v_ijk

We are nearly ready to determine the final state vector (position and velocity vectors) of the satellite. Several final vectors and terms are required. First, we need an intermediate vector that will be determined using the following equation:

Y_i = N₂₂r₃₂ - N₃₂r₂₂
Y_j = N₃₂r₁₂ - N₁₂r₃₂
Y_k = N₁₂r₂₂ - N₂₂r₁₂

Y_i = 7.2727036 x 10⁹ km³
Y_j = 8.0465103 x 10⁹ km³
Y_k = -9.0278558 x 10⁹ km³

Next, we need a handy value to "tidy up" the loose values determined in the previous step:

W = [ m / (N₁N₂) ]^1/2

W = 3.7649279 x 10^-6 km^-1·s^-1

Finally, the velocity vector can be found by using the following equation:

v_i = W [ Y_i / r₂ + N₁₃ ]
v_j = W [ Y_j / r₂ + N₂₃ ]
v_k = W [ Y_k / r₂ + N₃₃ ]

v_i = 3.8589872 km/s
v_j = 4.2763114 km/s
v_k = -4.8070493 km/s

Finally, the entire "state vector" satellite orbit elements are known and are stated in their entirety below. The epoch of this state vector corresponds to the second observation of the satellite.

BACK TO STEP #12

PROCEED TO STEP #14