Permanent Night?

Question

Suppose the earth still goes around the sun every year but you keep one side of the earth always facing the sun, so one side always sees the sun and the other side never sees it. As seen from the earth, the sun is stationary in the sky. Now in this supposed situation the stars would:

a) also seem stationary in the sky.

b) would seem to go once around the earth every day.

c) would seem to go once around the earth every year.

The answer is: c. Let's first diagram the problem. If we draw the sun in the middle of our page and then draw the earth orbiting around it with the earth's position at the top of the page above the sun labeled as position "A," the earth to the left of the sun as position "D," at the bottom of the page below the sun as position "C," and finally the earth to the right of the sun as position "B," with the star drawn above the earth at the top of the page (position A).

Now, as seen by someone standing in the middle of the dark side of the earth, the star is overhead when the earth is at position A. The star is underfoot one-half year later when the earth is at C and back overhead again one year later when the earth gets backto A. So even though the sun is frozen in the sky, causing one side of the earth to have a permanent day and the other side a permanent night, the stars would still seem to go around the sky once every year.

Thank God this is not now the existing situation, though there is reason to believe that some time in the distant future (when the earth's spin is reduced by tidal friction) this will become the existing situation.

Answer 1

C, For the hypothetical to occur, the earth's rotation about its axis would have to exactly match the orbital period of the earth.

To imagine what this earthling would see, just go outside every night at midnight. You would see the stars slowly rotating across the celestial sphere. This rotation would take exactly one year. The earthling on this hypothetical earth would see what we see at midnight, 24 hours a day, 365 days a year.

I note that the sidereal day would also be one year long, so B, in this case, is also an acceptable answer. See http://en.wikipedia.org/wiki/Sidereal_day regarding sidereal days.

Lastly, I note that the precession of the equinoxes would cause a slight foul up. The stars would not quite line up exactly on the year. They'd be off by a factor of 1/25,800. See http://en.wikipedia.org/wiki/Precession#Of_the_Earth.27s_axis (But this begs the question of whether a year on our hypothetical planet should be one orbit around the sun or when the earth's axis is in the same relative position to the sun as it was the previous year)

Answer 2

c.