# Ephemeris second

The ephemeris second is a historical measure of one second . In 1960 it replaced the mean solar second used at the time . Thus the definition of the second was no longer traced back to the daily rotation of the earth around itself (→ rotation ), but to the more even annual movement of the earth around the sun (→ revolution ).

In the course of the development of atomic clocks , the definition of the second was changed to atomic clocks in 1967.

## history

Originally, the second was defined as the 1 / 86,400th fraction of a mean sunny day (24 hours of 60 minutes of 60 seconds each). This mean solar day lasts a little longer than a complete rotation of the earth around itself, which only lasts about 23 hours 56 minutes and 4 seconds, which corresponds to a sidereal day .

At the beginning of the 20th century , when sufficiently accurate clocks were available for the first time to independently check the rotation of the earth, it became clear that the rotational speed of the earth is subject to slight fluctuations and, due to the tidal friction, a long-term slowdown (0.002 s per century). A unit of time derived from the Earth's rotation such as the solar second also shows these irregularities and is therefore not uniform enough for some technical and scientific purposes.

### Beginnings

The physical laws and therefore in particular the laws of motion of celestial mechanics underlying time goes by definition completely regular. If one therefore starts from an observed position of a celestial body and uses a suitable planetary theory to calculate the point in time at which, according to the theory, this position is assumed, the points in time determined in this way basically form a uniform time scale ; The prerequisite is that the planetary theory used depicts physical reality with sufficient accuracy. At the end of the 19th century , sophisticated theories were already available that allowed this method to be used.

Although the movements of the celestial bodies are not strictly regular due to their mutual disturbances, the disturbances are subject to very precisely known physical laws and can therefore be calculated with almost any precision.

In contrast to this, the fluctuations in the earth's rotation are only partially accessible for calculation.

### definition

In the 1950s, as part of the redefinition of the time scale, a new definition of the second was introduced, which was not based on the rotation , but on the orbital motion of the earth. According to S. Newcomb , the geometric mean ecliptical longitude of the sun observed from Earth is

${\ displaystyle L = 279 ^ {\ circ} 41'48 {,} 04 '' + 129,602,768 {,} 13 '' \ cdot T + 1 {,} 089 '' \ cdot T ^ {2}}$,

where the time that has passed since January 0, 1900 (= December 31, 1899) 12 h UT is in Julian centuries of 36525 days each. ${\ displaystyle T}$

This formula describes the apparent movement of the sun along the ecliptic , circling the sky once a year, i.e. covering 360 ° or 1,296,000  arc seconds ( ). According to the above formula, the mean length of the sun increases with speed ${\ displaystyle ''}$

${\ displaystyle {\ frac {\ mathrm {d} L} {\ mathrm {d} T}} \, = \, 129,602,768 {,} 13 ^ {\ frac {''} {\ mathrm {J century }}} \, + \, 2 \ cdot 1 {,} 089 ^ {\ frac {''} {\ mathrm {century ^ {2}}}} \ cdot T}$.

Note that the speed is not strictly constant, but increases slightly over time (second term in the above formula). This is because the speed is measured with respect to the vernal equinox , which in turn moves as a result of precession and whose precession movement is currently slightly accelerating due to planetary disturbances.

In particular, the speed of the sun at time T  = 0 (i.e. on January 0, 1900, 12 h  UT):

{\ displaystyle {\ begin {aligned} {\ frac {\ mathrm {d} L} {\ mathrm {d} T}} (T = 0) & = {\ frac {129,602,768.13 \, \ mathrm { Arc seconds}} {36,525 \, \ mathrm {days}}} \\\\ & = {\ frac {360 ^ {\ circ}} {31,556,925.9747 \, \ mathrm {ephemeris seconds}}} \\\\ & = {\ frac {0.041 \, 068 \, 638 \, 974 \, 4 \, \ mathrm {arc seconds}} {\ mathrm {ephemeris second}}} \ end {aligned}}}.

This connection was originally obtained by observing the course of the sun and taking the solar second as a basis. It has now been reversed and used to redefine the second. The duration of the second should be chosen so that the above relationship, which was previously only given within the scope of the observation accuracy, was exactly fulfilled by the new second . This also gave a definite time scale for the complete solar theory, which contained planetary disturbances and other side effects, and by means of which one could deduce the relevant point in time from an observation.

The period of time that the mean length of the sun needs to cover 360 ° is also called a tropical year . The definition was therefore:

 "An ephemeris second is the fraction of 1 / 31,556,925.9747 of the tropical year on January 0, 1900 at 12 o'clock ephemeris time ."

Note that the definition to the tropical year length on refers 0. January 1900, but not that the length of the tropical year at 0. January 1900 began . If you insert into the first equation and solve for , you find that the sun only  needed 31,556,925.97 21 ephemeris seconds to cover a full 360 ° between January 0, 1900 and January 0, 1901; its speed had increased slightly during this period compared to the initial value. ${\ displaystyle L = 279 ^ {\ circ} 41'48 {,} 04 '' + 360 ^ {\ circ}}$${\ displaystyle T}$

The definition of the ephemeris second, on the other hand, only refers to the momentary (in technical jargon: instantaneous ) speed of the increase in length on January 0, 1900: the length of the ephemeris second is to be chosen so that the speed at this point in time assumes the numerical value mentioned above.

This is comparable to stating that a vehicle is currently moving at a speed of, for example, 85 kilometers per hour. The current speed is expressed by the extrapolated distance that the vehicle would cover if it were constantly moving at this speed all the time. If the speed changes, it is not a statement of how long the vehicle needs to actually cover a distance of 85 kilometers. To do this, all current speeds along the route would have to be known.

### The End

The ephemeris second was ratified in 1960 by the General Conference for Weights and Measures  (CGPM) as a time unit of the SI system , but was replaced by the atomic second in 1967 by resolution of the 13th  General Assembly of the CGPM. Their definition was chosen in such a way that it coincided with the ephemeris second within the scope of the measurement accuracy . For practical purposes, therefore, the ephemeris second can be considered identical to the atomic second.

Even today, the ephemeris day is occasionally found as an astronomical unit of time. This means a period of 86,400 ephemeris seconds or atomic seconds.