In this video we will be starting with our study of sundials for that we will take the Earth the sun and Earth’s orbit around the sun and we have made certain simplifying assumptions #1 We have assumed Earth’s orbit to be perfectly circular and Earth’s motion to the uniform around it and #2 we have assumed Earth’s axis to be normal or perpendicular to the plane of its orbit. Both these assumptions are of course not
correct. Our Earth’s orbit is kind of elliptical and Earth’s axis is inclined at 23.5 degrees with the normal but there will be appropriate corrections because of this which we will see in later videos. So right now let us get the simple thing down Then we are going to consider two cities on Earth’s equator. Say here is one city with this beautiful monument and diametrically opposite to that – 180 degrees apart that is another city with an equally beautiful monument Now born the cities are proud of their monuments and … they use them for time keeping. They use it in two different ways. Say in the city here – those folks use the sun as their time keeper They take the line of sight to the sun and when it is aligned with their monument or the plumb line there so when it is perfectly overhead when the sun is at the highest point in the sky they say it is 12:00 Noon The folks in this city … they don’t use the sun. Maybe they keep up at night or may be they like astronomy, but they use stars for keeping time So here is a distant star that they will be using for keeping time but the processes is more or less the same
They’d be taking the line of sight to the star which is practically at infinity and when it aligns with their monument – the plum line they would say it is midnight. So in the position shown over here this city is having 12:00 Noon While the other city is having 12:00 Midnight So both cities are right now 12 hours apart Now let’s see what happens as the Earth rotates So I’ll just zoom in to these two cities and we will start rotating the Earth So it has gone 90 degrees … 180 degrees … 270 degrees and … back to 360 So the Earth has undergone one complete rotation like this and you will see at the end of it, both these monuments have aligned with their respective lines of sight that they
use for time keeping. This monument is aligned with the line of sight to the sun and this monument is also aligned with the line of sight to the distant star So both the city folks would considered this as one day and they would agree that a passage of time equal to one day has occured So there is no problem here! But the motion that we considered in this process is only the rotational motion of the Earth. You will see the Earth is not going anywhere it is just rotating in its own place which is not correct the Earth has this whole orbit to cover so that orbital motion we haven’t considered so we have to now see what is the effect of orbital motion on this whole time keeping business. So let us set it in motion, this time not only the rotational but also the orbital motion would be considered and you’ll see this is going to have some effect on
the lines of sight. So let us observe them You’ll see the line of sight to the sun is changing its direction but line of sight to the star is not changing its direction at all. It is keeping parallel to itself. How can that be? This happens with all the distant objects you can do this on a moonlit night – if it is safe, as you walk just keep watching the moon overhead and you’ll feel as if the moon is walking with you This happens with far away mountains also while you’re traveling in a train or something those mountain seem to keep up with the
train There is nothing surprising about it the star is so far away, that even if Earth moves from one point in its orbit to the diametrically opposite point that displacement is hardly anything compared to the distance to the star. So we’ll keep seeing
the star at the scene place. It’s as if the Earth hasn’t moved at all So we will get an impression as if the star is moving with the Earth and this line of sight will remain unaltered. Now this is going to have a profound effect on the timekeeping process. The folks in this city are going to say that we do see the star overhead again and therefore we reckon this to be one day! So these folks would say one day has elapsed While the people in this city are going to say, well the son hasn’t come overhead yet and therefore the day is not over. There is still some time to go. In fact they’re going to wait for this much off extract rotation of the Earth, for the day to be over so the duration of the day the very definition of the time period that they call as one day, are now different! Naturally these two days are given two different labels. The day based on stars is called Sidereal Day While the day based on the sun is called the Solar Day. The Sidereal Day is about 23 hours 56 minutes but because of this extra rotation involved in
the solar day, it is about four minutes longer making it twenty four hours in solar dials of course we are going to use the Solar Day.