# Calculate exact time of Solar midnight

I want to calculate real time of midnight (Solar midnight), but I am unable to find any formula or algorithm for that. I have times of sunrises and sunsets for every day of year. How can I get Solar midnight times from them?

Thank you all.

## 2 Answers

Maybe finding the Julian date will help you. Julian days are used for astronomical purposes. Every day midnight occurs exactly when the J.D. (Julian date) is *.5. So you can convert the J.D. to U.T. (Universal time) and then to your local time.

• I don't think this is a good answer, the Julian date does not depend on the local longitude as the solar midnight does. From the Wikipedia link: Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Universal time" – yannn Feb 7 '17 at 4:25

The formula for calculating the Local Time equivalent for Local Solar Time is $LST=LT+\frac{TC}{60}$, where $TC$ is the Time Correction factor $TC=4(Longitude-LSTM)+EoT$. $LSTM$ is the Local Solar Time Meridian, calculated by $15º-ΔT_{GMT}$, where $ΔT_{GMT}$ is the difference, in hours, from GMT. (For instance, here on the east coast of the US, this value is -4 in the summer and -5 in the winter.) $EoT$ is the Equation of Time, $EoT=9.87sin(2B)-7.53cos(B)-1.5sin(B)$, where $B=\frac{360}{365}((day\ of\ year)-81)$.

If you rearrange that first equation to calculate $LT$ in terms of $LST$, you'll get $LT=LST-\frac{TC}{60}$. Set $LST$ to 12 to calculate solar noon and 24 to calculate solar midnight.

Equations from here.