STEP 1: ORBIT ELEMENTS

vijk



 
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
Second Geocentric Range r2 7,194.4110 km
Gravitational Parameter m 398600.44 km3/s2
Modulus of First N Row N1 1.4336385 x 1010 km3
Modulus of Second N Row N2 1,961,484.1 km2

 

-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 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:

Yi = N22r32 - N32r22
Yj = N32r12 - N12r32
Yk = N12r22 - N22r12

Yi = 7.2727036 x 109 km3
Yj = 8.0465103 x 109 km3
Yk = -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-1Ěs-1

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

vi = W [ Yi / r2 + N13 ]
vj = W [ Yj / r2 + N23 ]
vk = W [ Yk / r2 + N33 ]

vi = 3.8589872 km/s
vj = 4.2763114 km/s
vk = -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.

Orbit Element Symbol Value
Epoch Time tepoch 23:05:28.22 UTC January 3, 2012
x Position x 5052.4587 km
y Position y 1056.2713 km
z Position z 5011.6366 km
x Velocity 3.8589872 km/s
y Velocity 4.2763114 km/s
z Velocity ż -4.8070493 km/s


BACK TO STEP #12

PROCEED TO STEP #14



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Step 13: Velocity Vector Was Last Modified On September 23, 2013