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Sidereal

This time, we will learn both some Science and a new word in English. We will see what the word sidereal means. In the process, we will learn something new about Earth.

But let us get there slowly and begin with one basic question. How many rotations does the Earth make on its axis in a single day? Sounds like a stupid question, right? After all, is not the very definition of a day, based on the time taken for the Earth to complete one rotation? That is, if the Sun is on top of your head today, the time taken for it to again be at the same position is what we call a single day. Yes, the definition of a day is the time taken for the Earth to come back again to the same position with respect to the Sun. But what is interesting is that Earth makes more than one rotation in a day. Let us see how.

By definition, the Earth revolves around the Sun once a year, that is 365 days. But for understanding how Earth does more than one rotation to complete a day, let us consider for simplicity, that the Earth takes only 4 days to go around the Sun. Keep in mind that after a rotation the Earth gets back to the same position as it was at the beginning of the rotation. So earth will have to go through the following stages to complete a rotation. To see the effect of rotation, I have coloured 2 halves of the Earth in two different colours.

Picture - 1. Different stages of rotation

 

This is pretty straightforward and elementary. But keep this image in mind when we look at the next picture.

Assuming, that one day is one rotation (which is incorrect as I am trying to convince you), given below is the position of the Earth with respect to the Sun, on all these 4 days at the end of each rotation.

Picture - 2. How the Earth would be if it rotated only once each day, and completed a revolution in 4 days

One way to look at picture-2 is the normal way, that is to look at it from your perspective. The other way is to look at it from the sun’s perspective. All the positions A, B, C and D look the same to us, but as you can see, at position A, parts of both the blue and green halves are exposed to the Sun, but at position B, only the blue half is exposed to the Sun, similarly at position C, the other parts of the 2 halves are exposed, and at position D, only the green half gets to see the sun.

At position B, the green half is completely hidden from the Sun. But since a day has passed, and our assumption was that 1 day is 1 rotation, should not the same parts of the Earth be exposed to the Sun again, since one rotation is over? But that does not seem to happen. Therein, lies the problem.

For the Earth to be in the same position with respect to the Sun (which is more important to determine the time of day, than it being in the same position with respect to us), one rotation is not sufficient. To see how much extra is needed look at picture – 3.

This is how it should ideally be, for the Earth to be looking at the Sun the same way, at the end of each day. At position B, though we see only the green half (the blue half is hidden from us), the sun is able to see parts of both the blue and green halves (a little bit of visualisation on your own is needed here).

Picture - 3. Ideally, this is how a 4 day revolution should happen. With the Earth showing the same face to the Sun at the end of each day.

But to come to position B, the earth has to make an extra quarter rotation (refer to Picture-1).

The extra quarter rotation it needs to make is because, in that one day, the earth has done 1 quarter of its revolution around the sun (remember in our example, it takes 4 days to go around the Sun).  Since it has made a quarter revolution, it has to make a quarter rotation extra to get the Earth back in the same position with respect to the Sun.

Thus, the earth should have rotated a quarter rotation more, at the end of a day, for it to be at the same position with respect to the Sun, since that is when the green and blue halves are again exposed to the Sun. As in Picture – 2, a single rotation does not suffice. Thus, a day would not mean 1 rotation but 1 + 1/4 rotation.

So 1 day≠1 rotation.

QED.

The Earth’s revolution around the Sun is the key here. Since the Earth keeps moving around the Sun (apart from its rotating on its own axis) the way it is exposed to the Sun keeps changing. Thus rotation has to compensate for this change caused by revolution. Thus one rotation is not sufficient for a day.

Now coming back to our real Earth, which takes 365 days to complete a trip around the sun. In this case, the Earth will complete 1/365 ths of a trip (revolution) in a day. So the Earth has to make an extra 1/365 rotation on its axis for it to be at the same position again with respect to the Sun.

Thus 1 day = 1 rotation + 1/365ths of a rotation.

I forgot something. Wait a minute, let me recollect. Ah, yes. Sidereal. I had told you I would explain what it is, and we are almost there. Throughout the post,  I kept saying that the Earth must be at the same position with respect to the Sun, and not with respect to “us”. But who are “us”? Imagine you are on a star other than the sun. From there if you see, the Earth will be in the same position after just 1 rotation itself. It does not need any extra time, since the Earth is not revolving around the star from which we are looking at it. Thus, with respect to that star, a day is equal to 1 rotation (not exactly, there too, day lengths will change for each star, but it is a good approximation for the purpose of this article).

Now we have arrived. Sidereal means, with respect to any fixed star. The sun cannot be a fixed star, because relative to us, it moves. But the stars other than the Sun are relatively fixed. Thus a sidereal day is about 23 hours 56 minutes, which is, less than the average solar day (which means a day with respect to the sun) of about 24 hours.

A small teaser to end the post. If the Earth is rotating in the opposite direction as it is rotating now, then revolution would be helping rotation to complete a day, so to say. That would mean that a day would require less than one rotation. That is, some of the rotation needed to be achieved for one day, is contributed to, by the revolution. Thus even before a rotation is complete, the Earth comes back to the same position as it was a day before. In such a scenario, a solar day is shorter than a sidereal day. Try thinking that out yourself.

With the pictures that are present above for our Earth, and imagining how that will change if the direction of the Earth’s rotation changes, this hypothetical situation, too, must then become as clear as, if I may say so, day.

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Categories: Physics Tags: , ,
  1. Arvind
    January 12, 2011 at 12:59

    You might want to add an arrow to the figures showing the way the earth rotates to clarify it.

    • January 13, 2011 at 07:10

      I just added it. My initial hesitation in giving a direction was that I was worried a bit that it would confuse people given that they are watching a 2-D picture. But still, I think adding it makes sense. Thanks.

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