Rotation of Earth relative to a distant star

[Sara Samuel]

Homework Statement

On the Earth the Sun appears to rise and set about 365 times in one year. During the same 365 days, how many times does the Earth rotate on its axis relative to a distant star (a star beyond the Sun and out of our solar system)?

Homework Equations

The Attempt at a Solution

 

[hjelmgart]

Think you should at least think of the stars and the sun fixed. Now the Earth moves around the sun while it rotates. There is 360 degrees in one rotation, but 365 rotations in a year, however, since the Earth moves around relative to the sun, the position of the distant star would change over time.

So what you need to do, is to figure out how the distant star moves relative to the sun - seen from earth. You should find, that the star arrives a few minutes later relative to the axis of the Earth each day compared to the sun, due to the Earth rotating about the sun.

In the end, your answer should actually be, what explains, why we count 365 days per year.

 

[haruspex]

hjelmgart's method is fine, but you will find it a little easier if you treat the distant star as effectively at infinity.
Or draw this diagram:
- sun and Earth at some instant, Earth shown as a circle
- 'another' Earth after moving an angle theta around the sun
- mark the position on Earth where the sun appears overhead on each of the two Earth's
If exactly N days have elapsed between the two Earth positions, that will be the same physical location on earth. What angle has the Earth rotated through on its own axis?
Hint: you will need to know the relationship between the direction the Earth spins on its own axis and the direction in which it orbits the sun.

 

[Sara Samuel]

Thanks a lot!