How do sunrise and sunset times change with altitude?

Hi, I am a professional airline pilot and an amateur astronomer and would appreciate it if could provide me with a formula or method in how to calculate the affect of altitude on sun set/rise at different latitudes and if there is any way to predict time of sun set/rise while flying.

At most latitudes on the Earth, the effect of increased altitude is the same: it makes the Sun rise earlier and set later than it would at that same location from the ground. To make things simple, let's assume that you are in a plane over the ocean, at the equator at sunset. In that case, straightforward trigonometry indicates that at a typical commercial airplane altitude of 12000 metres, you can see an extra 2 degrees "around" the Earth. Since the Earth moves around the Sun at a rate of a quarter of a degree a minute, it means that at this altitude, sunset occurs 8 minutes later than it would from the ground. 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.

Now, all of this is complicated somewhat by the fact that you don't stay in one place in a plane, but you travel in a given direction: if this direction is predominantly East or West, then the plane's motion will completely change the answer we got above (in particular, travelling West at sunset can lengthen the latter significantly in a commercial jet). So, the results above are valid in a plane if a) the plane is moving rather slowly (like a personal plane) or b) the plane is travelling in the North-South direction.

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