[Physics] Why does the Sun always rise in the East

Question

Why does the Sun always rise in the East?

Earth is rotating on its own axis & also revolves around the Sun, then how come the Sun always rises in the East?

Answer 1

Whether the sun "rises" in the east depends on your position on earth, and the time of the year. In northern latitudes, during the summer, the sun rises significantly North of East, and in the winter it rises in the South. For example, today's sunrise/sunset directions in Umeå Sweden, look like this (source: www.suncalc.net)

The yellow line shows the direction of sunrise, the orange line the current direction of the sun, and the red line the direction at sunset.

As you can see, the sun never gets close to being in the East...

The reason for this is the fact that the earth's axis of rotation is not perpendicular to its plane of rotation about the sun (the ecliptic). The same mechanism that causes summer and winter in the higher latitudes gives rise to this changing direction.

But as for the fundamental question: the rotation of the earth about its axis is much faster than the rotation of the earth about the sun - so the rotation of the earth is dominating the direction of the sunrise. Now if the earth stopped rotating altogether, the sunrise would be in the "Westerly direction", since the direction of both rotations (seen from say the North Star) is in the counterclockwise direction. It would just rise and set only once a year... But the year is 365.24 days, and while that is so, the sun will rise "mostly in the east".

A small addendum: because the earth's orbit is elliptical, its angular speed relative to the sun changes a little bit with the seasons. This is enough to make a sundial "off" by up to 15 minutes, depending on the time of year. This is captured in the "equation of time" and shown, for example, in this graph (from http://upload.wikimedia.org/wikipedia/commons/0/02/Tijdvereffening-equation_of_time-en.jpg):

And just for your amusement - on October 25th, the sun briefly rises in the South on Svalbard (Spitsbergen) before disappearing for the winter...