# How much earlier/later is sunrise/sunset at 40,000 feet?

If I'm over New York City, and sunrise is 6am, I will see the sunrise earlier when I'm at 40,000 feet on the plane.
I think that latitude plays a role here, but using NYC as an example, how much earlier/later (later for sunset, as I will see the sun for a longer period at that height) are these events on a plane than on the ground?

• @J.Hougaard even if it is purely geometry, tha answer (and its consequences) may be useful for this community. Feb 12 '17 at 15:34
• Most religions have exceptions and 'rules of thumb' for people who can't observe rituals as usual, because of illness, travel etc. Asking your religious leader is probably best here, because it sounds like your primary concern is religious, not physical. Feb 12 '17 at 18:25
• @Pondlife leaving the theological discussion out, I am asking how much earlier or later events are at 40,000 feet, not what my religious leader might or might not say about the situation. Most leaders in my religion say to go by where one is relative to the ground. That requires figuring out where you are and what time sunrise is. Im asking how to figure that out. Feb 12 '17 at 20:01
• "The variation with altitude is approximately linear, and so we conclude that sunset is later by 1 minute for every 1.5 kilometres in altitude, and that sunrise is earlier by the same amount." curious.astro.cornell.edu/about-us/161-our-solar-system/… Feb 14 '17 at 3:18
• @Bitrex expand that into an answer and it looks good enough to be accepted. Thanks! Feb 14 '17 at 7:18

From the surface we see the sun cross a line of 90 degrees to the vertical (horizontal), from 40,000 feet it would be $\sin^{-1}(\frac{R}{R + 40,000 \text{feet}})$ or 86.5 degrees. From altitude, we see around an extra 3.5 degrees.