From the north pole, how high is the sun @ midnight on the summer solstice ?
With or without considering the effects of refraction of the atmosphere?
Two more questions:
- do you already understand how to calculate the angle at noon on summer solstice?
- what level of accuracy are you aiming for?
I suggest drawing a diagram that shows the Earth at summer solstice, including:
the Earth's axis, tilted with respect to the vertical at the angle of inclination, towards the sun (assumed to be off to the side, horizontally)
the Tropic of Cancer
two parallel horizontal light rays, striking the Earth at the T of C and at the North Pole
a line tangent to the Earth's surface, indicating the horizon at the North Pole
If you draw the diagram correctly, the geometry of the situation should give you your answer quickly.
The time at the North Pole is Universal Time, but this doesn't matter at all. Here declination = altitude all of the time. Even if you were standing on a spinning disk platform going any speed, it wouldn't matter.
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