**Introduction**

We normally associate a day that lasts 24 hours
long. However, the true solar is day not
constant and varies during the time of the year. The true solar day is defined as two
successive transits through a given point.
For example, think of it as the time it would take for the sun to make a
round trip from the highest point in the sky only to return to the same point
again.

What causes the true solar day to not be
constant? The sun moves along the ecliptic
and the speed about the ecliptic isn’t constant. Earth’s orbit around the sun is not a perfect
but it is an elliptical orbit. The speed
of the orbit is greatest when the Earth is nearest to the Sun (about January
3), and the slowest when the Earth is furthest away from the sun (about July
3).

The equation of time describes the difference
in time (seconds, minutes, or hours) between the true solar time and time as we
normally know it (a day takes 24 hours).
If we used a sundial to measure time and compare it against a mechanical
watch, the equation of time would demonstrate the approximate difference.

For the program and the equation presented in
this blog entry, if the result is positive, that means the watch is “slow” compared
to the true solar time. If the result is
negative, that means that the watch is “fast” compared to the true solar
time.

I am curious to see if the clock apps on our
smart phones follow the mechanical watches or true solar time.

The equation presented in the program EQT was
developed by GS Campbell and JM Norman (

*An Introduction to Environmental Biophyiscs*). This is one of many ways the equation of time is calculated. A simple internet research and research through books and articles will show many forms of the equation of time.
The angle measurement used in this equation is
radians.

EQT (in hours) =3600^-1*(−104.7*SIN(F)+596.2*SIN(2*F)+4.3*SIN(3*F)-12.7*SIN(4*F)-

429.3*COS(F)-2*COS(2*F)+19.3*COS(3*F))

where F=π/180*(279.5+360/365*n);

A 365 day year
assumed.

Note:
Please keep in mind that every equation of time is an approximation.

Equation of Time (HP Prime) |

**HP Prime: EQT**

EXPORT EQT(n)

BEGIN

// n = day number (1 to 365)

// 2015-02-18

// hours, UC Berkeley approx

LOCAL F,E;

// radian mode

HAngle:=0;

F:=π/180*(279.5+360/365*n);

E:=3600^-1*(−104.7*SIN(F)+596.2*SIN(2*F)

+4.3*SIN(3*F)-12.7*SIN(4*F)-

429.3*COS(F)-2*COS(2*F)+19.3*COS(3*F));

RETURN E;

END;

**TI-84+: EQT**

Disp “N=DAY NO.”

Prompt N

Radian

π/180*(279.5+360/365*N)→F

3600^-1*(−104.7*SIN(F)+596.2*SIN(2*F)

+4.3*SIN(3*F)-12.7*SIN(4*F)-

429.3*COS(F)-2*COS(2*F)+19.3*COS(3*F))→E

Disp “HOURS:”, E

Resources:

Baldocchi,
Dennis. “Lecture 7, Solar Radiation,
Part 3, Earth-Sun Geometry” September
10, 2012. Retrieved February 17,
2015. URL: http://nature.berkeley.edu/biometlab/espm129/notes/Lecture%207%20Solar%20Radiation%20Part%203%20Earth%20Sun%20Geometry%20notes.pdf

Meeus, Jean. “Mathematical Astronomy Morsels” 2

^{nd}Ed. Willmann-Bell Inc.: Richmond, VA 2000 pp. 337-346
This blog is
property of Edward Shore – 2015.

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