a_W

Now that we have determined the semi-major axis and inclination of the satellite's orbit, we can use this knowledge to determine the orbit's right ascension of ascending node (RAAN). This value denotes the point at which the satellite's orbit plane crosses the Earth's equatorial plane as the satellite crosses (ascends) from the southern to the northern hemisphere.

First, we need the average right ascension of the satellite streak:

a_av = [ a₁ + a₂ ] / 2

a_av = 291°.66717

Next, we can calculate the RAAN. Be very careful when considering the conditions or the determined orbit can have the wrong plane!

If Da>0 and Dd>0 then a_W = a_av - sin^-1 [ tand_av / tan(i) ]

If Da>0 and Dd<0 then a_W = a_av - 180° + sin^-1 [ tand_av / tan(i) ]

If Da<0 and Dd>0 then a_W = a_av + sin^-1 [ tand_av / tan(i) ]

If Da<0 and Dd<0 then a_W = a_av + 180° - sin^-1 [ tand_av / tan(i) ]

Da > 0 and Dd < 0

a_W = 136°.66

RAAN is normally expressed in degrees, not hours. The RAAN indicates the right ascension of the node created by the intersection of the equatorial plane of the Earth and the satellite's orbit as the satellite ascends (moves from south to north).

PROCEED TO STEP #7