Local Horizon and Sundials

Rosa M. Ros

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International Astronomical Union

Technical University of Catalonia, Spain

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Goals

• Understand the diurnal movement of the Sun
• Understand the annual movement of the Sun
• Understand the movement of the celestial sphere
• Understand the construction of sundials

The Earth rotates and moves�rotation (day / night)� orbital position (seasons)

Activity 1: Four Earth spheres with �the Sun (a lamp) in the middle.�t�The line from the centre of the Sun to the centre of the Earth makes a 23.5° angle with the ground�(which represents the plane of the Equator).

Summer in the Northern Hemisphere

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Winter in the Southern Hemisphere

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Winter in the Northern Hemisphere

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Summer in the Southern Hemisphere

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Activity 2: Parallel Earth � �

� A spotlight illuminates two spheres in the same way and produces the same areas of light and shadow�

Activity 2: Parallel Earth

* Remove the globe from its mounting, take it outside and stand it on a glass

�* Carefully orientate its rotational axis with a compass

�* Turn it so our location is at the top

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Activity 2: Parallel Earth

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Place:

* a doll indicating our position

�* pieces of clay to mark the light / shadow line

(it advances with time)

�* pieces of toothpick to create shadows to study

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Activity 2: Parallel Earth

* The North Pole is on the sunny side so it is summer in the Northern Hemisphere (the midnight sun)��  * The South Pole is in shadow and therefore in the Southern Hemisphere it is winter

Activity 2: Parallel Earth

�* The North Pole is within the area at darkness, so it is in the Northern hemisphere's winter.��* South Pole is illuminated and so it is summer in the Southern hemisphere.

Activity 2: Parallel Earth�

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When the day / night shadow line passes through both poles, it is the first day of spring or the first day of autumn.

Activity 2: Parallel Earth

North H. summer North H. equinoxes North H. winter

South H. winter South H. equinoxes South H. summer

Rotation and celestial movements of day and night�

• Not the same

when seen

from inside

and outside

Celestial sphere "from outside"

... it seems that everything is understood

… but after class, ... he is disconcerted

All schools have an "Astronomy Laboratory"

• They have a playground or school yard
• They have the sky above
• They have clear days and nights
• THESE MUST BE USED!

Activity 3: We will build a model of the horizon visible from school

Begin by photographing all round your location

• local horizon

Rosa M. Ros

Let’s glue the photos together on a supporting platform

• local horizon

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… we must adjust the photographed horizon to align it with the real horizon

• The N - S line and local meridian

Rosa M. Ros

To position the model we can use the compass direction, or better, we can use the projection of the pole above the horizon

Introducing the Earth’s rotation

• axis of the Earth

The altitude of the pole is equal to your latitude

Indicate the apparent path of the sun on the first day of spring or autumn

• Use the Sunrise or Sunset photos

Movement due to Earth’s rotation: �Note the angle of the Sun’s path

• Day - several images near sunset

Movement due to Earth’s rotation: �Note the angle of the star trails

• Night – a time exposure of the stars

Rotational movement in the model

The inclination of the Sun’s apparent path and of the star trails depend on latitude

Solar paths on first day of each season (note the different durations)

• Summer Solstice
• Autumnal / Vernal Equinox
• Winter Solstice

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Orbital motion leads to the seasonal positions

• Summer
• Spring / Autumn
• Winter

• Angle between equator and Tropic of Cancer or Tropic of Capricorn = 23.5 º

The Earth’s orbital motion leads to the change of the position of sunsets every day

• 3 sunsets:

Winter – Spring or Autumn – Summer

Viewing the �"meridian" in the model

Rosa M. Ros

…around the pole - circles

…near the equator the paths change from concave to convex

…the model is no more than an Equatorial Sundial!

…other sundials can be made from the equatorial one

… the horizontal sundial

…and the vertically oriented E-W sundial

… and with the Sun (or with a flashlight) we observe the model acting like a sundial

The three sundials in the model

Activity 4: Let's see how to build a �very simple “equatorial” sundial!

• Northern Hemisphere

• Southern Hemisphere

Activity 4: “equatorial” sundial!

• Fold the pattern along the dotted line
• Cut the stylus for your latitude. The yellow part goes above the plane

Activity 5: How to Read the Time

Solar Time + Total Adjustment = Wristwatch Time

Total Adjustment =

• Longitude Adjustment
• Summer / Winter Adjustment
• Equation of Time Adjustment

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Activity 5: Read the time, Longitude Adjustment

• The world is divided into 24 time zones from the Zero or Greenwich meridian.
• We must know the local longitude and "Standard"

meridian longitude of your area.

• Use sign + to the East and sign - to the West.
• Write longitudes in h, m and s (1º=4m).

Activity 5: Read the time, �Summer / Winter Adjustment

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• Many countries add an hour in summer.
• This change of clocks for summer / winter is a decision of the government of the country.

Activity 5: Read the time, �Equation of Time Adjustment

• The Earth revolves around the Sun according the law of areas, i.e. not a constant motion. We define the average time (of mechanical watches) as the average over a full year.
• The equation of time is the difference between "Real Solar Time" and "Mean Time” in minutes of time

Activity 5: Reading Time

Example 1: Barcelona (Spain) on May 24^th

For example at 12h of solar time (noon), our watches indicated

(Solar time) 12h + 47.9 m = 12h 47.9 m (wristwatch time)

Activity 5: Reading Time

Example 2: Tulsa, Oklahoma (USA) November 16^th

For example at 12h solar time (noon), our watches will indicate

(Solar time) 12h + 8.7 m = 12h 8.7 m (Wristwatch time)

the model serves to orientate us …

… to observe and understand …

Conclusions

• We understand the "views" of the model from inside and outside
• We reach levels of abstraction that let us read books and make comments
• We feel oriented to the real horizon
• We see that the sunrise is not always due East and that the Sunset is not always due West

Rosa M. Ros

Thank you very much �for your attention! �