanating from a point source. Guess also considered the problem but for a spherical source of radiation and found that for particles far from the source the resultant forces are in agreement with those concluded by Robertson.
The dimensionless dust parameter
is the ratio of the force due to radiation pressureRadiation pressure
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...
to the force of gravity on the particle:
where
is the Mie scattering coefficient, and is the density and is the size of the dust grain.The Equations of Motion for the dust grain are expressed by
where
is the stellar radius.