The positions of relative equilibrium in the circular orbit of an elastic artificial satellite and their stability

1992 ◽  
Vol 56 (4) ◽  
pp. 518-526
Author(s):  
S.V. Chaikin
Keyword(s):  
Circular Orbit ◽  
Artificial Satellite ◽  
Relative Equilibrium

Optimization of the spacecraft final orbit and the trajectory of the apsidal impulse launch, with due regard to spent stage jettisons into the atmosphere

2019 ◽  
Author(s):  
I.S. Grigoryev ◽  
A.I Proskuryakov
Keyword(s):  
Circular Orbit ◽  
Parametric Analysis ◽  
Artificial Satellite ◽  
Optimal Number ◽  
Elliptical Orbit ◽  
Additional Mass ◽  
Fuel Distribution ◽  
Mass Consumption ◽  
Earth Space ◽  
Near Earth Space

The article considers the idea of reducing littering the near-Earth space by means of spent stage jettisons into the Earth's atmosphere. A solution to the problem of optimization of the apsidal impulse transfer between the reference circular orbit of an Earth’s artificial satellite and the final elliptical orbit is proposed. A parametric analysis of the obtained solutions is performed, a simple pulse choice scheme close in functionality to the optimal one is proposed. Questions about the optimal number and location of pulses and the optimal mass of the first stage are investigated. An assessment of the additional mass consumption associated with the stage jettisons into the atmosphere comparing with the simple separation of the stages is performed. It was found that in the case of optimal fuel distribution among the tanks such mass consumption is small when a final ascent pulse is 1.5 km/s.

The repositioning maneuver of artificial Earth satellite in a circular orbit with a supporting acceleration

10.12737/2412 ◽  
2013 ◽  
Vol 4 (4) ◽  
pp. 3-15
Author(s):  
Михаил Бурдаев ◽  
Mikhail Burdaev
Keyword(s):  
Energy Efficiency ◽  
Program Implementation ◽  
Circular Orbit ◽  
Artificial Satellite ◽  
Earth Satellite ◽  
Artificial Earth Satellite ◽  
Artificial Earth ◽  
Repositioning Maneuver

The paper reveals the maneuver entity of reposition artificial satellite on a circular orbit with a supporting acceleration. A maneuver program implementation with using of constant thrust motors is found and proved. An energy efficiency of maneuver under various conditions of its implementation is determined

Spiral and Elliptical Orbits

1957 ◽  
Vol 61 (558) ◽  
pp. 422-423 ◽  
Author(s):  
Rear-Admiral Brian Egerton R.N. (Retd.)
Keyword(s):  
High Altitude ◽  
Circular Orbit ◽  
Artificial Satellite ◽  
Tangential Velocity ◽  
Radius Vector ◽  
The Earth ◽  
Starting Point ◽  
Air Resistance ◽  
Sufficient Distance ◽  
Elliptical Orbits

An Artificial Satellite set to start on a circular orbit round the Earth, will have to be given a known velocity, at right angles to the radius vector, which depends upon its distance from the Earth's centre.It will, from the start, begin to spiral downwards towards the Earth, owing to the resistance of the atmosphere, but if it begins its path at a sufficiently high altitude, the decrease of height after one revolution will be small.Should the initial “ tangential ” velocity be greater than the value calculated for a circular orbit, the satellite will, according to the text books, describe an ellipse instead of a circle; and, if at a sufficient distance for the air resistance to be at first ignored, will return after one revolution to the distance at which it started, this point being the perigee of the ellipse. It will never return to a point outside the starting point.

scholarly journals Relative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational torques

2019 ◽  
Vol 18 (2) ◽  
pp. 21-32
Author(s):  
E. V. Barinova ◽  
I. A. Timbai
Keyword(s):  
Circular Orbit ◽  
Aerodynamic Drag ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Mass Center ◽  
Atmospheric Density ◽  
Force Coefficient ◽  
Aerodynamic Moment ◽  
Gravitational Moment ◽  
Proper Rotation

Motion of a dynamically symmetric CubeSat nanosatellite around the mass center on the circular orbit under the action of aerodynamic and gravitational torques is considered. We determined the nanosatellite equilibrium positions in the flight path axis system. We took into account the fact that the CubeSat nanosatellite has a rectangular parallelepiped shape and, therefore, the aerodynamic drag force coefficient depends on the angles of attack and proper rotation. We obtained formulae which allow calculating the values of the angles of attack, precession and proper rotation that correspond to the equilibrium positions, depending on the mass-inertia and geometric parameters of the nanosatellite, the orbit altitude, and the atmospheric density. It is shown that if the gravitational moment predominates over the aerodynamic one, there are 16 equilibrium positions, if the aerodynamic moment predominates over the gravitational one, there are 8 equilibrium positions, and in the case when both moments have comparable values there are 8, 12 or 16 equilibrium positions. Using the formulae obtained, we determined the equilibrium positions of the SamSat-QB50 nanosatellite. We calculated the ranges of altitudes where SamSat-QB50 nanosatellite has 8, 12, or 16 relative equilibrium positions.

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.

Artificial satellite orbit computations

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.

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

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