Abstract
The disturbing function of the Moon (Sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the Moon (Sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elementsl, l′, F, D and Γ of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements ω and Ω of the satellite so that analytic integration is simple and the results accurate over a long period of time.
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Abbreviations
- G :
-
the gravitational constant
- M :
-
the mass of the Earth
- m′ :
-
the mass of the Moon
- m″ :
-
the mass of the Sun
- r :
-
the geocentric position vector of the satellite
- r :
-
|r|
- ř :
-
r/r
- r′ :
-
the geocentric position vector of the Moon
- r′ :
-
|r″|
- rř′ :
-
r′/r′
- r″ :
-
the geocentric position vector of the Sun
- r″ :
-
|r″|
- ř″ :
-
r″/r″
- a′ :
-
the mean distance of the Moon from the Earth, defined in such a manner that the constant part in the expansion of the lunar parallax equals unity
- a″ :
-
the mean geocentric distance of the Sun
- γ′:
-
the angle betweenr andr′
- γ″:
-
the angle betweenr andr″
- λ, μ, ν, λ′, μ′, ν′, λ″, μ″, ν″:
-
the rectangular components ofř, ř′ andř″ respectively in the geocentric equatorial coordinate system
- R c :
-
the equatorial radius of the Earth
- g :
-
the mean anomaly of the satellite
- n :
-
the mean motion of the satellite
- f :
-
the true anomaly of the satellite
- e :
-
the eccentricity of the satellite orbit
- i :
-
the inclination of the satellite orbit
- Ω:
-
the longitude of the ascending node of the satellite
- ω:
-
the argument of perigee of the satellite
- \(\tilde \omega \) :
-
ω+Ω
- a :
-
the semimajor axis of the satellite orbit
- δa :
-
the perturbations ina caused by the Moon (primed)/Sun (double primed)
- δe :
-
the perturbations ine caused by the Moon (primed)/Sun (double primed)
- δi :
-
the perturbations ini caused by the Moon (primed)/Sun (double primed)
- δg :
-
the perturbations ing caused by the Moon (primed)/Sun (double primed)
- δΩ:
-
the perturbations in Ω caused by the Moon (primed)/Sun (double primed)
- δω:
-
the perturbations in ω caused by the Moon (primed)/Sun (double primed)
- ε:
-
the obliquity of the ecliptic
- J 2,J 4 :
-
zonal harmonic coefficients in the Earth's gravitational potential (J 2=1.082 19×10−3 andJ 4=−2.123×10−6)
- t 0 :
-
Julian date of January 0.5, 1900 (2 415 020.0 days)
- t−t 0 :
-
number of days from January 0.5, 1900
- T :
-
number of Julian Centuries (36 525 days) from January 0.5, 1900
- :
-
geocentric mean longitude of the Moon
- :
-
geocentric mean longitude of the lunar node
- :
-
geocentric mean longitude of the lunar perigee
- l ⊙ :
-
geocentric mean longitude of the Sun
- \(\Gamma \equiv \tilde \omega \odot \) :
-
geocentric mean longitude of the solar perigee
- :
-
argument of the principal elliptic term
- \(l' \equiv l \odot - \tilde \omega \odot \) :
-
argument of the annual equation
- :
-
argument of the principal term in latitude
- :
-
half argument of the variation
References
Brouwer, D.: 1959,Astron. J. 64, 378–397.
Kaula, W. M.: 1962,Astron. J. 67, 300.
Kozai, Y.: 1959,Smithsonian Inst. Astrophys. Obs. Rept., No. 22, 7–10.
Murphy, J. and Felsentreger, T.: 1966, NASA TN D-3559.
Musen, P., Bailie, A., and Upton, E.: 1961, NASA TN D-494.
Musen, P. and Estes, R.: 1971, NASA-X-550-71-342.
Musen, P. and Felsentreger, T.: 1972, NASA-X-550-72-192.
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Estes, R.H. On the analytic lunar and solar perturbations of a near Earth satellite. Celestial Mechanics 10, 253–276 (1974). https://doi.org/10.1007/BF01586857
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DOI: https://doi.org/10.1007/BF01586857