N

 3563.8925 km 5052.4587 km 6016.5229 km r = -346.24563 km 1056.2713 km 2392.5540 km 6251.1122 km 5011.6366 km 3143.8252 km

 Variable Symbol Value First Geocentric Range r1 7,204.0002 km Second Geocentric Range r2 7,194.4110 km Third Geocentric Range r3 7,197.6732 km

 -8,338,127.7 km2 -8,669,878.9 km2 16,044,659 km2 Z = 13,722,552 km2 14,268,579 km2 -26,405,705 km2 5,513,829.1 km2 5,733,199.8 km2 -10,610,000 km2

Another intermediate matrix will be required before we can finally determine the velocity vector of the satellite. The intermediate "N Matrix" is determined by using the following equations:

N11 = r1Z12 + r2Z13 + r3Z11
N21 = r1Z22 + r2Z23 + r3Z21
N31 = r1Z32 + r2Z33 + r3Z31

N12 = Z11 + Z12 + Z13
N22 = Z21 + Z22 + Z23
N32 = Z31 + Z32 + Z33

N13 = (r2-r3)r11 + (r3-r1)r12 + (r1-r2)r13
N23 = (r2-r3)r21 + (r3-r1)r22 + (r1-r2)r23
N33 = (r2-r3)r31 + (r3-r1)r32 + (r1-r2)r33

 -7.0410564 x 109 km3 -963,347.6 km2 14,100.605 km2 N = 1.1587796 x 1010 km3 1,585,426 km2 17,389.173 km2 4.6560117 x 109 km3 637,028.9 km2 -21,954.234 km2

We can also define two values using this matrix that will be used in the next step:

N1 = [ (N11)2 + (N21)2 + (N31)2 ]1/2
N2 = [ (N12)2 + (N22)2 + (N32)2 ]1/2

N1 = 1.4336385 x 1010 km3
N2 = 1,961,484.1 km2

BACK TO STEP #11

PROCEED TO STEP #13

 SITE MAP Step 12: N Matrix Was Last Modified On September 23, 2013