Is it reliable to watch the sunrise on the plane?

First of all, I regret to give my conclusion that there is no simple way to "calculate" the time to see the sunrise during the flight.

Generally speaking, the calculation error of sunrise is very large, so it is difficult to meet the requirements of the topic.

So, if we want to solve this problem, what are the difficulties?

First of all, the equatorial plane of the earth and the orbital plane of the earth are not parallel, which leads to the constant change of the direct point of the sun in a year (which is also the reason why there are four seasons on the earth). In summer in the northern hemisphere, the direct point of the sun is north of the equator, and the Tropic of Cancer can illuminate the summer solstice (about 23.5 degrees north latitude). Similarly, in winter, the direct point of the sun is south of the equator, and the tropic of Capricorn (23.5 degrees south latitude) can shine from winter to sun.

The direct point of the sun can vary within such a large range. Even if you don't fly, I believe everyone has experienced the phenomenon of early sunrise in summer and late sunrise in winter. The sunrise time at a fixed place can be several hours apart, not to mention on the plane.

Second, the factors mentioned above are different at different latitudes, and the farther north, the more obvious this difference is. On the equator, the sunrise time is almost unchanged, but at the latitude of Beijing (40 degrees north latitude), the sunrise time can change by three hours, not to mention the higher latitude areas.

Unfortunately, however, the flight from Istanbul to Shanghai will even pass through the area of 45 degrees north latitude ([3]), which greatly increases the uncertainty of calculation. This factor is related to the location of the starting point and the end point, and there is no comparability between different routes.

Third, it is not easy to know the flight path of the plane accurately. Although long-haul flights usually fly along the great circle route (see [1], [2]), due to various reasons (using high-altitude airflow, no-fly zone, avoiding dangerous weather, etc.). ), the route often changes, even the return route of the same flight is different, which also brings difficulties to the calculation.

But! As a technical house, how can you be stumped by this kind of problem! If you want to calculate, of course, you can calculate, considering the relative position of the sun and the earth, considering the latitude and longitude of the starting point and the ending point, and considering the route trajectory (I will simply calculate according to the great circle route). The specific process is too complicated, so I don't want to go into details. All kinds of trigonometric functions, spherical geometry, linear algebra ... Although I had fun in the process, it is really appetizing to post the process now.

Post a result ~

= = = = = = = = = = = = = = = Update13-1-07 = = = = = = = = = = = = = = = = =

Last night, I was half asleep. I misread the figures and mistakenly thought that the plane took off from Istanbul at 3 o'clock, so the original picture was wrong. Now let me correct it.

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First of all, suppose the subject flies from Istanbul to Shanghai around the vernal equinox and autumnal equinox, and leaves at 3 am local time. I assume that the flight time of the plane is 10 hour (in fact, it may be a little longer, after all, it does not strictly follow the great circle route. @ unixater？ The answer is 10h 16min, which has no essential influence). Then let's see what happens.