A problem I couldn't solve -- Number of Earth rotations in a year....

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Homework Help Overview

The discussion revolves around determining the number of rotations of Earth around its own axis in one year, specifically from the perspective of an observer located at the Sun. Participants are exploring the nuances of how to define and measure these rotations, considering various interpretations of the problem.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the precise definition of "rotations" and whether it refers to how many times the Earth's prime meridian aligns with a line drawn from the Sun to the Earth. There is also discussion about how this relates to solar days and the implications of leap years.

Discussion Status

The discussion is ongoing, with participants providing insights and raising questions about the original problem statement. Some have suggested considering the observer's perspective and how it affects the interpretation of Earth's rotations. There is a recognition of the complexity involved in defining the problem accurately.

Contextual Notes

Participants note that the problem statement may not include all necessary details, such as whether to account for leap years or the specific frame of reference for the observer. There is also mention of the potential confusion arising from the Earth's rotation direction and its implications for the observer's measurements.

  • #31
J Hann said:
Can't one also just add the angular velocity of the Earth (w.r.t. the fixed stars) and the angular velocity
of the Earth about its axis.
What is the difference between those two quantities?

You mean the "angular velocity of the Earth [about the sun] with respect to the fixed stars", perhaps? If so then no, you would not want to add those two quantities together.
 
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  • #32
jbriggs444 said:
What is the difference between those two quantities?

You mean the "angular velocity of the Earth [about the sun] with respect to the fixed stars", perhaps? If so then no, you would not want to add those two quantities together.

That's probably not the best way to describe it, but if you let
wf = Earth's rotation relative to the fixed stars
ws = Earth's rotation relative to it's orbit around the sun
we = rotation perceived on earth
Then we + ws = wf
Probably, a better way to describe it is that relative to the fixed stars the rotation of the Earth about its axis is 366 / yr
The perceived rotation on Earth is 365 / yr.
The difference is due to the Earth in its orbit is rotating from east to west at 1 rotation /yr or, in
other words, if the Earth had no rotation about its axis, an observer on Earth would see the sun
rise once in the west and set once in the east per year effectively losing a day
from the 366 rotations about its axis per year.
Phileas Fogg learned this in his journey of "80 Days Around the World".
Since he traveled from west to east he saw the sun rise 80 times while his
companions in London only observed 79 sunrises.
(The Earth under him rotated one time from east to west during his journey)
 

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