document.write( "Question 153054: The moon travels an elliptical path with Earth as one focus. The maximum distance from the moon to Earth is 405,500 km and the minimum distance is 363,300 km.
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\n" ); document.write( "(2) For a planet or satellite in an elliptical orbit around a focus of the ellipse, perigee (P) is defined to be its closest distance to the focus and apogee (A) is defined to be its greatest distance from the focus. Show that $\"%28A-P%29%2F%28A%2BP%29\"$ is equal to the eccentricity of the orbit.
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Algebra.Com's Answer #112525 by Edwin McCravy(20056) $\"\"$ $\"About$

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\n" ); document.write( "The moon travels an elliptical path with Earth as one focus. The maximum distance from the moon to Earth is 405,500 km and the minimum distance is 363,300 km.
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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" );
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document.write( "Here is a sketch:\r\n" );
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document.write( " The ellipse represents the orbit of the moon. \r\n" );
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document.write( "So the coordinates of M are (4.055,0)\r\n" );
document.write( "and the coordinates of N are (-3.633,0)  \r\n" );
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document.write( "The ellipse has 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" );
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document.write( "midpoint = (, ),\r\n" );
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document.write( "midpoint = (,) = (0.211,0)\r\n" );
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document.write( "and find that the center of the ellipse is R(0.211,0)\r\n" );
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document.write( "Since the focus of the ellipse is the earth at (0,0) \r\n" );
document.write( "and the center of the ellipse is at R(0.211,0), the value of c\r\n" );
document.write( "is c=0.211 units (distance from center to focus).  That is c = 211 km.\r\n" );
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document.write( "the value of a is a=  (the distance from the ellipse's center\r\n" );
document.write( "(.211,0) to vertex M(4.055,0) is 4.055-.211 or 3.844 units, or a = 384400 km.\r\n" );
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document.write( "Therefore the eccentricity =  \r\n" );
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document.write( "(2) For a planet or satellite in an elliptical orbit around a focus\r\n" );
document.write( "of the ellipse, perigee (P) is defined to be its closest distance to\r\n" );
document.write( "the focus and apogee (A) is defined to be its greatest distance from \r\n" );
document.write( "the focus. Show that  is equal to the eccentricity \r\n" );
document.write( "of the orbit.\r\n" );
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document.write( "Now don't confuse the small  for the semi-major axis\r\n" );
document.write( "with the capital  for the apogee.\r\n" );
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document.write( "(3) Find the Apogee and the Perigee of problem (1)\r\n" );
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document.write( "Apogee = 405,500 km\r\n" );
document.write( "Perigee = 363,300 km \r\n" );
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document.write( "Checking the eccentricity using  =  \r\n" );
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document.write( "Edwin

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