Expert: Jayendra Upadhye - 2/15/2005

Question
If you please I would like to know what is the effect of the altitude on astronomical morning twilight , and would that also be effected by city latitude .
As an example :city of Rome.
astronomical Morning twilight: 06:00 am on the ground what it will be at these altitude
astronomical Morning twilight:  at 25000 ft. ?
astronomical Morning twilight : at 30000 ft. ?
astronomical Morning twilight:  at 35000 ft. ?
thank you .  

Answer
Hello Sami,
by definitions (ref:-http://www.sunrisesunset.com/definitions.html)
Astronomical Twilight
Astronomical twilight is defined when the sun is 18 degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening the sun does not contribute to sky illumination; for a considerable interval after the beginning of morning twilight and before the end of evening twilight, sky illumination is so faint that it is practically imperceptible.


But this is truly an interesting question.
Brings to mind an interesting excercise i did some years ago, which determined the horizon width of a point a given hieght from the surface of the earth.

That excercise is connected to this issue.
you see, if you consider twilight as the time when a given locale is "on the edge" of day night line of the earth, then it follows that sunlight is incident at angle 0 to it.
[ie, sunlight apporaches that locale at a line parallel to the earth's surface, in an east to west direction.]
Also it means sunlight represents a line that is a tangent to the earth's surface, touching the earth at the point in question.

Now if there is a mountain 25000 feet high, further to the west, on the night side, so that its peak will just intercept this tangent line, you will have morning twilight on the peak, even though it is still late night at the bottom of the mountain! Also the person on that peak will see sunlight approaching him at a -ve angle too (sunlight from below!]

This is the reason why we see high clouds on the horizon, lit from below in the evenings! if you have noticed such things that is!

Simple trigonometry tells us that if earth's radius is H,
hieght of mountain = h then angle subtended by the horizon point, to the earth's center with respect to plumb line thru the point at height h will be
theta = cos inverse of H / (H + h)
H = 6.3710 × 10^6 met = 3.33 * 6.3710 × 10^6 feet
1 - h = 25000 ft
for 25000 feet, angle
theta =
cos inverse ((3.33 * 6.3710) * 1000000/((3.33 * 6.3710) * 1000000 + 25000))
= 2.78 deg
At 360 deg / 24 hrs, the horizon point has twilight hours
2.78 deg * 24 hrs / 360 deg = 0.185 hr or 11.12 min before 6 am!

2 - at 30000 feet, angle
theta =
cos inverse ((3.33 * 6.3710) * 1000000/((3.33 * 6.3710) * 1000000 + 30000))
= 3.05 deg
At 360 deg / 24 hrs, the horizon point has twilight hours
3.05 deg * 24 hrs / 360 deg = 0.203 hrs or 12.2 min before 6 am!

3 - at 35000 feet, angle
theta =
cos inverse ((3.33 * 6.3710) * 1000000/((3.33 * 6.3710) * 1000000 + 35000))
= 3.288 deg
At 360 deg / 24 hrs, the horizon point has twilight hours
3.288 deg * 24 hrs / 360 deg = 0.2192 hrs or 13.152 min before 6 am!

That 18 deg stuff in the definitions does not alter our results, as that is common to all 3 situations. What applies to tanget point will apply to a point preceding it by 18 degrees, timewise.

I tried to locate tables showing altitudewise twilight variation tables, but without success.
hope this satisfies you.
jayen