VERNAL EQUINOX DAY - MARCH 20th 2010

This is the date (near March 20) when night and day are nearly the same length, and it marks the beginning of spring in the northern hemisphere. Equinox literally means "equal night". Come equinox day the sun shines directly on the equator and you have 12 hours of day and night, all around the world. However, the length of night and day across the world is nearly, but not entirely, equal - depending on location. As you observe, you come to realize that it is not the complete truth that every day the sun rises in the East and sets in the West. Equinox day offers opportunities to find facts about the way nature and science works in our lives.

Finding your location by just observing the sun movement in heavens is something unimaginable for a layman but we, astronomers can do that quite easily. March 20th is a BIG opportunity for us to find our location on the globe by observing the shadows formed by sun on that day. Working with hi-tech instrumentation and finding your coordinates is the thought which comes to your mind, but one can use sun and a small stick as his/her instruments and find the same. Of course you have to apply your brains to get meaning out the data you collect!!!! That shows us if you use logical reasoning and observe natural phenomenon carefully, you can find so many answers in science.

SPACE encourages students, teachers and school management to come forward and participate in this amazing experiment utilizing the phenomenon of Equinox. The activity and experiments would be conducted all across India in various centers of SPACE like schools, SNCs etc. The results from all the centres would be collated and each experiment team will be able to find the latitude of their location plus the difference in longitude corresponding to each other

Date: 20th March 2010

Timings: 11.00 am to 1 pm

Venue: School, home, public place

Experiments: Finding Local Noon and sun angle

So on 20th March observe the shadow formed by sunlight and find your location on Earth!!!

ACTIVITIES SUGGESTED:

Finding local Noon

Finding Sun Angle

Equinox day 20th March 2010 - Form

Equinox day 20th March 2010
Find your longitude and latitude by observing the shortest shadow

Name:
School:
SPACE club: Yes/No
Space Nodal Centre: Yes/No
Shortest shadow time (hr:min:sec):
Sun Angle:
School Address:

City:
Telephone:
e-mail:
Other Details you want to put:

Send the completed Form fully filled back to SPACE office addressed to: SPACE, WZ-19, First Floor Asalatpur, A3 Block, JanakPuri, Delhi 110058 or mail the filled doc file to info@space-india.org

How to measure sun angle with Gnomon

Materials needed

1. Gnomon with base

2. A plumb line (thread and nut)

3. Drawing Board of Half imperial Size or 40cmx 40cm square board (husk, ply) 12 mm thick

4. A Sheet of white paper, pencil, fine thread, a nut or other suitable weight for plumb line

5. Spirit level

Preparation

1. Paste/ tack white paper on drawing board/square board.

2. Make the board horizontal by using the spirit level.

3. Measure length of Gnomon several times. Record the Average length in millimetres. This is the height of the gnomon, H.

4. Place the three legged base centrally on the board Fix with three pins.

5. Mark with pencil the centre of the hole in the middle

6. Assemble the gnomon rod into the central hole

7. Make a plumb line by attaching a the weight to the end of a string

Your gnomon is now ready for use

Marking the shadow

1. Find a site that is flat and open sky where the sun is visible between 11a.m and 1 pm (A terrace for instance SouthEast to SouthWest segment)

2. Find a flat surface. Place the base board and check with the spirit level to ensure that the surface is perfectly horizontal.

3. Place Gnomon with base on the surface. Adjust the base board so that the gnomon is vertical. Check using a plumb line. This is very important

4. Between 11 am and 1 pm mark the tip the shadow formed by the gnomon every 5 minutes. Ensure that the stick is vertical throughout the observations.

5. Remove Gnomon from board.

6. Draw a smooth curve joining all the points through all the observations

7. Measure the shortest distance from the curve to the base of the pencil in millimeters several times. Record the average. This is the length L of the shadow

8. Construct a similar right angle triangle with sides proportional to the Gnomon height H and shadow length L, using a large scale factor. For example draw a horizontal line AM=2L; Draw a line 

AP perpendicular to it at one end, of length 2H. Join PM.

9. Measure the angle MAP. This is the angle between the vertical in your location and the direction of the noon day sun. This is the Sun angle and on the day of the equinox, this is the latitude of your location. The angle MPA is the altitude of the sun at the time of local noon.

See attached images for further clarification. For detailed information see demonstration video on the activity at youtube.

Setting up gnomon

Checking the board level with Spirit level

putting the gnomon on the board

Using plumb line to make gnomon vertical

Marking tip of the shadow by pencil

Marking the curve after the shadow markings

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:

aa.usno.navy.mil

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.

ACTIVITY: Latitude Measurement – using sun angle

If we place a gnomon at different locations on earth and closely watch the shadow during daytime, we will observe that the angle between the vertical and the mid day sun will be different at different places (or latitudes). Can we use this to find the latitude of a place? Or can we use this method to find out the difference in latitude for two different places? Should we walk all around the earth and find the circumference and then the radius of the earth to do so? Well we don’t have to go to so much trouble. Should we use a map with a scale that was made over hundreds of years by other people walking long distances and surveying the land? No! There is no need to do it. Should we copy the radius of the earth from a handbook and use it? No! No!

This is getting a bit irritating! Lets go to the heart of the matter right away. As before A and B are two locations on the surface of the earth of radius R. Two sticks (Gnomon) of equal length (AP=BQ) are placed in the two locations. The shadow length AM is shorter than shadow length BN. The direction of the mid -day sun at A and B are MP and NQ. The shorter shadow implies that the sun has a higher altitude at A than at B. The angle APM between the vertical and the direction of the sun at A can be measured by constructing similar triangles on paper or by using trigonometry. The angle BQN between the vertical and the direction of the sun at B, can be similarly measured

Look at the figure below. Let the circle below represent the earth. The vertical at A and B is defined as the line joining the centre of the earth to the points A and B respectively. The verticals through them are OAP and OBQ respectively. The shortest shadow is cast by the mid day sun. The rays of the sun falling on the earth may be considered parallel, as the sun is very far compared to the size of the earth. From measurement we know the angles APM and BQN and the difference between them. It is clear from the geometry that this is equal to the angle AOB subtended by the arc AB at the centre of the earth.

Suppose the direction of the noon day sun at station A is as shown in the diagram below

ie the sun is exactly overhead at noon at A and casts no shadow! The angle POQ is still the difference in the angle between the vertical angle of the noon sun at the two places. From simple geometry angle POQ = angle BQN, the vertical angle of the noon sun at B. So you can easily measure it at B. If station A is at the equator, it directly measures the LATITUDE at B! Now March 20 is the equinox day, On this the sun shines directly over the equator. If we perform the experiment by measuring the vertical angle of the noon day sun on that day everywhere in the world we can measure our own latitude!

WHAT are we assuming here?

The Earth is spherical.

The Sun is very very far as compared to the size of the earth

The sun shines exactly overhead on the equator on March 20, 2010, the equinox day. This we took from an Astronomy Handbook as the day when sun’s declination is 0 degrees.

We can also measure latitude on any day of the year. But that is another measurement and another adventure in science!

Reference:

How to Measure Sun angle with gnomon

What is Latitude and Longitude

Any location on Earth is described by two numbers--its latitude and its longitude. If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use.
Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols (0, ', ") e.g. 350 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.


Calculations often represent angles by small letters of the Greek alphabet, and that way latitude will be represented by λ (lambda, Greek L), and longitude by φ (phi, Greek F). Here is how they are defined.


Latitude
The latitude angle lambda
Imagine the Earth was a transparent sphere (actually the shape is slightly oval; because of the Earth's rotation, its equator bulges out a little). Through the transparent Earth (drawing) we can see its equatorial plane, and its middle the point is O, the center of the Earth.
To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude λ--northern latitude if north of the equator, southern (or negative) latitude if south of it.

[How can one define the angle between a line and a plane, you may well ask? After all, angles are usually measured between two lines!
Good question. We must use the angle which completes it to 90 degrees, the one between the given line and one perpendicular to the plane. Here that would be the angle (900-λ) between OP and the Earth's axis, known as the co-latitude of P.]


Lines of latitude

On a globe of the Earth, lines of latitude are circles of different size. The longest is the equator, whose latitude is zero, while at the poles--at latitudes 900 north and 900 south (or -900) the circles shrink to a point.

Longitude
On the globe, lines of constant longitude ("meridians") extend from pole to pole, like the segment boundaries on a peeled orange.


Every meridian must cross the equator. Since the equator is a circle, we can divide it--like any circle--into 360 degrees, and the longitude φ of a point is then the marked value of that division where its meridian meets the equator.




Longitude lines or "meridians"

What that value is depends of course on where we begin to count--on where zero longitude is. For historical reasons, the meridian passing the old Royal Astronomical Observatory in Greenwich, England, is the one chosen as zero longitude. Located at the eastern edge of London, the British capital, the observatory is now a public museum and a brass band stretching across its yard marks the "prime meridian." Tourists often get photographed as they straddle it--one foot in the eastern hemisphere of the Earth, the other in the western hemisphere. In the medieval times Ujjain was designated as zero longitude for Indian calculations of astronomical tables. Kanchipuram and Kurukshetra also served similarly

A lines of longitude is also called a meridian, derived from the Latin, from meri, a variation of "medius" which denotes "middle", and diem, meaning "day." The word once meant "noon", and times of the day before noon were known as "ante meridian", while times after it were "post meridian." Today's abbreviations a.m. and p.m. come from these terms, and the Sun at noon was said to be "passing meridian". All points on the same line of longitude experienced noon (and any other hour) at the same time and were therefore said to be on the same "meridian line", which became "meridian" for short.