Dynamical time scale
Encyclopedia
Dynamical time scale has two distinct meanings and usages, both related to astronomy:
where R is the radius
of the star, G is the gravitational constant
, M is the mass
of the star and v is the escape velocity
. As an example, the Sun
dynamical time scale is approximately 1133 seconds. Note that the actual time it would take a star like the Sun to collapse is greater because internal pressure is present.
The 'fundamental' oscillatory mode of a star will be at approximately the dynamical time scale. Oscillations at this frequency are seen in Cepheid variables.
) was both irregular on short time scales, and was slowing down on longer time scales. The suggestion was made, that observation of the position of the Moon, Sun and planets and comparison of the observations with their gravitational ephemerides would be a better way to determine a uniform time scale. A detailed proposal of this kind was published in 1948 and adopted by the IAU
in 1952 (see Ephemeris time - history).
Using data from Newcomb's Tables of the Sun
(based on the theory of the apparent motion of the Sun by Simon Newcomb
, 1895, as retrospectively used in the definition of ephemeris time), the SI
second
was defined in 1960 as:
Caesium
atomic clocks became operational in 1955, and their use provided further confirmation that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a precision measure of time interval. After three years of comparisons with lunar observations it was determined that the ephemeris second corresponded to 9,192,631,770 +/- 20 cycles of the caesium resonance. In 1967/8 the length of the SI second was redefined to be 9,192,631,770 cycles of the caesium resonance, equal to the previous measurement result for the ephemeris second (see Ephemeris time - redefinition of the second).
In 1976, however, the IAU
resolved that the theoretical basis for ephemeris time was wholly non-relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time
(TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET.
During the period 1991-2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions. The current fundamental relativistic time scales are Geocentric Coordinate Time
(TCG) and Barycentric Coordinate Time
(TCB); both of these have rates that are based on the SI second in respective reference frames (and hypothetically outside the relevant gravity well), but on account of relativistic effects, their rates would appear slightly faster when observed at the Earth's surface, and therefore diverge from local earth-based time scales based on the SI second at the Earth's surface. Therefore the currently defined IAU time scales also include Terrestrial Time
(TT) (replacing TDT, and now defined as a re-scaling of TCG, chosen to give TT a rate that matches the SI second when observed at the Earth's surface), and a redefined Barycentric Dynamical Time (TDB), a re-scaling of TCB to give TDB a rate that matches the SI second at the Earth's surface.
- In one use, which occurs in stellar physics, the dynamical time scale is alternatively known as the freefall time scale, and is in general, the length of time over which changes in one part of a body can be communicated to the rest of that body. This is often related to the time taken for a system to move from one equilibrium state to another after a sudden change.
- In another use, in connection with time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time-like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris timeEphemeris timeThe term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
scale (ET).
Stellar physics
For a star, the dynamical time scale is defined as the time that would be taken for a test particle released at the surface to fall under the star's potential to the centre point, if pressure forces were negligible. In other words, the dynamical time scale measures the amount of time it would take a certain star to collapse in the absence of any internal pressure. By appropriate manipulation of the equations of stellar structure this can be found to bewhere R is the radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
of the star, G is the 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...
, M is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
of the star and v is the escape velocity
Escape velocity
In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity...
. As an example, 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...
dynamical time scale is approximately 1133 seconds. Note that the actual time it would take a star like the Sun to collapse is greater because internal pressure is present.
The 'fundamental' oscillatory mode of a star will be at approximately the dynamical time scale. Oscillations at this frequency are seen in Cepheid variables.
Time standards
In the late nineteenth century it was suspected, and in the early twentieth century it was established, that the rotation of the Earth (i.e. the length of the dayDay
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...
) was both irregular on short time scales, and was slowing down on longer time scales. The suggestion was made, that observation of the position of the Moon, Sun and planets and comparison of the observations with their gravitational ephemerides would be a better way to determine a uniform time scale. A detailed proposal of this kind was published in 1948 and adopted by the IAU
IAU
IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners...
in 1952 (see Ephemeris time - history).
Using data from Newcomb's Tables of the Sun
Newcomb's Tables of the Sun
Newcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...
(based on the theory of the apparent motion of the Sun by Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
, 1895, as retrospectively used in the definition of ephemeris time), the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
was defined in 1960 as:
- the fraction 1/31,556,925.9747 of the tropical yearTropical yearA tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
for 1900 January 0 at 12 hours ephemeris time.
Caesium
Caesium
Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...
atomic clocks became operational in 1955, and their use provided further confirmation that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a precision measure of time interval. After three years of comparisons with lunar observations it was determined that the ephemeris second corresponded to 9,192,631,770 +/- 20 cycles of the caesium resonance. In 1967/8 the length of the SI second was redefined to be 9,192,631,770 cycles of the caesium resonance, equal to the previous measurement result for the ephemeris second (see Ephemeris time - redefinition of the second).
In 1976, however, the IAU
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
resolved that the theoretical basis for ephemeris time was wholly non-relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time
Barycentric Dynamical Time
Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system...
(TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET.
During the period 1991-2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions. The current fundamental relativistic time scales are Geocentric Coordinate Time
Geocentric Coordinate Time
Geocentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth...
(TCG) and Barycentric Coordinate Time
Barycentric Coordinate Time
Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system...
(TCB); both of these have rates that are based on the SI second in respective reference frames (and hypothetically outside the relevant gravity well), but on account of relativistic effects, their rates would appear slightly faster when observed at the Earth's surface, and therefore diverge from local earth-based time scales based on the SI second at the Earth's surface. Therefore the currently defined IAU time scales also include Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
(TT) (replacing TDT, and now defined as a re-scaling of TCG, chosen to give TT a rate that matches the SI second when observed at the Earth's surface), and a redefined Barycentric Dynamical Time (TDB), a re-scaling of TCB to give TDB a rate that matches the SI second at the Earth's surface.