The earth makes a complete rotation on its axis in 24 hours. Through what angle will it turn in 3 hours 20 minutes and how long will it take to turn through 130 degree?
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Answer:
Step-by-step explanation:
How quickly does the Earth rotate through an angle of one minute?
It is an interesting question, and a little tricky because of the phrase, "angle of 1 minute".
The business about telescopes and motors turns out not even to matter when answering the question. Let's start with first principles:
The Earth rotates in a complete circle every day. A circle is 360 degrees. Each degree is 60 angular minutes. Not real minutes as in time, but minutes of angle. It's just a way of measuring very small angles. So in 1 day, the Earth turns by 360 degrees * 60 minutes per degree = 21600 angular minutes.
In terms of time, 1 day is made up of 24 hours, and each hour is made up of 60 minutes. So 1 day is 24 hours * 60 minutes per hour = 1440 temporal minutes (but see note below).
The question is really asking, how long does it take the Earth to turn 1 angular minute? Well, that would be 1440 temporal minutes per day / 21600 angular minutes per day = about .07 temporal minutes per angular minute. In temporal seconds, .07 minutes = .07 * 60 = 4 seconds.
So the answer is that it takes 4 seconds for the Earth to turn 1 angular minute.
To check our work multiply 4 temporal seconds * 21600 minutes in a circle = 86400 temporal seconds in a circle. Does that work out? 86400 / 60 = 1440 minutes. 1440 / 60 = 24 hours. So yeah, I guess it checks out.
Let's check our work again. A typical amateur telescope at low power will just fit the full Moon in the eyepiece. Visually, the diameter of the Moon is 1/2 angular degree, or about 30 angular minutes. Our results say that if you aim the telescope at the Moon, and then don't move it, the Moon will no longer be visible in about 4 seconds * 30 = 120 seconds or 2 temporal minutes. From my experience, that is about right.
Note: The Earth actually rotates about 23 hours 56 minutes, but I think we can round it to 24 for the purposes of this problem.
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The earth makes a complete rotation on its axis in 24 hours. Through what angle will it turn in 3 hours 20 minutes and how long will it take to turn through 130 degree?
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Answer:
Step-by-step explanation:
How quickly does the Earth rotate through an angle of one minute?
It is an interesting question, and a little tricky because of the phrase, "angle of 1 minute".
The business about telescopes and motors turns out not even to matter when answering the question. Let's start with first principles:
The Earth rotates in a complete circle every day. A circle is 360 degrees. Each degree is 60 angular minutes. Not real minutes as in time, but minutes of angle. It's just a way of measuring very small angles. So in 1 day, the Earth turns by 360 degrees * 60 minutes per degree = 21600 angular minutes.
In terms of time, 1 day is made up of 24 hours, and each hour is made up of 60 minutes. So 1 day is 24 hours * 60 minutes per hour = 1440 temporal minutes (but see note below).
The question is really asking, how long does it take the Earth to turn 1 angular minute? Well, that would be 1440 temporal minutes per day / 21600 angular minutes per day = about .07 temporal minutes per angular minute. In temporal seconds, .07 minutes = .07 * 60 = 4 seconds.
So the answer is that it takes 4 seconds for the Earth to turn 1 angular minutes
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