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In what direction and at what speed (in units of arc minutes/minute) must the telescope move in order to keep stars in the same position in the field of view of the telescope?

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Answer:

The telescope must move in the direction opposite to the Earth's rotation, and at a speed of 1 arc minute per minute (or 15 arc seconds per second) to keep stars in the same position in the field of view.

This is because the Earth rotates from west to east, causing the stars to appear to move in the opposite direction (east to west) in the sky. To compensate for this motion, the telescope must be moved in the opposite direction, at a rate that matches the Earth's rotation.

1 arc minute per minute is equivalent to 15 arc seconds per second, which is the rate at which the stars appear to move due to the Earth's rotation.

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