The motion of an artificial satellite in the vicinity of the critical inclination

The problem of the critical inclination in the artificial satellite theory can be regarded as a problem of resonance arising from the near-commensurability 1:1 between the anomalistic and the draconitic frequencies of the motion, n1 and n2. Let us define the main problem by the potential function (1) with (2)

Download Full-text

The motion of a lunar orbiter

Symposium - International Astronomical Union ◽

10.1017/s0074180900105686 ◽

1966 ◽

Vol 25 ◽

pp. 373

Author(s):

Y. Kozai

Keyword(s):

Degrees Of Freedom ◽

Dimensional Space ◽

Artificial Satellite ◽

Equations Of Motion ◽

Triaxial Ellipsoid ◽

The Moon ◽

Secular Motion ◽

The Earth ◽

Close Satellite ◽

The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Download Full-text

Artificial satellite orbit computations

Symposium - International Astronomical Union ◽

10.1017/s0074180900105662 ◽

1966 ◽

Vol 25 ◽

pp. 363-371

Author(s):

P. Sconzo

Keyword(s):

Artificial Satellite ◽

Satellite Orbit ◽

Artificial Satellites ◽

Orbital Elements ◽

Differential Correction ◽

Gravitational Effects ◽

Short Intervals ◽

The Subject ◽

Introductory Discussion ◽

Orbit Computation

In this paper an orbit computation program for artificial satellites is presented. This program is operational and it has already been used to compute the orbits of several satellites.After an introductory discussion on the subject of artificial satellite orbit computations, the features of this program are thoroughly explained. In order to achieve the representation of the orbital elements over short intervals of time a drag-free perturbation theory coupled with a differential correction procedure is used, while the long range behavior is obtained empirically. The empirical treatment of the non-gravitational effects upon the satellite motion seems to be very satisfactory. Numerical analysis procedures supporting this treatment and experience gained in using our program are also objects of discussion.

Download Full-text