Sunrise Times Math Problems

Question

Hi,

Say have a a time of 5:25 am and it's that time at 18 degrees.

I also have a time of 5:57 am and it's that time at 12 degrees.

Finally, I have a time of 6:29 am and its that time at 6 degrees.

How can I find out what time it is at 16.1 degrees?

This is in reference to: https://www.timeanddate.com/astronomy/different-types-twilight.html

The different types of twilight have different degrees in relation to the horizon and I'd like to find on any given day what time it is at 16.1 degrees. Thanks again.

Answer 1

I am not an astronomer, but I believe this problem could be solved using proportions.

Every 32 min (5:57am – 5:25am = 6:29am – 5:57am = 32 min) the twilight changes by 6°

At 5:25am it was 18°, at 5:57am it was 12°. 

Let 5:25am be the initial moment. In 32 min the twilight changes by 18° - 12° = 6°.

In what time t (from 5:25am) the twilight will change to 16.1° (in other words, changes by

18° - 16.1° = 1.9°)?

Make proportion: 32 / 6 = t / 1.9

Solve it: t = 32(1.9)/6

If you want to find the time in seconds, it is convenient to find solution as a mixed number:

t = 32(19/10)/6 = (32•19) / (10•6) = 608/60 = 10 and 8/60, or 10 min 8 sec.

So, the twilight will be 16.1° at 5:25am + 10 min 8 sec = 5:35:08am.