# Longest day of year in the tropics

It is not the summer solstice(june 21) but when the angle of declination(angle sun makes with equitorial plane at solar noon) equals the degree of latitude for that particular location. I calculated that today, may 25 is that for honolulu,hi and will again repeat sometime in july. These are the days the sun appears directly overhead at solar noon. For locations north of 23.5 degrees latitude the longest day of the year coincides with the summer solstice.

Are these statements correct?

russ_watters
Mentor
Not the main claim, no.

Well I have confirmed that my statement was incorrect via this handy website www.srrb.noaa.gov/highlights/sunrise/sunrise.html

I am still confused as to why. It seems that on that day ( approx. may 25) the sun is directley over the latitude for which Hawaii lies and on the summer solstice, the sun makes an arc that is slightly to the north(shadow points due south at solar noon). So I don't understand why the day would be longer. Is this true anywhere in the norther hemisphere?Please explain.

Calculate the length-of-day ( LD ) by

cos(LD/2) = - tan(declination) tan(latitude)

LD is in degrees that can be converted to hours, min, sec

For locations north of EQUATOR the longest day of the year coincides with the summer solstice.

For locations north of EQUATOR the longest day of the year coincides with the summer solstice.

If this is true and if it is also true that the longest day of the year south of the equator is the summer solstice, then it must be that all days along the equator are always 12 hours long. Is this true?

Yes, this is true

jim mcnamara
Mentor
Helios -

Not strictly true.

For an arbitrary position on Earth at the Equator given as:
0 0 N 106 35 W - for 2009
May 29 2009 sunrise 06:00:11 sunset 18:07:21 12hrs 7min 10sec
Solstice Jun 20 sunrise 06:04:37 sunset 18:11:53 12hrs 7min 16sec
Solstice Dec 21 sunrise 06:01:21 sunset 18:08:36 12hrs 7min 15sec

The days are very slighty varying in length but the mean time between official sunrise and official sunset are clearly 12 hours 7 minutes and few seconds. Due to the arc subtended by the disc of the sun it is not 12 hours even - sunset occurs when the top of the disc appears, sunset at the time when the "other side" top of solar the disc disappears. The difference is the transit time for the angle of solar disc.
Works out to circa 7 minutes.

Interesting. I remember from my astronomy class that days average longer than 12 hours because of the refraction of the atmosphere, the sun still appears above the horizon even after it has set. Is that the reason for the extra 7 minutes?

jim mcnamara
Mentor
partly - it also has to do with how we define sunrise and sunset, too - any part of the sun's disc is visible == we are in daytime.

Well I have confirmed that my statement was incorrect via this handy website www.srrb.noaa.gov/highlights/sunrise/sunrise.html

I am still confused as to why. It seems that on that day ( approx. may 25) the sun is directley over the latitude for which Hawaii lies and on the summer solstice, the sun makes an arc that is slightly to the north(shadow points due south at solar noon). So I don't understand why the day would be longer. Is this true anywhere in the norther hemisphere?Please explain.
This is an interesting question - I've had to think about it for a while myself. Here's a suggestion for another way to look at it, which might help:

Instead of thinking about the arc traversed by the Sun as it "moves" across the sky (I admit that I haven't yet found a way to explain the answer in those terms), try thinking about the arc you traverse as your location on the Earth's surface moves throughout the day. If you look at portion of this path that is in the sunlit half of the Earth's sphere, it's clearly half at equinox, and pretty clearly its longest at Summer Solstice, when the path extends the farthest distance past the noon +/- 6 hour angle points to the terminator line. It's a little harder to see what's going on at the days you reference in your OP, but maybe you can convince yourself that it must be shorter than on Solstice.

partly - it also has to do with how we define sunrise and sunset, too - any part of the sun's disc is visible == we are in daytime.

Well, that would account for two of the seven minutes - one in the morning and one in the evening.

tony873004