New! Enter your latitude and longitude.Today's sunrise/sunset calculation for 39.040759 °N, 77.04876 °W.
Find today's Julian date (days since Jan 1, 2000 + 2451545): Julian date: 2459041
Now, calculate J
n
_{*} = (J_{date} - 2451545 - 0.0009) - (l_{w}/360)n = round(n _{*})n _{*} = (2459041 - 2451545 - 0.0009) - (77.04876/360) = 7495.7850756667n = round(7495.7850756667) = 7496
Now J
J
_{*} = 2451545 + 0.0009 + (l_{w}/360) + nJ _{*} = 2451545 + 0.0009 + (77.04876/360) + 7496 = 2459041.2149243
Using J
M = [357.5291 + 0.98560028 * (J
_{*} - 2451545)] mod 360M = [357.5291 + 0.98560028 * (2459041.2149243 - 2451545)] mod 360 = 7745.8006283629 mod 360 = 185.80062836293 We need to calculate the equation of center, C:
C = (1.9148 * sin(M)) + (0.0200 * sin(2 * M)) + (0.0003 * sin(3 * M))
C = 1.9148 * sin(185.80062836293) + 0.0200 * sin(2 * 185.80062836293) + 0.0003 * sin(3 * 185.80062836293) = -0.18959122346086 We need λ which is the ecliptical longitude of the sun:
λ = (M + 102.9372 + C + 180) mod 360
λ = (185.80062836293 + 102.9372 + -0.18959122346086 + 180) mod 360 = 468.54823713947 mod 360 = 108.54823713947
Finally, calculate J
J
_{transit} = J_{*} + (0.0053 * sin(M)) - (0.0069 * sin(2 * λ))J _{transit} = 2459041.2149243 + (0.0053 * sin(185.80062836293)) - (0.0069 * sin(2 * 108.54823713947)) = 2459041.2185505
Now, to get an even more accurate number, recursively recalculate M using J
I1: M = 185.80420228783, C = -0.18970766002373, λ = 108.5516946278, J
_{transit} = 2459041.2185508I2: M = 185.80420261828, C = -0.1897076707895, λ = 108.55169494749, J _{transit} = 2459041.2185508I3: M = 185.80420261828, C = -0.1897076707895, λ = 108.55169494749, J _{transit} = 2459041.2185508Ok, translate this into something we understand. i.e. When is Solar Noon?
J
_{transit} =
2459041.2185508 = 07/10/2020 at 13:14:42 -0500
Alrighty, now calculate how long the sun is in the sky at latitude 39.040759: Now we need to calculate δ which is the declination of the sun:
δ = arcsin( sin(λ) * sin(23.45) )
δ = arcsin(sin(108.55169494749) * sin(23.45)) = 22.164683561829 Now we can go about calculating H (Hour angle):
H = arccos( [sin(-0.83) - sin(l
_{n}) * sin(δ)] / [cos(l_{n}) * cos(δ)] )H = arccos((sin(-0.83) - sin(39.040759) * sin(22.164683561829))/(cos(39.040759) * cos(22.164683561829))) = 110.51810214081
Just as above, calculate J
J
_{**} = 2451545 + 0.0009 + ((H + l_{w})/360) + nJ _{**} = 2451545 + 0.0009 + ((110.51810214081 + 77.04876)/360) + 7496 = 2459041.5219191
We can use M from above because it really doesn't change that much over the course of a day, calculate J
J
_{set} = J_{**} + (0.0053 * sin(M)) - (0.0069 * sin(2 * λ))J _{set} = 2459041.5219191 + (0.0053 * sin(185.80420261828)) - (0.0069 * sin(2 * 108.55169494749)) = 2459041.5255455
Now I'm going to cheat and calculate J
J
_{rise} = J_{transit} - (J_{set} - J_{transit})J _{rise} = 2459041.2185508 - (2459041.5255455 - 2459041.2185508) = 2459040.9115561Using the same idea, figure out when sunrise and sunset are:
J
_{rise} =
2459040.9115561 = 07/10/2020 at 05:52:38 -0500
J _{set} =
2459041.5255455 = 07/10/2020 at 20:36:47 -0500
A couple anomalies occur. At high latitudes, you will sometimes get H = 0. This means that either the sun does not rise (in the winter) or the sun does not set (in the summer) on that day. |

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