Question

Some telescopes can be moved by computer control to a given location in the sky, say a star an astronomer wishes to observe. Such telescopes sometimes have acquisition TV monitors with a field of view of about 50 arc seconds (1 arc-second = 1/60 are minute, which in turn equals 1/60 of one degree of arc). Now, on the celestial equator, how many arc-seconds of right ascension does the rotation of the Earth cause to pass by a given point in one second of time? If the astronomer's clock is off by 10 seconds, should he expect to see the star on his TV when the telescope moves there? Do you expect the same result if the astronomer's object is near the North celestial pole?

Answer 1

To find out how many arc-seconds of right ascension the rotation of the Earth causes to pass by a given point on the celestial equator in one second of time, you need to know the rate at which the Earth rotates and how this corresponds to right ascension.

The Earth completes a full rotation of 360 degrees in approximately 24 hours, or 86,400 seconds. Therefore, the rate of Earth's rotation in degrees per second is:

360 degrees / 86,400 seconds ≈ 0.0041667 degrees per second

Now, to convert this rate to arc-seconds per second, remember that there are 60 arc-seconds in 1 arc-minute and 60 arc-minutes in 1 degree, so:

0.0041667 degrees/second * 60 arc-seconds/arc-minute * 60 arc-minutes/degree = approximately 15 arc-seconds per second.

So, on the celestial equator, the Earth's rotation causes approximately 15 arc-seconds of right ascension to pass by a given point in one second of time.

Now, if the astronomer's clock is off by 10 seconds, the Earth's rotation will cause 15 arc-seconds/second * 10 seconds = 150 arc-seconds of right ascension to pass by the given point. Therefore, if the astronomer's clock is off by 10 seconds, he should expect the star to be off by 150 arc-seconds in right ascension when the telescope moves there.

If the astronomer's object is near the North celestial pole, the situation is different. Near the celestial pole, objects appear to move much more slowly in the sky due to the Earth's rotation. In fact, right at the North celestial pole, objects do not appear to move at all (this is true for the North Star, Polaris).

Therefore, if the object is near the North celestial pole, even if the astronomer's clock is off by 10 seconds, the change in right ascension will be minimal, and the object will likely still be within the telescope's field of view on the TV monitor.

Step-by-step explanation: