Project Paridhi

– Lets Measure the Earth again

OBJECTIVE

TO MEASURE THE CIRCUMFERENCE OF THE EARTH USING ERATOSTHENES METHOD – Using simple, backyard tools!

HISTORY‡ Eratosthenes was the first person

to calculate the circumference of the Earth

‡ He derived that the Earth is round and thus its circumference can be easily measured.

‡ He knew that the Sun would be overhead in Syene ( which is on tropic of Cancer ) at MID-DAY day of Summer Solstice as sunlight lit a very deep well.

‡ On the same day, even at MID-DAY , The things would cast a shadow.

‡ The then measured the distance between the two places and use the following explanation to calculate the Circumference of Earth.

• You have to calculate the distance between you and the point where the Sun is overhead

• Also find ANGLE ‘θ’

What is SUN ANGLE ?

Paridhi Experiment

Any Object will cast its shortest shadow exactly at Local Noon.On the day of Experiment, that shortest shadow will be a “ Zero “ shadow or no shadow for some place.You have to find the shortest shadow for your location by marking the shadows at regular intervals. The procedure is mentioned in the following slidesTo mark a shadow, you have to identify the umbra and penumbra first

MATERIAL REQUIRED GNOMON STICK (or any vertical object such as Pepsi Bottle or cricket stump!) DRAWING BOARD and PINSSPIRIT LEVEL AND PLUMBLINE (OPTIONAL) PENCIL, LONG RULER, PROTRACTOR WHITE SHEETCALCULATOR

Setup Procedure

Make sure the drawing board is leveled. Use a spirit leveler. The bubble should come in the center

Secure the A4 sheet to the board. Use thumb pins on three corners first to fasten the paper.

On the fourth corner, place the gnomon base and make sure that its center is on the paper as shown in the picture.

Place the gnomon. Check if it is perpendicular by using a plum line as shown in the picture.

Experiment Procedure

Mark the edge of the Dark Shadow “ Umbra “.

Make sure a sharpened pencil is handy.

Make sure not draw a line or a circle. Make a pin point. Just a small dot

Make shadows after a regular interval of 5 minutes. Use a watch to keep time.

As the local noon approaches, mark shadows in every 2 minutes to increase accuracy.

Experiment Procedure

After marking all the shadow points, make a point through the Gnomon base. There is a small void in the center.

Connect all the marked dots to the single dot as shown in the picture.

Measure the length of all the shadows.

Note down the length of the shortest Shadow.

Measure and note down the length of the Gnomon stick.

Calculations* IDENTIFY THE LATITUDE WHERE SUN

WILL BE OVERHEAD.

* CALCULATE NORTH-SOUTH DISTANCE BETWEEN YOUR CURRENT LOCATION AND THE ABOVE - ‘Distance’

* * DRAW AN L SHAPED ANGLE WITH THE GNOMON HEIGHT AND SHADOW.

* MEASURE THE ANGLE θ BETWEEN THE SHADOW AND THE GNOMON STICK.

* USING THIS EQUATION:

(360°/θ)* (distance) = Circumference

WE CAN FIND THE EARTH’s CIRCUMFERENCE!

CALCULATIONS

Use the formula

Circumference of Earth = (360 x D)/ θ

Where

D = Distance between you and point where Sun is overhead

Θ = The Sun Angle you calculated

( You will get Sun Angle from the Experiment )

PARIDHI WEBSITE – www.space-india.org/projectparidhi

For submitting results, please go through the registration process. This is important.

DATA SUBMISSION

GOOGLE EARTH: To find Distance between your location and Where the Sun comes overhead.

It has feature which can be used to measure the distance between two points.

This feature is called “ Ruler “ For Summer Solstice find distance till - Tropic of

Cancer For Winter Solstice find distance till – Tropic of

Capricorn For Spring and Autumn Equinox find distance till

Equator The feature is simple to use and will require some

practice and curiousity.

Google Earth Software

PRECAUTIONS

Measure accurately the length of the object and the shadow

Mark the center of the base of the object correctly

Make sure that the object does not move while taking readings.

Find the distance (as the crow flies) between your location and Tropic of Cancer/Capricorn – during Solstice or Equator – during Equinox! You can use Google Earth or other tools.

JOIN HANDS WITH US FOR PARIDHI!Website:http://goo.gl/ij1yx

Or http://space-india.org/spaceindiaorg/paridhi/