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$\begingroup$ @PM 2Ring The Hughes reference (1989) is good, but note the accuracy limitation stated in the abstract (mainly due to omitting lunar & planetary effects)): "An equation is developed which gives the Equation of Time as a function of Universal Time. This enables it to be calculated for any epoch within 30 centuries of the present ...
I'm working on an on-line app to show the Equation of Time for arbitrary eccentricity and obliquity of the Earth's orbit. It looks good for small eccentricities and obliquities: but for bigger ones the components of the Equation (the so called Equation of the Center and Projection to the Equator) loose all the "sine-like" look:
Note that there's a units mismatch in equation (1). Equation (2) yields a result in units of sidereal seconds while equation (3), when multiplied by time of day, yields a result in units of radians. The latter needs to be converted to sidereal seconds. To do this, simply multiple both terms in equation (3) by $\frac{86400}{2\pi}$:
$\begingroup$ @David Hammen Can you explain what the fractional day is - is it not the time dealt with later in the OPs equation? or is it taking account of the half day start point of J2000, what form should the hours take and how are the seconds dealt with? wikipedia has decimal time as a 10hr100m100s format used in the French revolution so ...
The equation of time is the cumulative sum of differences between mean and apparent solar day length. Like a mathematical function and its derivative, zero crossings of one should roughly correspond to maxima or minima of the other.
Solving the second equation for quasar APM 8279, with Z = 3.911, T = 12.10 By . Lookback time also describes the distance the quasar's light travelled through an expanding universe before reaching the observer.
Equation of Time (derivation Analemma) Ask Question Asked 1 month ago. Modified 1 month ago. Viewed 354 ...
Black holes evaporate very, very slowly by emitting Hawking radiation, and eventually they disappear, maybe even during the lifetime of the universe ($\sim 1.5 \times 10^{18}{\rm s}$).
At the same time, using the same set of equation , if I compute GMST for 1987 April 10 at 00:00:00, the computed and URL values are the same. April 10 at 00:00:00: JD=2446895.5 JC=-0.127296372 GMST = 13.18 hour (Computed) & 13.17954 hour (URL) Kindly help me to understand where exactly lies the problem.
If I do a quick Google search for amsterdam sunrise, I immediately get the time back: 6:42 AM. How is this time calculated? (I mean how it is really calculated, not how Google get it, with is probably from a table. Of course I mean sunrises and sunsets in the future, not from the past. $:)$)