099 FINDING THE LATITUDE AND LONGITUDE OF PLACES USING SUN OBSERVATIONS

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099 FINDING THE LATITUDE AND LONGITUDE OF PLACES
USING SUN OBSERVATIONS
To proceed with the experiments discussed here
you need to know the exact directions from your
place of observation. The place of observation
should be a open place with level ground. Finding
the north using a compass cannot be considered as
very accurate as the direction of the earths
magnetic poles are not aligned with the Earths
rotational axis
MATERIAL REQUIRED
gnomon
A thin straight metal rod (about 20 cm length)
can make a simple gnomon
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FINDING THE TRUE NORTH AND DIRECTIONS
A thin straight metal rod (about 20 cm length)
can make a simple gnomon. Ensure that it is
perpendicular to a levelled ground by checking
with a plumb-line (a string tied with a small nut
will do) and a spirit-level. Marking the central
point on the edge of the shadow of the gnomon at
regular intervals of time demonstrates the
movement of the Sun through the day
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Suns Shadow Movement (Watch that the shortest
occurs during the local noon)
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With reference to the diagram to determine the
direction North mark the edge of the shadow at a
given instance of time in the morning and draw a
circle with radius equal to the distance between
the shadow mark and the point where the gnomon
sits in the ground. In the evening the shadow
will reach a point on this circle when the Suns
Altitude is the same as its morning intersection
point. Joining the midpoint of the chord drawn
between these two equal altitude points and the
centre of the gnomon gives accurate North-South
directions. Now mark the north south line using
paint
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LATITUDE MEASUREMENT (ON EQUINOX DAYS)
Measuring shadow angle and Time An equinox in
astronomy is the moment when the Sun passes over
the equator. The event occurs twice a year about
March 20 and September 23. (These dates may vary
slightly. Check up the exact dates with your
planetarium) The word equinox from the Latin word
for equal night. The equinoxes are the two days
each year when the middle of the Sun is an equal
amount of time above and below the horizon for
every location on Earth.
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These measurements should be taken on one of the
two equinox days. Keep the gnomon on the north
south line marked by you. In the morning the
length of the gnomon will be longer. As the Sun
moves up in the sky it will shorten and it will
be the smallest at your north south line. Measure
the length of the shadow from the base of the
gnomon
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Take a graph paper. Draw a straight line (AB)
having the length of the gnomon. Using a
protractor draw a vertical line at one end of
this line (BC). This second line (BC) should have
the length of the shortest shadow. Now connect
the other ends of the lines (AC). Using a
protractor measure the angle F as shown in the
Figure. This gives the value of the observers
latitude
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Longitude Measurement (Dec 25 Apr 15 June 14
and Sep 2)
The plane of the Earths equator is not aligned
with the plane of its orbit around the Sun. It is
offset by an angle of about 23.5 degrees. This
makes variations in the lengths of the durations
of the day-time and the night-time during the
course of a day. Also the orbit of the Earth
around the sun is an ellipse and not a circle. So
Earth moves faster near the Sun and slower when
it is away from the Sun following Keplers II
law. Because of these two reasons the Sun time
will not be accurate always. Only on December 25
April 15 June 14 September 2 the sundials will
show correct time. We can make use of this
advantage for estimating the longitude of our
observing site.
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On one of these days use the gnomon and make
continuous observations and find out the time
when the shadow crosses the north south line.
(This is your local noon). Note down the time
(t1). IST is the time along 82.5 degree
longitude. At 82.5 degree latitude local noon (on
these 4 days) will occur at 12 noon (t2)exactly
Find the difference (t - in minutes) between t1
and t2. Earth completes 360degrees in 24 hrs so
it turns 1 degree in 4 minutes. Divide t by 4.
This gives difference (L - in degrees) between
your longitude and standard (82.5 degree)
longitude of the Central station of India. If the
local noon occurred after 12 noon (IST) then
subtract L from 82.5 else add to 82.5
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For Chennai local noon will occur about 09 min
after 12.00 hrs (IST). So longitude will be 80.25
degrees For Delhi local noon will occur about
21 min after 12.00 hrs (IST). So longitude will
be about 77.2 degrees For Kolkata local noon
will occur about 23.5 min earlier than 12.00 hrs
(IST). So longitude will be 88.4 degrees
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Latitude and longitudes can be estimated on all
days
In the experiments we have explained the methods
of estimating the latitude on Equinox days and
Longitudes on December 25 April 15 June 14
September 2 when the sundials will show the
right time (time correction zero).
After gaining experience using the Equation of
time we can estimate the time correction for any
day and we can perform the experiment to estimate
the longitude. Similarly using the Indian
Astronomical Ephemeris or free-wares like
starcalc we can find the Declination of the Sun
(in our experiment as the days were equinoxes we
used zero declination) and we can perform the
experiment to estimate the latitude.