Analysis of an Artificial Satellite Orbit around the Earth Under an Influence of a Rotating Gravitational Field

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.

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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.

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The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

Informacionno-technologicheskij vestnik ◽

10.21499/2409-1650-2018-1-12-22 ◽

2018 ◽

Vol 15 (1) ◽

pp. 12-22

Author(s):

V. M. Artyushenko ◽

D. Y. Vinogradov

Keyword(s):

Remote Sensing ◽

Gravitational Field ◽

State Vector ◽

Semimajor Axis ◽

The State ◽

Zonal Harmonics ◽

The Earth ◽

Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

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Spheric radial basis functions in Mahalanobis measuring for displaying local field features

Geodesy and Cartography ◽

10.22389/0016-7126-2019-952-10-2-9 ◽

2019 ◽

Vol 952 (10) ◽

pp. 2-9

Author(s):

Yu.M. Neiman ◽

L.S. Sugaipova ◽

V.V. Popadyev

Keyword(s):

Gravitational Field ◽

Quadratic Form ◽

Local Field ◽

Euclidean Distance ◽

Basis Functions ◽

Spherical Functions ◽

Local Models ◽

Stationary Field ◽

Modeling Process ◽

The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

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Perturbative effects of antenna radiation reaction on artificial satellite orbit

Aerospace Science and Technology ◽

10.1016/j.ast.2011.08.012 ◽

2012 ◽

Vol 23 (1) ◽

pp. 352-357 ◽

Cited By ~ 2

Author(s):

A. Heilmann ◽

Luiz Danilo Damasceno Ferreira ◽

C.A. Dartora ◽

K.Z. Nobrega

Keyword(s):

Artificial Satellite ◽

Satellite Orbit ◽

Radiation Reaction ◽

Antenna Radiation

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Gravity assists maneuver in the problem of extension accessible landing areas on the Venus surface

Open Astronomy ◽

10.1515/astro-2021-0013 ◽

2021 ◽

Vol 30 (1) ◽

pp. 103-109

Author(s):

Natan A. Eismont ◽

Vladislav A. Zubko ◽

Andrey A. Belyaev ◽

Ludmila V. Zasova ◽

Dmitriy A. Gorinov ◽

...

Keyword(s):

Gravitational Field ◽

Entry Angle ◽

Gravity Assist ◽

Flight Duration ◽

The Earth ◽

Gravity Assists ◽

Primary Basis ◽

Venusian Surface ◽

Research Show

Abstract This study discusses the usage of Venus gravity assist in order to choose and reaching any point on Venusian surface. The launch of a spacecraft to Venus during the launch windows of 2029 to 2031 is considered for this purpose. The constraints for the method are the re-entry angle and the maximum possible overload. The primary basis of the proposed strategy is to use the gravitational field of Venus to transfer the spacecraft to an orbit resonant to the Venusian one – with the aim of expanding accessible landing areas. Results of the current research show that this strategy provides an essential increase in accessible landing areas and, moreover, may provide an access to any point on the surface of Venus with a small increase in ∆V required for launch from the Earth and in the flight duration. The comparison with the landing without using gravity assist near planet is also given.

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Analytical Techniques for the Optimisation of Rocket Trajectories

Aeronautical Quarterly ◽

10.1017/s0001925900002705 ◽

1963 ◽

Vol 14 (2) ◽

pp. 105-124 ◽

Cited By ~ 7

Author(s):

Derek F. Lawden

Keyword(s):

Gravitational Field ◽

Artificial Satellite ◽

Analytical Techniques ◽

Present Position ◽

Mayer Problem ◽

Special Cases ◽

Minimum Expenditure ◽

Law Of Attraction ◽

Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

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Motion of a satellite in the earth’s gravitational field

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1960.0004 ◽

1960 ◽

Vol 254 (1276) ◽

pp. 48-65 ◽

Cited By ~ 14

Keyword(s):

Gravitational Field ◽

Spherical Harmonics ◽

Main Part ◽

Equations Of Motion ◽

Orbital Elements ◽

Partial Derivatives ◽

Rates Of Change ◽

Zonal Harmonics ◽

The Earth ◽

Secular Terms

The equations of motion of a satellite are given in a general form, account being taken of the precession and nutation of the earth. The main part of the paper deals with the motion arising from the gravitational field of the earth, expressed as a general expansion in spherical harmonics. By evaluating the partial derivatives in Lagrange’s planetary equations, • expressions are obtained for the rates of change of the orbital elements. Particular consideration is given to the form of the expressions for the secular terms arising from the first four zonal harmonics.

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