Is this system symetric enough? - classical dynamics

[Choi hoseung]

I'm designing a satellite( flying in formation).
It looks like 3 couples of daughter-satellites(180degree apart) orbiting around the mother satellite in 3 orthogonal planes to measure flyby anomally effect. I want to measure the effect in 3-separate directions. But I'm afraid that the orbiting pairs would effect each others in non-linear way. Will the other two couples the ohter? then at least is it possible to calibrate that effect in systematic calculation? or is the effect only able to be computed numerically? - I need it to be solvable in analytic way.

to make it celarer, let's say:
at time = 0;
mother is at the origin(0,0) - Center of Mass
daughter-x1 at (-1,0,0) x2 (1,0,0)
y1 (0.2.0) y2(0.-2.0)
z1(0.0.3) z2(0.0-3) (distinct separations to avoid collision)
then, they start to orbit in independent periods.


- one more, if this system it self orbit around the earth, is the fluctuation(due to varying configuration of its daughters) of mother's kinetic energy predictable? how about individual daughters kinetic energy?

 

[LightHero]

The answer to your questions depends on the specific model you are using. It is possible to calculate the non-linear effects of the orbiting pairs on each other, but it would likely require numerical methods as opposed to analytical. If the system is orbiting around the Earth, then the fluctuation of the mother's kinetic energy can be predicted, but again this will depend on the specific model you are using. The same applies to the individual daughters' kinetic energies.