Monday, March 8, 2010

Activity - How to find Longitude by shadow measurements

When we want to know the time, we consult a watch. The time the watch gives us is called the Indian Standard Time. The life of our country is regulated by this time. We all know that this time we use in our day to day life is the local time of a place which is on a longitude which divides India into two halves in the east-west direction. That place is at 82.5 degrees E away from the Greenwich which is the zero longitude. 'E' shows that it is east of Greenwich. It falls in between two big cities, Allahabad and Varanasi. So whenever someone asks you the time, you look at you watch and tell him/her the time of the place at 82.5 degrees and not the time at your place. That's why when it is noon or rather the LOCAL noon at your place your watch does not show 12 o'clock in the afternoon! If you are east of the 82.5 degrees then your local noon will happen before the IST noon and vice versa for the person west of 82.5 degrees.
For finding more about the latitude and longitude, please refer to the accompanying doc “Latitude and Longitude”
This difference can be used to get your longitude. Lets see it this way. The whole earth is 360 degrees and it takes 24 hours by your watch to rotate back to same point after one rotation.


So 24 hours = 360 degrees
1 hour = 360/24 = 15 degrees
4 minutes = 1 degree
Now if two places are separated by 15 degrees in longitude on the earth, they will have a difference of 1 hour in their time. You already know that at the local noon the shadow of your gnomon is the shortest. So by measuring the difference (in time) in the local noon at two difference places, we can get the longitude difference.

In our experiment on 2oth March this year, we are going to measure the time of shortest shadow at our place and we have the time at which the shortest shadow forms at the meridian at IST (82.50E). Let this be T.
The time difference expressed in minutes and divided by 4 should give us gives us the difference it degrees in Longitude.

But there is a complication! The standard time refers to the local noon at 82.50 for a FICTITIOUS SUN! The earth DOES NOT go around the sun at a uniform rate! It moves faster in winter and slower in summer. Again the axis of rotation of the earth is tilted its orbit around the sun. Both these make the sun act like a clock that runs sometimes slow and sometimes fast! This is very inconvenient to say the least. So our day to day watch pretends that there is a fictitious sun that keeps uniform time throughout the year. The time it takes for the earth around the sun once is divided by 365 and then by 24 to define a standard hour. Standard times of all countries use this method.

So the local noon at 82.50 east occurs LATER than 12 o'clock on the watch on some days and EARLIER on other days! This correction, which changes throughout the year, is called the equation of time. Fortunately it is the SAME at ALL longitudes and latitudes and is known for every date. So it can be eliminated while taking the difference between IST meridian and our local meridian.


How to do it?

Get the local noon time in IST by looking at the watch (the time at which we get the shortest shadow in our place) “t “ by observing the shortest shadow formation by observing the gnomon shadow.

We know the local noon time at 82.50 as this is the IST we all use.
Local noon time on 20th March, 2010 at 82.50 =12:08 PM (this is calculated with ephemeris and softwares)
You can also do the same for any place on earth by using the following page on the internet:

Find (T-t) in minutes and divide by 4 to get the longitude difference.

Add or subtract ( if you are east of the IST timeline then add and if you are west to IST timeline then subtract from 82.50 E and find YOUR longitude!

In understanding how science works it is always much much better to assume concepts and the minimum number of known quantities. Then the measurement gives support to the CONCEPT assumed rather than claiming accuracy of a number which experts have already measured in any case! More than that it teaches us that cooperation is as IMPORTANT in science as it is in other aspects of life, if not more so.

1 comment: