Solar Eclipse

Of all the celestial wonders ,Solar eclipse is one of the events many people can observe if they are at the right time, and the right place without instruments. And its mechanism,or why it happens, is also widely known and there are so many references. Recently there are a lot of well written web site to offer us an abundant good informations. A good example is Solar Eclipse: Why Eclipses Happen by Ron Hipschman.

Any diagram,which shows a side view of the alignments of the three participants(Sun, Moon & Earth),is widely out of scale.

What we do explore here is how to describe this astronomical phenomenon using the actual object sizes and distances between them.

How the alignment looks like in the true scale.

The sizes of the Sun , Moon, and the Earth
	Radius-km(mile)	Ratio to Earth's Radius
Sun	695,000km (431,945)	109
Earth	6,378km (3,964)	1.0
Moon	1,737.4km (1,079.8)	0.273

The Earth's distance to the Sun and Moon
	Nearest distance -km(mile)	Farthest distance-km(mile)	Variance in %
Sun	Perihelion--147,101,455km (91,341,000)	Aphelion --152,098,155km (94,448,000)	3 %
Moon	Perigee--356,749km (221,000)	Apogee --406,282km (253,000)	12 %

As a first model, earth's distance to the Sun and Moon are set to the mean value,i.e.

To the Sun: 149,600,000 km

To the Moon: 384,400 km

Then,this model looks like this.

**********************************solar_eclipse_model_1.dwg ********************************

To create this drawing :
Load eclipse_model_s.lsp (load "eclipse_model_s")
Then from command line, type test

As seen in this drawing, it is very difficult (if not impossible) to draw lines from the Sun tangent to the Moon, then extending to the Earth. So each of the three objects is displayed in three separate view ports, and all the line drawing operations become possible by switching from one view port to the other.

***************************solar_eclipse_model_0.dwg ***************************

To create this drawing :
Load solar_eclipse.lsp (load "solar_eclipse")
Then from command line, type (setup_solar_eclipse)
Texts in each viewport is added using TEXT command and text height is adjusted for each viewport.

Total Darkness(Umbra) and Partial Darkness(Penumbra) Area display

Model-1: Widest darkeness Area :

This happens when the Earth is farthest from the Sun, and the Earth is closest to the Moon.i.e.

Distance To the Sun: 152,000,000 km

Distance To the Moon: 356,700 km

Then,this model gives the following shadows of the Moon (Umbra & Penumbra) on the Earth.

Diameters of the Umbra & Penumbra are 260 km( 162 miles ), and 6700 km( 4164 miles ),respectively.

****************************************solar_eclipse_00.dwg ****************************************

To create this drawing :
Load solar_eclipse.lsp (load "solar_eclipse")
Then from command line, type case_1

Basic assumptions

References

Atlas of the SKIES, Surrey,England: TAJ Books,2003
Brewer, Bryan : Eclipse. Seattle,Washington: Earth View, 1978 This book was published in time for the total eclipse on Feb 26,1979,along Columbia River, in Oregon,USA.
Chambers,G.F.: The Story of Eclipses. D.Appleton & Co.,New York,1912.
Dyson,F. and Woolley,R.v.d.R.: Eclipses of the Sun and Moon, Oxford Univ. Press,London,1937.
Flammarion,C.: The Flammarion Book of Astronomy,Simon & Schuster,New York,1964
Mitchell,S.A.: Eclipses of the Sun,Columbia Univ. Press,New York,Fifth edition ,1951
Todd,M.L.: Total Eclipses of the Sun,Little,Brown, & Co.,Boston,1900.

Go to Fun_Math Content Table Earth Moon & Sun

All comments should be sent to Takaya Iwamoto

Last Updated July 9-th, 2006