Surveying Outer SpaceSurveying Outer Space

By Eddie Minaya, Raman By Eddie Minaya, Raman Allawirdi John Jacobson, Luis Allawirdi John Jacobson, Luis

FloresFlores

SpaceSpace

Mathematics and its application to Mathematics and its application to surveying outer space.surveying outer space.

Purpose?Purpose?• To answer some of the most profound To answer some of the most profound

questions in history.questions in history.

The Radius of the EarthThe Radius of the Earth

One of the first questions was asked by One of the first questions was asked by Eratosthenes a Greek astronomer, Eratosthenes a Greek astronomer, geographer, and librarian.geographer, and librarian.

Eratosthenes assumed that the earth was Eratosthenes assumed that the earth was a perfect sphere.a perfect sphere.

He also used Alexandria and Syene as two He also used Alexandria and Syene as two points for measurement.points for measurement.

He knew that from Alexandria and Syene He knew that from Alexandria and Syene was 5,000 stadia (approximately 600ft.) was 5,000 stadia (approximately 600ft.)

C = 2C = 2rrs/c=angle/360s/c=angle/3605,000/C = 7/3605,000/C = 7/3605,000/25,000/2r = 7/360r = 7/360

Radius = 39,789 stadiaRadius = 39,789 stadia Thus his approximation of the earth’s Thus his approximation of the earth’s

radius is 4,574 miles. radius is 4,574 miles. Today's accepted radius is 3,963 Today's accepted radius is 3,963

miles and 13.5 miles less at the miles and 13.5 miles less at the poles. poles.

Distance From The Earth To The Moon

Its All Basic Geometry

Before Measuring You Need To Assume Two Things

1. We know the radius of the earth is approximately 3.963 miles.

2. We have to assume that the earth is perfectly spherical.

2/)180( AOBOBAOAB o

OABOAAPAB cos22

OBACBA

OABCAB

AOBBCA

o

o

180

180

BCAABABCAC sin/sin/

)sin/(sin BCAABABCAC

2/122)]180cos(2[ oACOAACOAOC

Johannes Kepler

2nd law3rd law

1st law

EllipsesEllipse - set of all points in a plane, the sum of whose distances form two fixed points in the plane is constant.

Orbits and Effects on Time• The larger the orbit the

longer the year

1 Mars Year = 365/N(365+N)earth days

(N=the number of extra days it takes the Earth to catch up to Mars after the next synod)

Mars Year

• 322 Days to catch up to Mars•1 Mars Year = 365/322(365+322) earth days•1.13(687) earth days•1 Mars Year = Approximately 776 earth days

Parallax

• The (apparent) displacement of a fixed object with respect to background.

• Caused by displacement of the observer.

-

Using Parallax Measurements to Determine the Distance to Alpha Centauri

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<http://litlotrs.blogspot.com/2007_04_01_archive.html>.<http://litlotrs.blogspot.com/2007_04_01_archive.html>. Brinkworth, Carolyn, and Claire Thomas. "Faulkes Brinkworth, Carolyn, and Claire Thomas. "Faulkes Telescope Educational Guide - Stars - Telescope Educational Guide - Stars -

An An Overview." Overview." University of LeicesterUniversity of Leicester. 1 July 2001. Web. 13 July 2010. . 1 July 2001. Web. 13 July 2010. <http://www.le.ac.uk/ph/faulkes/web/stars/r_st_overview.html>. <http://www.le.ac.uk/ph/faulkes/web/stars/r_st_overview.html>.

"May 2008." "May 2008." InfidelicacyInfidelicacy. Web. 07 July 2010. . Web. 07 July 2010. <http://infidelicacy.blogspot.com/2008_05_01_archive.html>.<http://infidelicacy.blogspot.com/2008_05_01_archive.html>.

Penna, Michael A. Penna, Michael A. Surveying Outer Space: Applications of Trigonometry to Astronomy / by Surveying Outer Space: Applications of Trigonometry to Astronomy / by Michael A. Penna.Michael A. Penna. Newton, MA: Edc/umap, 1982. Print. Newton, MA: Edc/umap, 1982. Print.

"Long Waves of Time." "Long Waves of Time." Visual Statistics with MultimediaVisual Statistics with Multimedia. Web. 07 July 2010. . Web. 07 July 2010. <http://www.visualstatistics.net/East-West/Long Waves of Time/Long Waves of Time.htm>.<http://www.visualstatistics.net/East-West/Long Waves of Time/Long Waves of Time.htm>.

"Groundwater/Surface Water Quantity: Water Quantity & Hydrology - Hydrologic Cycle - Alberta "Groundwater/Surface Water Quantity: Water Quantity & Hydrology - Hydrologic Cycle - Alberta Environment." Environment." Government of AlbertaGovernment of Alberta. Web. 14 July 2010. . Web. 14 July 2010. <http://www3.gov.ab.ca/env/water/GWSW/quantity/learn/what/HC_Hydrocycle/HC1_what<http://www3.gov.ab.ca/env/water/GWSW/quantity/learn/what/HC_Hydrocycle/HC1_what_is.html>. _is.html>.

  "Space Wallpaper - Earth and Moon Wallpaper." "Space Wallpaper - Earth and Moon Wallpaper." Desktop Wallpaper for Computer, IPhone, PSP, IPad Desktop Wallpaper for Computer, IPhone, PSP, IPad Also Screensaver M.mAlso Screensaver M.m. Web. 14 July 2010. . Web. 14 July 2010. <http://www.desktopexchange.com/gallery/Space_wallpaper/Earth_moon>. <http://www.desktopexchange.com/gallery/Space_wallpaper/Earth_moon>.