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The LANDSAT C Earth resources satellite has a nearly circular orbit with an eccentricity of 0.00132. At perigee the satellite is at an altitude (measured from the earth's surface) of 417km.
Generally the equation for perigee radius is mathematically given as
[tex]r_p = R_E+Z_P\\\\=6378+417\\\\=6795km[/tex]
the equation for orbit is
[tex]r_p = \frac{h^2}{u}*\frac{1}{1+e}\\\\6795 = \frac{h^2}{398600}*\frac{1}{1+0.00132}\\\\h = 52077.5km^2/s[/tex]
the equation for velocity at perigee is mathematically given as
[tex]V_p = \frac{h}{r_p}\\\\= \frac{52077.5}{67.95}\\\\=7.67km/s[/tex]
the equation for Apagee radius is mathematically given as
[tex]r_a = \frac{h^2}{u} * \frac{1}{1-e}\\\\= \frac{52077.5^2}{398600} * \frac{1}{1-0.00132}\\\\= 6812.97km[/tex]
the equation for altitude at Apagee is mathematically given as
[tex]Z_a = r_a - R_E\\\\=6812.97-6378\\\\=434.96km[/tex]
the equation for period
[tex]Period T = \frac{2\pi}{u^2} * (\frac{h}{\sqrt1-e^2})^3\\\\= \frac{2\pi}{398600^2} * (\frac{52077.5}{\sqrt1-0.00132^2})^3\\\\= 5585.41s[/tex]
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