Da

 Element Symbol Value Epoch to 05:54:21.171 UTC December 16, 2007 Inclination i 51o.9970 R.A. of the Ascending Node aW0 251o.0219 Eccentricity e 0.0001492 Argument of Perigee w0 33o.8641 Mean Anomaly at TLE Epoch Mo 326o.2322 Mean Motion n 12.62256095 orbits / solar day Propagation Time Dt 1.7677141 solar days Mean Anomaly at Time t M(t) 1.37777389 radians (78o.940629) True Anomaly at Time t n(t) 78o.95065818 Semi-major Axis a 7791.787473 km Perigee Distance P 7790.624938 km Geocentric Distance r(t) 7791.564499 km Precessed R.A. of Asc. Node aW(t) 245o.6400244 Precessed Arg. of Perigee w(t) 37o.77767416

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) - 360o { INTEGER [ ( w(t) + n(t) ) / 360o ] }

m(t) = 116o.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-sin2isin2m(t)]1/2 }
for 0o < i < 90o AND 0o < m
(t) < 180o OR 90o < i < 180o AND 180o < m(t) < 360o

Da = 360o - cos-1 { cosm(t) / [1-sin2isin2m(t)]1/2 }
for 0o < i < 90o AND 180o < m
(t) < 360o OR 90o < i < 180o AND 0o < m(t) < 180o

Da = 129o.278845

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 SITE MAP Step 8: Finding the R.A. Difference Was Last Modified On January 02, 2012