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

[Nagendra kamath]

< Mentor Note -- thread moved to HH from the technical physics forums, so the Homework Help Template is filled out farther down the thread >

The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.

 

[jbriggs444]

The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.

The first step is to clearly define the problem. Rotations are particularly tricky to nail down precisely. Do you mean:

We draw a line from center of Sun to center of Earth and ask "how many times does Earth's prime meridian pass through this line over the course of a solar year"?

Would the answer to this question differ from "how many solar days are there in a solar year"?

 

[berkeman]

The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.

Welcome to the PF.

Is this question for schoolwork? If so, I can move your thread to the Homework Help forums for you.

 

[Nagendra kamath]

Welcome to the PF.

Is this question for schoolwork? If so, I can move your thread to the Homework Help forums for you.

Yes this is for school work sorry I didn't know where to put it I am new to the forum

 

[Nagendra kamath]

The first step is to clearly define the problem. Rotations are particularly tricky to nail down precisely. Do you mean:

We draw a line from center of Sun to center of Earth and ask "how many times does Earth's prime meridian pass through this line over the course of a solar year"?

Would the answer to this question differ from "how many solar days are there in a solar year"?

Sir the answer to this is to be kept in Earth days ...

 

[berkeman]

Yes this is for school work sorry I didn't know where to put it I am new to the forum

No worries, I'll move it for you. Please copy/paste this Homework Help Template into your next reply, and fill it out based on the questions you have been asked so far (likd the definition of the exact problem. Thanks!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Nagendra kamath]

1. Problem statement, all variables and given / known data
The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.
Options ,1. 365 ,2. 1 ,3. 364 ,4. 366

Homework Equations

[/B]
Don't know in what way I have to approach

3.The attempt at a solution
I know that sun rotates round it's axis at 24 days/ rotation
So if the observer is watching Earth from sun he can see Earth only for 12 days for the other half of the rotation he will be on the opposite side of Earth so I think we he doubles the value that he gets for the first 12 days for 24 days...

 

[berkeman]

1. Problem statement, all variables and given / known data
The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.
Options ,1. 365 ,2. 1 ,3. 364 ,4. 366

Homework Equations

[/B]
Don't know in what way I have to approach

3.The attempt at a solution
I know that sun rotates round it's axis at 24 days/ rotation
So if the observer is watching Earth from sun he can see Earth only for 12 days for the other half of the rotation he will be on the opposite side of Earth so I think we he doubles the value that he gets for the first 12 days for 24 days...

Perfect, thanks!

So imagine that you are sitting at the north pole of the Sun. You can see the Earth all year long. Does that change your answer?

 

[Nagendra kamath]

Perfect, thanks!

So imagine that you are sitting at the north pole of the Sun. You can see the Earth all year long. Does that change your answer?

Yes it does ...but looking at the options I am not able to pick the correct one

 

[berkeman]

Yes it does ...but looking at the options I am not able to pick the correct one

The Earth has spun 365 times in that year with respect to the sun, but what else has happened?

 

[Nagendra kamath]

What if it's a leap year ? They haven't mentioned about what kind of year it is...so...are we supposed to ignore the fact of the year being a leap year?

 

[berkeman]

What if it's a leap year ? They haven't mentioned about what kind of year it is...so...are we supposed to ignore the fact of the year being a leap year?

That's a good point, but it seems like they are ignoring that5 subtlety.

Hint -- would it make a difference it the Earth were spinning the opposite way? Which way does the Earth spin with respect to how it moves around the Sun?

 

[Nagendra kamath]

Earth rotates west to east at its axis and if we observe from sun's and Earth's North Pole the Earth would appear to revolve in a counterclockwise direction about the Sun

 

[jbriggs444]

The number of rotations of Earth around its own axis in one year as measured by an observer from the sun.

What do you think that it means for the Earth to rotate once about its axis as measured by an observer from the sun? For instance, does it mean "how many times the Sun observer can look down into noontime London?

Or, in other words, exactly what measurement is the observer on the sun performing?

 

[Nagendra kamath]

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What do you think that it means for the Earth to rotate once about its axis as measured by an observer from the sun? For instance, does it mean "how many times the Sun observer can look down into noontime London?

Or, in other words, exactly what measurement is the observer on the sun performing?

I think he has fixed a point on Earth like you mentioned about London...

 

[jbriggs444]

If an observer on the sun can look down on London, would an observer in London be able to look up at the sun?

Does that lead you toward an answer to the question?

Edit: Ignoring cloud cover -- which, for London, is a pretty big thing to ignore.

 

[haruspex]

What if it's a leap year ?

Leap years are an invention so that a new year always starts at midnight. In reality, using 24 hour days, the number of days in a year is about 365.24... But the options are whole numbers, so the fraction of a day is being ignored.

 

[CWatters]

Perhaps consider how many rotations of the Earth would be seen from the sun (over the course of a year) if the Earth didn't rotate on its axis at all.

Is it 0, 1 or -1?

 

[Nagendra kamath]

Perhaps consider how many rotations of the Earth would be seen from the sun (over the course of a year) if the Earth didn't rotate on its axis at all.

Is it 0, 1 or -1?

Well if Earth didn't rotate the answer will be 0 right ?

 

[berkeman]

Well if Earth didn't rotate the answer will be 0 right ?

Not as seen from the Sun...

 

[berkeman]

One of the problems with this thread is the original problem statement. Are you sure that is the complete statement that was given to you? Can you see how the answer will depend on the point of view of the observer?

 

[Nagendra kamath]

One of the problems with this thread is the original problem statement. Are you sure that is the complete statement that was given to you? Can you see how the answer will depend on the point of view of the observer?

It is the original statement asked in an entrance test of a reputed institution

 

[Nagendra kamath]

Not as seen from the Sun...

Well if Earth isn't rotating i think this is what will happen so it seems as if there is no rotation...I don't know am I right?

 

[gneill]

In your drawing, how does the observer judge the direction that the spot on the Earth is facing in his frame of reference? Does he think an observer on that spot would only ever see the same patch of sky?

A truly non-rotating Earth would not change direction with respect to distant background stars.

 

[ehild]

Just think of the Moon. You always see the same face from the Earth. So it does not rotate with respect to the Earth, but does it rotate with respect to the far away stars?
Do an experiment. You are the Moon, and you orbit around the chandelier, so as you turn toward it during your whole route. Do you rotate with respect to the room? If you see the window opposite to you initially, do you see it when you are halfway around the chandelier?

 

[Nagendra kamath]

Just think of the Moon. You always see the same face from the Earth. So it does not rotate with respect to the Earth, but does it rotate with respect to the far away stars?
Do an experiment. You are the Moon, and you orbit around the chandelier, so as you turn toward it during your whole route. Do you rotate with respect to the room? If you see the window opposite to you initially, do you see it when you are halfway around the chandelier?

I didn't follow

 

[Nagendra kamath]

In your drawing, how does the observer judge the direction that the spot on the Earth is facing in his frame of reference? Does he think an observer on that spot would only ever see the same patch of sky?

A truly non-rotating Earth would not change direction with respect to distant background stars.

Take an arbitrary spot

 

[CWatters]

In your drawing the Earth _is_ rotating about it's own axis...

Try making another one with no rotation.

 

[Janus]

Sir the answer to this is to be kept in Earth days ...

A "solar day" is the time it take for the Sun to go from noon to noon as seen from a given spot on the Earth. It is the "Earth day" upon which we base our clocks.
What was being pointed out was that this would be equal to length of time that an observer on the Sun would see between two instances on exactly the same side of the Earth facing him.
From this, I find it a bit odd that this is the answer the question was looking for, since it is a bit obvious and just equals the number of days in a year. It seems more likely that what they were asking was how many rotations would the Earth make relative to some fixed reference as seen from the Sun. (Imagine an observer at the North pole of the Sun and constantly facing a fixed star vs one rotating to keep the orbiting Earth in front of him.)

 

[J Hann]

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. The comment about standing at the N pole of the sun is also
quite pertinent in visualizing the problem. In this sense does the moon rotate (w.r.t.) the
fixed stars or not?

 

[jbriggs444]

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.

 

[J Hann]

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)