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Paper Plate Education
"Serving the Universe on a Paper Plate"

Video Excerpts: Latitude by Polaris 

The following pictures and narration are excerpted from the Paper Plate Astronomy  video.

Here we will show how a navigator determines her latitude from the altitude of Polaris, the North Star.  

Dsc00001.jpg (153602 bytes)As our navigator’s ship travels from the equator...

Dsc00002.jpg (154383 bytes)...the altitude of Polaris above her horizon not only increases, but is congruent with her latitude.  

Dsc00003.jpg (158103 bytes)By the time she reaches 90 degrees of latitude...

Dsc00004.jpg (160566 bytes)...the altitude of Polaris is likewise 90 degrees.

Draw a circle to represent the earth on 10-inch white plate.  Extend the equator out to the edge,  and extend the north pole out to the edge, too. 

Dsc00005.jpg (144238 bytes) Label these the equator, celestial equator or C.E. , north, and Polaris at the north celestial pole.

Polaris is so far away that its starlight is coming in parallel to the north celestial pole.  

Dsc00006.jpg (159167 bytes)Draw several parallel lines to reinforce this notion.  Looking up any one of these lines of sight, no matter where you are on the earth will end on the north star.

Dsc00007.jpg (152615 bytes)Use a protractor and label the latitude, shown here in increments of 15 degrees.

From about this part of the earth...to about here, cut a slit along the perimeter of the earth.

Dsc00008.jpg (136410 bytes)Mark a 3 by 5 card as shown... Draw some water with a ship on it... [This is the direction our navigator would look toward the horizon, so ] label the red arrow “To Horizon”.  This the direction to our navigator’s horizon, up from which she measures the altitude of the stars.

Dsc00009.jpg (144468 bytes)Slip the card under the slit on the plate so the waterline is on the edge of the earth.  

Dsc00010.jpg (143040 bytes)With the vertical line visible at the earth’s center, mark the card.

Dsc00011.jpg (162672 bytes)Cut out around the ship and punch out the two holes, as shown.

Dsc00012.jpg (140884 bytes)On a second 3 by 5 card, draw a red arrow and label it North.  Swing an arc...punch a hole... and cut it out as shown.

Dsc00013.jpg (161907 bytes) Dsc00014.jpg (157665 bytes) Fasten the arrow cutout to the ship cutout at the 90 degree bend. 

Dsc00015.jpg (147211 bytes)And then affix the hole rig to the plate.

Using the Latitude by Polaris

Dsc00016.jpg (151434 bytes)If our ship begins a journey north at the equator, the navigator looks this way to see starlight from Polaris coming in tangent to the equator.  

Dsc00017.jpg (145667 bytes)From the perspective of the ship, the direction the North Star is straight ahead toward the northern horizon.  The altitude of Polaris is zero degrees.

Dsc00018.jpg (151370 bytes)As it travels north...

Dsc00019.jpg (160875 bytes)...the angle between the horizon and Polaris, the altitude, is 30 degrees...

Dsc00020.jpg (162554 bytes) At the same time, the angle from the equator to the ship’s position, the latitude, is also 30 degrees. 

The ship moves north.  

Dsc00021.jpg (154504 bytes)When the altitude of Polaris is 45 degrees, the ship’s latitude...

Dsc00022.jpg (154670 bytes)...is also 45 degrees. 

Dsc00023.jpg (156986 bytes)By the time the ship reaches the north pole, the pole star is directly overhead --altitude equals 90 degrees...

Dsc00024.jpg (155305 bytes)At the pole, the latitude is 90 degrees.

Dsc00025.jpg (152482 bytes)For a different perspective you can focus in on the ship to see the angular height of Polaris rising congruent with angle of  latitude.

 

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Copyright 2012 Chuck Bueter.  All rights reserved.