1. From CIS to CTS
We must transform from Conventional Inertial System to Conventional Terrestrial System using siderial time, θ:
Rotation Matrix
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2. From q-system to CIS
3 rotations. Ri with integer i subscript is rotation about i-axis. Rxu is rotation from u to x.
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3. Elliptic orbit We use spherical coordinates r,λ in (q1,q2)-plane
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4. Angular momentum
λ is arbitrary := 0 !
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5. Integration
With u=1/r
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6. Integration
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7. If ellipse with center in (0,0)
Ellipse as solution
If ellipse with center in (0,0)
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8. Expressed in orbital plane
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9. Parameter change
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10. Further substitution
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11. Transformation to CIS
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12. Velocity
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13. From orbital plane to CIS.
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14. Determination of f .
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15. General equations of motion (Kaula 3.2)I2.1a
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16. Change of variables .
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17. Kaula (3.38) .
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18. We take the zero term out:
Force Function
We take the zero term out:
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19. Conversion of spherical harmonics (Kaula, 3.3)I2.2a
We want to express the terms in the expansion in Kepler variables: .
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20. Kaula 3.72, 3.73.
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21. Kaula 3.74.
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22. Kaula 3.75.
With C20= , e=0.001, a=1.2ae
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23. Orbit with repeating ground track
Applications
Orbit with repeating ground track
Orbit which gives resonance with specific term(s)
Orbit which is sun-syncroneous
Orbit which enables close ”encounter” with an object, such as the poles.
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24. Sol-synkron bane
Så må vi have:
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25. Geostationær
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