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Long term time-variation of osculating elements of satellite orbits perturbed by third body, including graphs of Kepler element variations along different orbits
Asymptotic solutions are developed for the motion of a geocentric satellite in the equatorial plane due to gravitational perturbations such as nonsphericity (especially oblateness) of the primary body. Axisymmetric potentials are considered. A class of transformations is developed and the equations of motion are solved by the method of generalized multiple scales. Further it is shown that the equations of motion can be transformed into the required form to within any specified degree of accuracy. The transformations form an Abelian group of infinite order which leaves the differential equations of motion invariant. Solutions are developed in terms of elementary functions instead of elliptic or other higher transcendental functions and are shown to agree with known results.
Perturbation analysis for angular orbital elements of Relay 2 satellite
A class of highly inclined lunar orbits is discussed for which earth perturbations have significant influence on the orbit evolution and the usefulness of the orbit for scientific exploration. The theory of the long-term motion of particles under third-body and zonal harmonic perturbations is taken as a starting point for investigations of orbits with relatively long lifetimes and evolutionary patterns that enhance the effectiveness of the satellite as a lunar farside relay. An equilibrium solution in the doubly-averaged three-body problem with oblateness is identified and the results of some numerical integrations are presented.
A first-order perturbation theory exists for the flyby problem with the Born approximation as the reference orbit.
Determining higher order perturbations for lunar orbiter by Krylov-Bololiubov and Poincare methods
Effective tidal Love numbers and phase angles for the O sub one, K sub one, M sub two, K sub two, P sub one, and S sub two, tides are recovered. The effective tidal phase angles tend to be on the order of a few degrees. The effective tidal Love numbers are generally less than the solid earth Love number K sub two, of about 0.30. This supports the contention that the ocean tides give an apparent depression of the solid earth Love number. Ocean tide amplitudes and phases are calculated for the above tides assuming K sub two = 0.30 and the solid earth lag angle O sub two = 0. The results show good agreement on GEOS-1 but not on GEOS-II.
A new NASA interplanetary flight project, called Jupiter Orbiter Probe (JOP), has been recently approved by Congress. JOP involves a dual mission intended to explore the planet Jupiter and its environment with an atmospheric probe and a planetary orbiter spacecraft. The probe and orbiter vehicles are to be launched in tandem as a single spacecraft during the time from December 1981 to January 1982. The spacecraft will arrive at Jupiter at the earliest on November 14, 1984. Navigating the JOP spacecraft will be a critical task for the JOP mission. Attention is given to aspects of probe and orbiter delivery, Jupiter orbit insertion and perijove raise, the Satellite Tour, navigation development and the navigation system, the probe delivery, example orbits, velocity perturbation and correction, orbit determination characteristics, orbit determination and control profile, and the correction velocity requirements.
IRIS_EFT is a scientific simulation that can be used to perform an Eclipse-Free- Time (EFT) assessment of IRIS (Infrared Imaging Surveyor) mission orbits. EFT is defined to be those time intervals longer than one day during which the IRIS spacecraft is not in the Earth s shadow. Program IRIS_EFT implements a special perturbation of orbital motion to numerically integrate Cowell's form of the system of differential equations. Shadow conditions are predicted by embedding this integrator within Brent s method for finding the root of a nonlinear equation. The IRIS_EFT software models the effects of the following types of orbit perturbations on the long-term evolution and shadow characteristics of IRIS mission orbits. (1) Non-spherical Earth gravity, (2) Atmospheric drag, (3) Point-mass gravity of the Sun, and (4) Point-mass gravity of the Moon. The objective of this effort was to create an in-house computer program that would perform eclipse-free-time analysis. of candidate IRIS spacecraft mission orbits in an accurate and timely fashion. The software is a suite of Fortran subroutines and data files organized as a "computational" engine that is used to accurately predict the long-term orbit evolution of IRIS mission orbits while searching for Earth shadow conditions.
Long term orbit calculation by superposition of gravity and drag perturbations, taking into account solar and geomagnetic induced density variations
Guidance perturbations for a low-thrust mars orbit mission using snap-8
The potential to perturb debris orbits using photon pressure from ground-based lasers has been confirmed by independent research teams. Two useful applications of this scheme are protecting space assets from impacts with debris and stabilizing the orbital debris environment, both relying on collision avoidance rather than de-orbiting debris. This paper presents the results of a new assessment method to analyze the efficiency of the concept for collision avoidance. Earlier research concluded that one ground based system consisting of a 10 kW class laser, directed by a 1.5 m telescope with adaptive optics, can prevent a significant fraction of debris-debris collisions in low Earth orbit. That research used in-track displacement to measure efficiency and restricted itself to an analysis of a limited number of objects. As orbit prediction error is dependent on debris object properties, a static displacement threshold should be complemented with another measure to assess the efficiency of the scheme. In this paper we present the results of an approach using probability of collision. Using a least-squares fitting method, we improve the quality of the original TLE catalogue in terms of state and co-state accuracy. We then calculate collision probabilities for all the objects in the catalogue. The conjunctions with the highest risk of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the collision probability in a 20 minute window around the original conjunction. We then use different criteria to evaluate the utility of the laser-based collision avoidance scheme and assess the number of base-line ground stations needed to mitigate a significant number of high probability conjunctions. Finally, we also give an account how a laser ground station can be used for both orbit deflection and debris tracking.
Applicability of halphen method to computing long- range effects in motion of celestial bodies on artificial satellites
Lunar and solar long period effects on motion and orbit stability of satellites
Computer derived orbital parameter variations for forty hour period after insertion into two reference Apollo lunar parking orbits
Perturbation solutions of differential equations of motion for low-thrust rocket trajectories
The objective was to assess the importance of solar eclipses on Lageos' orbit. Solar radiation pressure perturbs the orbit of the Lageos satellite. The GEODYN orbit determination computer program includes solar radiation pressure as one of the forces operating on the satellite as it integrates the orbit. GEODYN also takes into account the extinction of sunlight when Lageos moves into the Earth's shadow. The effect of solar eclipses on the semimajor axis of Lageos' orbit was computed analytically by assuming Lageos to be in a circular orbit, the Sun and the Moon to be in the plane of the orbit, and the Moon to be stationary in the sky in front of the Sun. Also, the magnitude of the radiation pressure is assumed to be linearly related to the angular separation of the Sun and Moon, and that Lageos is a perfect absorber of radiation. The computation indicates that an eclipse of the Sun by the Moon as seen by Lageos can affect the semimajor axis at the 1 centimeter (1 cm) level. Such a change is significant enough to include in GEODYN, in order to get an accurate orbit for Lageos.
We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However, it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand's theorem, which has been known since 1873.