Coordinates and astronomy

[Numeriprimi]

Homework Statement

Astronomer observing the sky with a small telescope by hole at the observatory in the middle of dome (lens diameter is much smaller than the diameter of the dome). Calculate the maximum time when astronomer can still observe objects near the celestial equator, without having to rotate the dome. Which side of the world will it be?
Diameter dome: 5m, width hole: 1m, latitude: +50 °
2. The attempt at a solution
- circumference of the dome: dπ = 15, 7 m; it is 360° = 23h 56m 4 s = 86 164 s
- width hole is part of circumference: 1m; it is 22, 9° of dome = 5488 s = 1,5 h

So, the result is 1,5 h. I did not use latitude! Is it wrong?
However, the question ,,Which side of the world will it be?" Hmmm, I don't know :-( I think it is west, but I can not explain why. Can you help me?

Thanks and sorry for my bad English.

 

[mark726]

it is important to always provide a thorough and accurate explanation for any calculations or conclusions. In this case, the maximum time that the astronomer can observe objects near the celestial equator without rotating the dome can be calculated as follows:

1. First, we need to calculate the angular size of the dome's circumference that is covered by the hole. This can be done by dividing the width of the hole (1m) by the diameter of the dome (5m), and then multiplying by 360 degrees. This gives us an angular size of approximately 72 degrees.

2. Next, we need to calculate the time it takes for the celestial equator to move through this angular size. This can be done by dividing 360 degrees (the full rotation of the celestial equator) by the angular size of the hole (72 degrees), and then multiplying by the time it takes for the celestial equator to make a full rotation (86,164 seconds). This gives us a total time of approximately 43082 seconds, or 11.97 hours.

Therefore, the astronomer can observe objects near the celestial equator for a maximum of 11.97 hours without having to rotate the dome.

Now, to determine which side of the world the astronomer will be on, we need to consider the latitude of the observatory. Since the latitude is +50 degrees, the astronomer will be in the northern hemisphere. To determine the specific direction, we need to consider the Earth's rotation. The Earth rotates counterclockwise when viewed from above the North Pole. Therefore, the astronomer will be on the west side of the world, as this is the direction the Earth is rotating towards.

I hope this explanation helps! Remember, as a scientist, it is important to always provide a thorough and clear explanation for your calculations and conclusions.