Equation of time

The equation of time: in the axis of abscises you have the days of the year counted from January, in that of the ordained you have the difference between the true and the half times (v-m).

The equation of time is the difference between mean solar time (usually measured by a clock) and apparent solar time (time measured by a sundial). This difference varies throughout the year and reaches a greater difference on November 3, when mean solar time is more than 16 minutes behind apparent solar time (specifically 16 minutes and 25 seconds on November 3), and on February 11, when mean solar time is 14 minutes and 12 seconds ahead of apparent time.

Mean solar time and apparent solar time are the same at four moments of the year: April 15, June 13, September 1, and December 25. The equation of time is represented graphically with a diagram called analemma, which is sometimes indicated as a legend on globes or terrestrial spheres and has the shape of a somewhat asymmetric 8. The analemma indicates the same information as that expressed through the attached graph, so this graph could also be considered as an open analemma.

Etymology

In ancient astronomy the word 'equation' ('equatio' in Latin) meant 'correction', and with this it was indicated that a value had to be added algebraically to correct it. In this way, the equation of time is the value that must be added to the value of apparent solar time to "correct" it. (make it 'regular'). Another example is the Copernican equation of center, widely used in the calculations of celestial mechanics to "correct" the the true anomaly.

Rationality

Repeated observation of the Sun in periods of 24 hours of average solar time; you can see the analem and the concept of equation of time.

The origin of this concept derives from the different speed of the earth's translation movement around the Sun, and also from the inclination of the Earth's axis of rotation with respect to the plane of its orbit. The Earth's orbit is called ecliptic (because it is in it that eclipses occur when the orbit of the Moon coincides at a point with that of the Earth and that of the Sun) and it is not circular but elliptical, with the Sun occupying one of the foci of the ellipse. According to the laws of orbital motion formulated by Kepler about translational motions, "equal times sweep equal areas", which means that the Earth slows down when it is further from the Sun (because its attraction is less when it is further away) and accelerates it when it gets closer.

If this difference in speed did not exist, the Earth would escape from the Solar System when it was further away, or it would collide with the Sun when it got closer. Thus, the terrestrial translation movement is a uniformly varied movement. However, it must be clarified that the difference in speed is not a cause but a consequence of the different mass of the stars (the Earth and the Sun) and the eccentricity of the ecliptic. The same thing happens with the Moon: when the Sun is farther from Earth and the Moon is closer, the lunar disk can completely cover the solar disk (in this case a total eclipse of the Sun could occur) while when it happens Otherwise (the Sun closer and the Moon further away), an annular eclipse of the Sun can occur, in which a luminous ring of the Sun remains around the shadow of the Moon.

Equation of time values

The values of the equation of time are usually published for each year in the nautical calendar, in the yearbooks of the observatories, in specialized magazines, etc. Generally in the section of solar ephemeris. The reason for this previous publication is to provide astronomers with the possibility of planning their observations. It is usually represented in the form of a table in which one of the entries is the day of the year and the output is the difference between average time and the true (m-v), or vice versa (v-m). In some empirical formulas given by observatories you can find out analytically the equation of time. One example is:

E(d)=595without (198or+1.9713ord)+442without (175or+0.9856ord){displaystyle Eleft(dright)=595sin left(198^{o+}1.9713^{odright)+442sin left(175^{o}+0.9856^{o}dright)}}}

Where the value obtained by this semi-empirical formula is in seconds (v-m), where d is the day of the year (of the year 2016). This equation is quite tight: it is accurate to within half a minute at most, and the coefficients 595 and 442 vary very little from year to year.