scholarly journals Nonsphericity of the Moon and Near Sun-Synchronous Polar Lunar Orbits

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Jean Paulo dos Santos Carvalho ◽  
Rodolpho Vilhena de Moraes ◽  
Antônio Fernando Bertachini de Almeida Prado
Keyword(s):  
Numerical Simulations ◽  
Artificial Satellite ◽  
Nonuniform Distribution ◽  
Second Order ◽  
The Moon ◽  
Disturbing Potential ◽  
Short Period ◽  
Coupling Terms ◽  
Lunar Artificial Satellite ◽  
Hori Method

Herein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness (J2) and the equatorial ellipticity (sectorial termC22). Using Lie-Hori method up to the second order short-period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun-synchronous polar lunar orbit is presented.

scholarly journals Planetary Satellite Orbiters: Applications for the Moon

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Jean Paulo dos Santos Carvalho ◽  
Rodolpho Vilhena de Moraes ◽  
Antônio Fernando Bertachini de Almeida Prado
Keyword(s):  
Orbital Motion ◽  
Artificial Satellite ◽  
Nonuniform Distribution ◽  
The Moon ◽  
Planetary Satellite ◽  
Frozen Orbits ◽  
Planetary Satellites ◽  
Families Of Periodic Orbits ◽  
Low Altitude ◽  
Tesseral Harmonics

Low-altitude, near-polar orbits are very desirable as science orbits for missions to planetary satellites, such as the Earth's Moon. In this paper, we present an analytical theory with numerical simulations to study the orbital motion of lunar low-altitude artificial satellite. We consider the problem of an artificial satellite perturbed by the nonuniform distribution of the mass of the Moon (J2–J5,J7, andC22). The conditions to get frozen orbits are presented. Using an approach that considers the single-averaged problem, we found families of periodic orbits for the problem of an orbiter travelling around the Moon, where frozen orbits valid for long periods of time are found. A comparison between the models for the zonal and tesseral harmonics coefficients is presented.

The motion of a lunar orbiter

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.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

scholarly journals The surface layer integral method for the modelling of the radial gravity gradient component over sea surface

2019 ◽  
Vol 9 (1) ◽  
pp. 127-132
Author(s):  
D. Zhao ◽  
Z. Gong ◽  
J. Feng
Keyword(s):  
Surface Layer ◽  
Integral Method ◽  
Integral Formula ◽  
Radial Component ◽  
Second Order ◽  
Sea Surface ◽  
Gravity Potential ◽  
Gravity Gradient ◽  
Disturbing Potential ◽  
Gradient Component

Abstract For the modelling and determination of the Earth’s external gravity potential as well as its second-order radial derivatives in the space near sea surface, the surface layer integral method was discussed in the paper. The reasons for the applicability of the method over sea surface were discussed. From the original integral formula of disturbing potential based on the surface layer method, the expression of the radial component of the gravity gradient tensor was derived. Furthermore, an identity relation was introduced to modify the formula in order to reduce the singularity problem. Numerical experiments carried out over the marine area of China show that, the modi-fied surface layer integral method effectively improves the accuracy and reliability of the calculation of the second-order radial gradient component of the disturbing potential near sea surface.

An Investigation of Screw Systems in the Finite Displacements of Bennett-Based 6R Linkages

1999 ◽  
Vol 122 (4) ◽  
pp. 426-430 ◽  
Author(s):  
Chintien Huang ◽  
Chi-Chih Sun
Keyword(s):  
Numerical Simulations ◽  
Second Order ◽  
Finite Displacement ◽  
Finite Displacements ◽  
Overconstrained Linkages

This paper investigates, via numerical simulations, the finite displacements of all the known Bennett-based 6R overconstrained linkages: Goldberg’s 6R, variant Goldberg 6R, Waldron’s hybrid 6R, and Wohlhart’s hybrid 6R linkages. An investigation of the finite displacements of nine distinct linkages reveals that every Bennett-based 6R linkage, except for the isomerization of Wohlhart’s hybrid linkage, inherits the linear properties of the Bennett mechanism. The relative finite displacement screws of some non-adjacent links of these linkages form screw systems of the second order. Thirty-one screw systems are reported in this paper. [S1050-0472(00)02204-2]

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

scholarly journals Searching for Orbits with Minimum Fuel Consumption for Station-Keeping Maneuvers: An Application to Lunisolar Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Numerical Simulations ◽  
Fuel Consumption ◽  
Total Variation ◽  
The Sun ◽  
The Moon ◽  
Station Keeping ◽  
Third Body ◽  
Lunisolar Perturbations ◽  
The Earth ◽  
New Criterion

The present paper has the goal of developing a new criterion to search for orbits that minimize the fuel consumption for station-keeping maneuvers. This approach is based on the integral over the time of the perturbing forces. This integral measures the total variation of velocity caused by the perturbations in the spacecraft, which corresponds to the equivalent variation of velocity that an engine should deliver to the spacecraft to compensate the perturbations and to keep its orbit Keplerian all the time. This integral is a characteristic of the orbit and the set of perturbations considered and does not depend on the type of engine used. In this sense, this integral can be seen as a criterion to select the orbit of the spacecraft. When this value becomes larger, more consumption of fuel is required for the station keeping, and, in this sense, less interesting is the orbit. This concept can be applied to any perturbation. In the present research, as an example, the perturbation caused by a third body is considered. Then, numerical simulations considering the effects of the Sun and the Moon in a satellite around the Earth are shown to exemplify the method.

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