Equation of time

The equation of time translates the variation, variable during the year, existing between the average solar time and the real solar time. It is the difference between the hour indicated by a perfectly regulated Horloge which would mid-April indicate midday at the time of the passage of the Sun to the Méridien for example (cf below) (average solar time), and that indicated by a Sundial (real solar time). The hour indicated by the clock during the year can be of 14 min 6 S in advance on that indicated by a sundial (at the beginning of year) and up to 16 min 33 late S (in autumn).

This variation results from the combination of the effects of two characteristics of the movement of the Ground around the Sun:

  • its elliptic Orbit (rather than circular);
  • the slope of its axis of rotation in the field of the orbit, which is the dominant cause.

Its value thus varies throughout the year and even during the day. It cancels four times per annum, towards mid-April, mid-June, at the beginning of September and Christmas. It reaches its maximum towards mid-February (about 14 min) and its minimum towards at the beginning of November (− 16 min approximately). When the equation of time is positive, the sun is late compared to average time, and when the equation of time is negative, the sun is advances compared to average time of it. Moreover the equation itself evolves/moves very slowly with the years for several reasons, and in particular because of variation of the eccentricity of the terrestrial Orbite and that of the Longitude of the Périhélie.

The equation of time is used to correct the hour given by the sundials to obtain average time. For this purpose, the equation of time is sometimes represented on the sundials by a curve called Analemme or curve into 8. Certain dials can even give average time directly, either because the time lines are transformed into corrected curves of the equation of time, or because the Gnomon received a form taking account of this correction. In both cases, it is necessary to take account of the period of the year or to have two dials.

It should be noted that in many countries, the equation of time is calculated like the difference between the real solar time and the average time solar, which is the opposite of the definition used in France. To read the hour on a Sundial, it is then necessary to cut off the value from the equation of time at the hour indicated by the shade of the style, and either to add it, like one usually does it in France. Two conventions are quite as valid because, insofar as the equation of time is not used to define the standard time, there is no official definition.

The equation of time is also at the origin of curiosities in connection with the days of the year when the Sun rises or lie down earliest or later. Thus, if the shortest day of the year is well the day of the Solstice of winter (about on December 21st) they are a few days before this solstice, about on December 13rd, that the Sun lies down earliest in the year. In the same way they is a few days after the solstice, about on January 3rd, as the Sun rises later (in fact, the importance of this variation also depends on the Latitude). The same shifts, reversed and less important, are found around the summer solstice.

The equation of time can be calculated, but one finds of them also tables detailed in the astronomical éphémérides.

Calculation of the equation of time

Simplified version

The equation of time can be approximate by the formula

E=-9.87 \ sin (2B) +7.53 \ cos (B)+1.5 \ sin (B)~

where E is expressed in minutes, and the quantity

B= \ frac {2 \ pi (N-81)}{364}

expressed in radians, depends on the number of the day of the year (N=1 on January first).

Full version

Stages of calculation:

M=M_0+M_1 (J-J_ {2000}) \ approx M_0+M_1 D \, avec J_ {2000} =2451545, M_0= \ rm 357,5291^o and M_1= \ rm 0,98560028^o/jour. J is the Jour Julien date considered. At first approximation, one can be satisfied to use the number d day in the year (d=1 on January first). C= \ left (2nd \ frac {1} {4} e^3 \ right) \ sin (M) + \ frac {5} {4} e^2 \ sin (2M) + \ frac {13} {12} e^3 \ sin (3M) où e=0,01671 represents the eccentricity trajectory of the Earth around the Sun. Numerical application:
C=1,9148^ \ circ \ sin (M) +0,0200^ \ circ \ sin (2M) +0,0003^ \ circ \ sin (3M) \,
  • Calculation of longitude écliptique
\ lambda_s=280,47^ \ circ+M_1 (J-J_ {2000}) +C \ approx 280,47^ \ circ+M_1 d+C \,
  • Contribution of the Obliqueness of the Earth: it is the reduction with the équateur
R= (there ^2) \ sin (2 \ lambda_s) + \ left (\ frac {1} {2} y^4 \ right) \ sin (4 \ lambda_s) - \ left (\ frac {1} {3} y^6 \ right) \ sin (6 \ lambda_s) \, où y= \ tan (\ epsilon/2) ; \ epsilon= \ rm 23,43929^o represents the slope of the axis of the Earth compared to the plan of the ecliptic . One obtains the same result with the formula:
R= \ left (- \ frac {1} {4} \ epsilon^2- \ frac {1} {24} \ epsilon^4- \ frac {17} {2880} \ epsilon^6 \ right) \ sin (2 \ lambda_s) + \ left (\ frac {1} {32} \ epsilon^4+ \ frac {1} {96} \ epsilon^6 \ right) \ sin (4 \ lambda_s) - \ frac {1} {192} \ epsilon^6 \ sin (6 \ lambda_s) \,
where \ epsilon must be expressed in radians. Numerical application:
R= -2,4680^ \ circ \ sin (2 \ lambda_s) + 0,0530^ \ circ \ sin (4 \ lambda_s) -0,0014^ \ circ \ sin (6 \ lambda_s) \,
  • Value of the equation of time (in minutes)
\ Delta T = (C+R) \ times 4

See too

Related articles

External bonds

Random links:Laborde de Monpezat | Richard Ian Cox | Diospyros blancoi | Government of the United Kingdom | Kyoichi Katayama | Wendell,_le_Massachusetts