10

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?

SE is Evil - Support Monica
  • 103
  • 3
Mennyg
  • 241
  • 1
  • 3
  • 7
  • You are right. earth sphericity make the horizon farther. sunrise is when sun appear at the horizon. I believe for your religion taking the official sunrise time on ground as a reference should be OK. – Manu H Feb 12 '17 at 10:32
  • @ManuH my question is how to calculate how much earlier or later the sun rises or sets – Mennyg Feb 12 '17 at 11:52
  • This is purely a geometry question. Maybe you should try http://math.stackexchange.com/ – 60levelchange Feb 12 '17 at 12:37
  • 3
    @J.Hougaard even if it is purely geometry, tha answer (and its consequences) may be useful for this community. – Manu H Feb 12 '17 at 15:34
  • 1
    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. – Pondlife Feb 12 '17 at 18:25
  • 1
    @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. – Mennyg Feb 12 '17 at 20:01
  • 4
    "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."

    http://curious.astro.cornell.edu/about-us/161-our-solar-system/the-earth/day-night-cycle/189-how-do-sunrise-and-sunset-times-change-with-altitude-intermediate

     – MattyZ Feb 14 '17 at 03:18
  • 5
    @Bitrex expand that into an answer and it looks good enough to be accepted. Thanks! – Mennyg Feb 14 '17 at 07:18
  • @MENNyg I believe that there are programs outthere to figure these things out. Myzmanim.com and Chai tables come to mind – SE is Evil - Support Monica Feb 14 '17 at 16:34
  • @Bitrex you should put your comment as an answer. Even if it is only an approximation, it is a good one and I think it is enough for to answer the question. – Manu H Feb 14 '17 at 16:50
  • Also not speed and direction can affect it (a little), example if plane is heading sunrise at mach 0.8 – jean Feb 14 '17 at 17:35

1 Answers1

5

There's two parts to the answer. One is the extra angular distance to the sun you get from altitude and the other is the time that it would take to traverse that distance.

For the angular distance, besides the surface geometry, there's some additional effects of refraction. I'm going to ignore that on the assumption that there will be some refraction both at the surface and at altitude, so it will mostly cancel out (and it's harder to calculate it).

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.

The time you get from that extra distance depends on the season and the latitude. If you were doing it over the arctic circle in december, you might get hours or days more sunlight.

If you have time to look it up, check the civil twilight calculator for your location. That's the time when the sun is 6 degrees below the horizon. That means you'd see sunset at that altitude about the midpoint of civil twilight.

Otherwise, you can make a broad guess that most places in mid-latitudes have a civil twilight that lasts about half an hour. So at altitude, you get about 15 more minutes. Maybe a couple minutes more near solstices, a couple minutes less near equinoxes.

BowlOfRed
  • 5,601
  • 1
  • 20
  • 33