Although we now know where the satellite is with respect to its own orbit plane, we still do not know where the satellite is in relation to the Earth's center. To do this, we first need to establish a relationship between the satellite's orbit plane and the Earth's equatorial plane. Fortunately, we can use the (precessed) R.A. of the Ascending Node, the (precessed) Argument of Perigee, the orbit Inclination and the True Anomaly to find this relationship, i.e. the difference in the R.A. coordinate between the satellite's geocentric position at time t and its precessed R.A. of Ascending Node. First, we need to determine the orbit's Argument of Latitude at Time t. This is simply the addition of the orbit's (precessed) Argument of Perigee and its True Anomaly: m(t) = w(t) + n(t) - 360^{o} { INTEGER [ ( w(t) + n(t) ) / 360^{o} ] } m(t) = 116^{o}.7283323 The determined Argument of Latitude can be directly projected onto the Earth's equatorial plane to find the R.A. difference (Da) with the help of the following conditional equation: Da
= cos^{-1} { cosm(t)
/ [1-sin^{2}isin^{2}m(t)]^{1/2}
} Da
= 360^{o} - cos^{-1} { cosm(t)
/ [1-sin^{2}isin^{2}m(t)]^{1/2}
}
Da
= 129^{o}.278845 |
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Step 8: Finding the R.A. Difference Was Last Modified On January 02, 2012 |