How to find sun’s height above horizon?

By Aurimas Valancius III e2012

Ecliptic

• The apparent yearly path of the Sun through the stars is called the ecliptic.

• This circular path is tilted 23.5 degrees with respect to the celestial equator because the Earth's rotation axis is tilted by 23.5 degrees with respect to it’s orbital plane.

Solstice• The farthest northern point above the celestial

equator is the summer solstice, and the farthest southern point is the winter solstice.

• The winter solstice usually occurs on December 21 to 22 each year in the Northern Hemisphere, and June 20 to 21 in the Southern Hemisphere.

Equinox• The ecliptic and celestial equator intersect at

two points: the vernal (spring) equinox and autumnal (fall) equinox.

• The Sun crosses the celestial equator moving northward at the vernal equinox around March 21 and crosses the celestial equator moving southward at the autumnal equinox around September 22.

Targets

• To find sun’s height above the horizon in equinox.

• To find sun’s height above the horizon in Solstice.

• To find sun’s height above the horizon in March 5.

• To compare results.

Hypothesis

• I think, that sun’s height over the horizon will be the highest in summer.

The way

• On the equinoxes the Sun moves along the horizon.

• The easiest way to find sun’s height over the horizon is when she is in equinox.– March 21– September 23

celestial equator

Equinoxes

• I need this formula:

– - the Sun's maximum angular distance

– - geographic latitude– - The Sun’s height over

the sky equator is 23.5 degrees.

N

S

Earth horizon

Equinox

• I found the Sun’s height over horizon in equinox:

550

Solstice in summer

• If I want to find sun's height when she is in solstice. I need to find .

--

+ +

03-21

06-22

12-23

09-22

Solstice in winter

• I found Sun’s height over horizon in winter.

--

+ +

03-21

06-22

12-23

09-22

Sun's height above the horizon on March 5

• I found Sun's height above the horizon on March 5 in Taurage.

--

+ +

03-21

06-22

12-23

09-22

03-05

• I found .

N – day number after March 21.

--

+ +

03-21

06-22

12-23

09-22

351

Sun's height above the horizon on March 5

• I found Sun's height above the horizon on March 5 in Taurage.

--

+ +

03-21

06-22

12-23

09-22

Trutnov

• I found Sun's height above the horizon on March 5 in Trutnov.

500

Madrid

• I found Sun's height above the horizon on March 5 in Madrid.

400

Nuremberg

• I found Sun's height above the horizon on March 5 in Nuremberg.

490

Athens

• I found Sun's height above the horizon on March 5 in Athens.

370

ResultsDay Results

Equinox 350

Solstice in summer 58.50

Solstice in winter 11.50

City Results Taurage 32.530

Trutnov 37.530

Madrid 47.530

Nuremberg 38.530

Athens 50.530

March 5

Inference

• My hypothesis had reasserted.• On the summer solstice the mid-day shadows

are much shorter because the Sun is much higher above the horizon.

• is same in all countries, but isn’t.• Sun’s height is the biggest in Athens.

Thank you for your attention