Sidereal Time and the Arctic Circle

[MrsTesla]

This may be a basic question, but why does the Sun rise at the same sideral time between December 22 and June 22 on the Arctic Circle? And how can I prove it?

 

[mfb]

You can find coordinates for the position of Earth, a point on the arctic circle, and the direction of Sun and prove that the line of sight is parallel to the horizon at the same sidereal time.

An interesting observation.

 

[Helios]

Once every sidereal day, at the Arctic circle, the ecliptic intersects with the entire horizon. In fact, the sun either rises or sets sidereal daily throughout the whole year! Also interesting is that, at the Arctic circle, when the sun rises ( or sets ), one could measure the ecliptic longitude of the Sun by measuring the azimuth of the sunrise! These are the not-too-commonly-known secrets of the Arctic circle.