Yarkovsky-O'Keefe-Radzievskii-Paddack effect
Encyclopedia
The Yarkovsky–O'Keefe–Radzievskii–Paddack effect, or YORP effect for short, is a second-order variation on the Yarkovsky effect
which changes the rotation rate of a small body (such as an asteroid
). The term was coined by Dr. David P. Rubincam in 2000.
In the 19th century, Yarkovsky
realised that the infrared
radiation escaping from a body warmed by the Sun carries off momentum
as well as heat
. Translated into modern physics, each photon
escaping carries away a momentum p = E/c where E (=hν) is its energy and c is the speed of light
. Radzievskii applied the idea to rotation based on changes in albedo
and Paddack and O'Keefe
realised that shape was a much more effective means of altering a body's spin rate. Paddack and Rhee suggested that the YORP effect may be the cause of rotational bursting and eventual elimination from the solar system of small asymmetric objects.
(then named ) and 1862 Apollo
. The spin rate of 54509 YORP will double in just 600,000 years, and the YORP effect can also alter the axial tilt and precession
rate, so that the entire suite of YORP phenomena can send asteroids into interesting resonant spin states, and helps explain the existence of binary asteroid
s
Observations show that asteroids larger than 125 km in diameter have rotation rates that follow a Maxwellian frequency distribution, while smaller asteroids (in the 50 to 125 km size range) show a small excess of fast rotators. The smallest asteroids (size less than 50 km) show a clear excess of very fast and slow rotators, and this becomes even more pronounced as smaller populations are measured. These results suggest that one or more size-dependent mechanisms are depopulating the centre of the spin rate distribution in favour of the extremes. The YORP effect is a prime candidate. It is not capable of significantly modifying the spin rates of large asteroids by itself, however, so a different explanation must be sought for objects such as 253 Mathilde
.
force from photons departing from any given surface element of the sphere will be normal to the surface, such that no torque
is produced. Energy reradiated from the wedges, however, can produce a torque because the wedge faces are not parallel to the sphere's surface. An object with some "windmill" asymmetry can therefore be subjected to minuscule torque forces that will tend to spin it up or down as well as make its axis of rotation precess
.
Note that the YORP effect is zero for a rotating ellipsoid if there are no irregularities in surface temperature or albedo
.
In the long term, the object's changing obliquity and rotation rate may wander randomly, chaotically or regularly, depending on several factors. For example, assuming the Sun
remains on its equator
, asteroid 951 Gaspra
, with a radius of 6 km and a semi-major axis
of 2.21 AU
, would in 240 Ma (240 million years) go from a rotation period of 12 h to 6 h and vice versa. If 243 Ida
were given the same radius and orbit values as Gaspra, it would spin up or down twice as fast, while a body with Phobos'
shape would take several billion
years to change its spin by the same amount.
Size as well as shape affects the amount of the effect. Smaller objects will spin up or down much more quickly. If Gaspra were smaller by a factor of 10 (to a radius of 500 m), its spin will halve or double in just a few million years. Similarly, the YORP effect intensifies for objects closer to the Sun. At 1 AU, Gaspra would double/halve its spin rate in a mere 100,000 years. After one million years, its period may shrink to ~2 h, at which point it could start to break apart.
This is one mechanism through which binary asteroid
s may form, and it may be more common than collisions and planetary near-encounter tidal disruption as the primary means of binary formation.
Asteroid was later named 54509 YORP
to honor its part in the confirmation of this phenomenon.
Yarkovsky effect
The Yarkovsky effect is a force acting on a rotating body in space caused by the anisotropic emission of thermal photons, which carry momentum...
which changes the rotation rate of a small body (such as an asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
). The term was coined by Dr. David P. Rubincam in 2000.
In the 19th century, Yarkovsky
Ivan Osipovich Yarkovsky
Ivan Osipovich Yarkovsky was a Russian-Polish civil engineer. He worked for a Russian railway company and was obscure in his own time. Beginning in the 1970s, long after Yarkovsky's death, his work on the effects of thermal radiation on small objects in the solar system was developed into the...
realised that the infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
radiation escaping from a body warmed by the Sun carries off momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
as well as heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
. Translated into modern physics, each photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
escaping carries away a momentum p = E/c where E (=hν) is its energy and 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...
. Radzievskii applied the idea to rotation based on changes in albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
and Paddack and O'Keefe
John A. O'Keefe
John Aloysius O'Keefe was a planetary scientist with the National Aeronautics and Space Administration from 1958 to 1995. He is credited with the discovery of Earth's "pear shape" using U.S. Vanguard satellite data collected in the late 1950s...
realised that shape was a much more effective means of altering a body's spin rate. Paddack and Rhee suggested that the YORP effect may be the cause of rotational bursting and eventual elimination from the solar system of small asymmetric objects.
Observations
In 2007 there was direct observational confirmation of the YORP effect on the small asteroids 54509 YORP54509 YORP
54509 YORP is an Apollo Near-Earth Object discovered on August 3, 2000 by the Lincoln Laboratory Near-Earth Asteroid Research Team at Socorro. Measurements of the rotation rate of this object provided the first observational evidence of the YORP effect, hence the name of the asteroid...
(then named ) and 1862 Apollo
1862 Apollo
1862 Apollo is a Q-type asteroid, discovered by Karl Reinmuth in 1932, but lost and not recovered until 1973. It is named after the Greek god Apollo....
. The spin rate of 54509 YORP will double in just 600,000 years, and the YORP effect can also alter the axial tilt and precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
rate, so that the entire suite of YORP phenomena can send asteroids into interesting resonant spin states, and helps explain the existence of binary asteroid
Binary asteroid
A binary asteroid is a system of two asteroids orbiting their common center of mass, in analogy with binary stars. 243 Ida was the first binary asteroid to be identified when the Galileo spacecraft did a flyby in 1993...
s
Observations show that asteroids larger than 125 km in diameter have rotation rates that follow a Maxwellian frequency distribution, while smaller asteroids (in the 50 to 125 km size range) show a small excess of fast rotators. The smallest asteroids (size less than 50 km) show a clear excess of very fast and slow rotators, and this becomes even more pronounced as smaller populations are measured. These results suggest that one or more size-dependent mechanisms are depopulating the centre of the spin rate distribution in favour of the extremes. The YORP effect is a prime candidate. It is not capable of significantly modifying the spin rates of large asteroids by itself, however, so a different explanation must be sought for objects such as 253 Mathilde
253 Mathilde
253 Mathilde is a main-belt asteroid about 50 km in diameter that was discovered by Johann Palisa in 1885. It has a relatively elliptical orbit that requires more than four years to circle the Sun. This asteroid has an unusually slow rate of rotation, requiring 17.4 days to complete a...
.
Example
Assume a rotating spherical asteroid has two wedges attached to its equator. The reactionReaction (physics)
The third of Newton's laws of motion of classical mechanics states that forces always occur in pairs. Every action is accompanied by a reaction of equal magnitude but opposite direction. This principle is commonly known in the Latin language as actio et reactio. The attribution of which of the two...
force from photons departing from any given surface element of the sphere will be normal to the surface, such that no torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
is produced. Energy reradiated from the wedges, however, can produce a torque because the wedge faces are not parallel to the sphere's surface. An object with some "windmill" asymmetry can therefore be subjected to minuscule torque forces that will tend to spin it up or down as well as make its axis of rotation precess
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
.
Note that the YORP effect is zero for a rotating ellipsoid if there are no irregularities in surface temperature or albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
.
In the long term, the object's changing obliquity and rotation rate may wander randomly, chaotically or regularly, depending on several factors. For example, assuming 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...
remains on its equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....
, asteroid 951 Gaspra
951 Gaspra
951 Gaspra is an S-type asteroid that orbits very close to the inner edge of the asteroid belt. Gaspra was the first asteroid ever to be closely approached when it was visited by the Galileo spacecraft, which flew by on its way to Jupiter on 29 October 1991.-Characteristics:Apart from a multitude...
, with a radius of 6 km and a semi-major axis
Semi-major axis
The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape...
of 2.21 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
, would in 240 Ma (240 million years) go from a rotation period of 12 h to 6 h and vice versa. If 243 Ida
243 Ida
243 Ida is an asteroid in the Koronis family of the asteroid belt. It was discovered on 29 September 1884 by Johann Palisa and named after a nymph from Greek mythology. Later telescopic observations categorized Ida as an S-type asteroid, the most numerous type in the inner asteroid belt. On 28...
were given the same radius and orbit values as Gaspra, it would spin up or down twice as fast, while a body with Phobos'
Phobos (moon)
Phobos is the larger and closer of the two natural satellites of Mars. Both moons were discovered in 1877. With a mean radius of , Phobos is 7.24 times as massive as Deimos...
shape would take several billion
1000000000 (number)
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001.In scientific notation, it is written as 109....
years to change its spin by the same amount.
Size as well as shape affects the amount of the effect. Smaller objects will spin up or down much more quickly. If Gaspra were smaller by a factor of 10 (to a radius of 500 m), its spin will halve or double in just a few million years. Similarly, the YORP effect intensifies for objects closer to the Sun. At 1 AU, Gaspra would double/halve its spin rate in a mere 100,000 years. After one million years, its period may shrink to ~2 h, at which point it could start to break apart.
This is one mechanism through which binary asteroid
Binary asteroid
A binary asteroid is a system of two asteroids orbiting their common center of mass, in analogy with binary stars. 243 Ida was the first binary asteroid to be identified when the Galileo spacecraft did a flyby in 1993...
s may form, and it may be more common than collisions and planetary near-encounter tidal disruption as the primary means of binary formation.
Asteroid was later named 54509 YORP
54509 YORP
54509 YORP is an Apollo Near-Earth Object discovered on August 3, 2000 by the Lincoln Laboratory Near-Earth Asteroid Research Team at Socorro. Measurements of the rotation rate of this object provided the first observational evidence of the YORP effect, hence the name of the asteroid...
to honor its part in the confirmation of this phenomenon.