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- We could
do it by the method used by Eratosthenes, but there is a simpler
method
- Go to a
beach on the west coast of your country where you can see the
sun dipping below the horizon into the sea at sunset. Choose a
beach with a tall building , or a high cliff, nearby. Do the following
experiment with the help of a friend.
- Your friend
stands on the beach . You stand on top of the building on the
terrace. Because you are at a height, you can see further.
- Both of
you watch the moment of the setting sun. Because you can see further,
you will continue to see the sun even after it has dipped below
the horizon for your friend on the beach.
- Your friend
signals to you the moment when she sees the sun dipping below
the sea horizon. You measure the time between this moment and
the moment when you see the sun dipping below the horizon. You
can measure the time with a stopwatch, or with your one second
pendulum.
- From a height
H, how
far can you see ? Lets call this distance X.
You can calculate X
from Pythagorus theorem . The answer is that you can see for a
distance X = 2 x
H x R, where R
is the radius of the earth.
- Lets say
that the time measured by you in step (5) above was half a minute.
The ratio of 24 hours to half a minute is 2880.
- This is
also the ratio of the circumference of the earth to X
(2 x pi x R ) /
X= (24 x 60) / (½) = 2880
- From this
we deduce that X
= (2 x pi x R) / 2880
Therefore, X² =
(4 x pi² x R² ) / (2880) ² = 2HR
Therefore, R =(
(2880) ² x H) / 2 pi²
- This gives
us the radius of the earth in terms of the height of the building.
All that we have to do now is to measure the height of the building.
How do you measure the height of a building
with a string and a stone ?
- In the above
we assumed that the time difference was one half minute. In the
actual measurement, lets say that it is T
seconds. By the same kind of argument as in 8 above we get
R=[( (24 x 60 x
60)/T )²]
x [H / (2 x pi²)]
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