Rugved Pund
Jyotirvidya Parisanstha
Pune
Observing a shadow of a pole, everyday at
the same time, helps us know to a lot
about the motion of sun in the sky.
 The shadow is a guide to the exact
angular position of the Sun at any time of
the day.
 Thus, the shadow is a very simple yet
effective tool in understanding the
complicated motion of the Sun in our sky.

The movement of the shadow can be better
understood using a sundial, but, even a simple
pole or a stick can prove to be a good way to
know the Sun.
 Shadows can tell us many things, like, the
North-South Apparent Motion, the Equation
of Time, the True North vs Magnetic North,
the Analemma and much more.
 Even, little mathematics is needed to
appreciate all its complicated paths.

If observed from any location in the
tropical region, the shadow appears to be
exactly under the object two times a year.
(Or one time if the location happens to
lie on the Tropical Lines).
 This happens when the Sun is exactly at
Zenith

The Sun exhibits Northward and
Southward apparent motions with its
maximum declination to be ±23.45˚.
 When the Sun has its declination equal to
the latitude of the place, then the sun is
exactly at zenith at the Local Solar Noon.
 This is a result of the tilt of the Earth’s
axis.

Northern Hemisphere
Equator
To study motion of the shadow and hence
the motion of the sun in the sky.
 Effect of Latitude on Sun’s Motion- daily
and yearly.
 Demonstrate the difference between the
Standard Time and Local Solar Time.

1.
Calculation of the day of Zero Shadow
for respective place (from its latitude).
2.
Set up the apparatus for observing and
verifying the phenomenon.
3.
Calculate the number of days the Zero
Shadow Day took place before the
Solstice, and add the same number of
days to get the next Zero Shadow Day.

To calculate the Sun’s declination for any
day of the year,
  284  n 
  23.45 sin 360

  365.25 
Rearranging equation to find zero shadow
day for respective latitude
 1    365.25 
n  sin 
 
  284
 23.45  360 

Here,
δ is declination of sun (degrees)/ latitude
n is the ordinal day number, with 1 from 1st
January.



The Equation of Time describes the lag or
the advance of the True Sun w.r.t. the Mean
Sun, thus describing the deviation of the time
of ‘Solar Noon’ from ‘Clock Noon’.
Use of Equation of Time tables is
recommended since the actual calculations
are complicated and extensive.
The value obtained is to be subtracted, to
correct Clock time for Solar time.
Whether the sun is at the zenith can be
verified in different ways.
 By making an ‘Inclino-meter’.
 By erecting any tube, pipe, pole etc
perpendicular to the ground.
 By hanging a ball at the tip of an overhang
bar.
JVP Zero Shadow Day
The phenomenon of Zero Shadow Day,
was used by Eratosthenes to find the
radius of Earth to surprising degree of
accuracy!
 By finding the angle the sun is from the
zenith (from the Inclino-Meter), and then
doing some very simple arithmetic, one
can easily find the radius of the earth.

7
d(AS)

360 Circumfere nce
The Zero Shadow Day activity helps the
students understand a lot about the
motion of the Sun in the sky especially
but not restricted to the North-South
Apparent Motion, Equation of Time, and
even the radius of the Earth.
 The calculations help one develop a deep
understanding of the Sun’s exact
movement across the Celestial Equator.

Thank You!
RUGVED PUND
[email protected]