document.write( "Question 152620: Would someone kindly help me with this algebra question?\r
\n" ); document.write( "\n" ); document.write( "A satellite has an elliptical orbit around the earth with one focus at the earth’s center, E. The earth’s radius is 4,000 miles. The highest point that the satellite is from the surface of the earth is 800 miles, and the lowest is 200 miles. What is the eccentricity of the satellite’s orbit? \r
\n" ); document.write( "\n" ); document.write( "Thank you in advance for sharing your valuable knowledge :0) !!!\r
\n" ); document.write( "\n" ); document.write( "Grateful,
\n" ); document.write( "Jai \n" ); document.write( "

Algebra.Com's Answer #112211 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Eccentricity = c/a \r\n" );
document.write( "where c is the distance from the center to the focus of the ellipse \r\n" );
document.write( "a is the distance from the center to a vertex \r\n" );
document.write( "\r\n" );
document.write( "Here is a sketch:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "On this graph 1 unit = 1000 miles. The circle represents \r\n" );
document.write( "the earth with the center at the origin. so point P has\r\n" );
document.write( "coordinates (4,0) and point Q has coordinates (-4,0) \r\n" );
document.write( "\r\n" );
document.write( "The green ellipse represents the orbit of the satellite. \r\n" );
document.write( "\r\n" );
document.write( "Where 1 unit = 1000 miles. So the satellite is 800 miles or 0.8 units\r\n" );
document.write( "from the earth's surface at point M, and 200 miles or 0.2 units from \r\n" );
document.write( "the earth's surface at point N. PM is 800 miles or 0.8 units and\r\n" );
document.write( "QN is 200 miles or 0.2 units. \r\n" );
document.write( "\r\n" );
document.write( "So the coordinates of M are (4.8,0)\r\n" );
document.write( "and the coordinates of N are (-4.2,0)  \r\n" );
document.write( "\r\n" );
document.write( "Unfortunately the software does not close the green ellipse at its \r\n" );
document.write( "vertices, but its vertices are at M and N. The center of the ellipse,\r\n" );
document.write( "R, is the midpoint between M and N, so we use the midpoint formula\r\n" );
document.write( "\r\n" );
document.write( "midpoint = (, ),\r\n" );
document.write( "\r\n" );
document.write( "midpoint = (,) = (0.3,0)\r\n" );
document.write( "\r\n" );
document.write( "and find that the center of the ellipse is R(0.3,0)\r\n" );
document.write( "\r\n" );
document.write( "Since the focus of the ellipse is at the center of the earth (0,0) \r\n" );
document.write( "and the center of the ellipse is at R(0.3,0), the value of c\r\n" );
document.write( "is c=0.3 units (distance from center to focus).  That is c = 300 miles.\r\n" );
document.write( "\r\n" );
document.write( "the value of a is a=  (the distance from the ellipse's center\r\n" );
document.write( "(.3,0) to vertex M(4.8,0) is 4.8-.3 or 4.5 units, or a = 4500 miles.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the eccentricity =  \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );