The contraction of satellite orbits under the influence of air drag. VIII. Orbital lifetime in an oblate atmosphere, when perigee distance is perturbed by odd zonal harmonics in the geopotential

This paper is devoted to developing the necessary orbital theory for predicting the lifetimes of satellites moving in an oblate atmosphere and subjected to the perturbations due to odd zonal harmonics in the geopotential. The effects of odd zonal harmonics and atmospheric oblateness are expressed as multiplying factors, F (oz) and F (ao), to be applied to the lifetime predictions calculated in the absence of the perturbations. The results are valid for the great majority of orbits about the Earth, and in particular for all orbital eccentricities between 0 and 1; but the limits set for the controlling parameters exclude ( a ) near-polar orbits with perigee heights lower than about 180 km, and ( b ) orbits having inclinations within a narrow band centred on 63.4°. The results show that, when the controlling parameters are at their upper limits, either F (oz) or F (ao) can change the lifetime by up to about 35%, and taken together they can produce changes of up to 60%, if the initial and final positions of perigee are at specified points on the orbit and the eccentricity exceeds 0.2. Such combinations of values rarely arise, however, and the effects are more often of order 10-20%. Even at these moderate levels, the effects need to be taken into account in order to make realistic estimates of the decay dates of satellites in the last few months of their lives.

Satellite orbits contracting under the influence of air drag experience 15th-order resonance when the track over the Earth repeats after 15 revolutions. If the orbital decay rate is slow enough, an orbit passing through the resonance is appreciably perturbed by the effects of 15th-order harmonics in the geopotential. We have used the observed perturbations in 23 resonant orbits, at various inclinations to the equator, to determine the harmonic coefficients of order 15 and degree 15, 16, 17,... 35. Analysis of the changes in orbital inclination on the 23 orbits gives the harmonics of odd degree, while those of even degree are found from the changes in eccentricity on 16 of the orbits. The values derived are given in tables 6 and 8. The coefficients of degrees 15, 16, 17,... 23, should be more accurate than any previously obtained; their average s. d. is 1.4 x 10 -9 , equivalent to 1 cm in geoid height. Comparisons with comprehensive Earth models show the Goddard Earth Model 10B to be the best, and a standard deviation of about 3 x 10 -9 in the GEM 10B 15th-order coefficients is indicated.


2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov

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.


2002 ◽  
Vol 12 (9) ◽  
pp. 85-86
Author(s):  
R. C. Rai ◽  
V. A. Bondarenko ◽  
J. W. Brill

We have searched for narrow-band-noise (NBN) modulations of the infrared transmission in blue bronze, using tunable diode lasers. No modulations were observed, giving an upper limits for NBN changes in the absorption coefficient of $\Delta \alpha_{NBN} < 0.3 $ / cm ($\approx \alpha/2000$). The implication of these results on proposed CDW properties and NBN mechanisms are discussed.


2009 ◽  
Vol 27 (11) ◽  
pp. 4221-4227 ◽  
Author(s):  
J. F. McKenzie

Abstract. This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona) are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.


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.


2021 ◽  
Author(s):  
Kiyoshi Kuramoto ◽  

&lt;p&gt;MMX (Martian Moons eXploration) is the 3rd sample return mission of JAXA/ISAS following Hayabusa and Hayabusa2. The MMX spacecraft will be launched in 2024 by an H-III rocket and make a round trip to the Martian system ~5 years. In the proximity of the Martian moons for 3 years, MMX will observe them along with the Martian atmosphere and surrounding space and conduct multiple landings on Phobos to collect Phoboss-indigenous materials. Owing to the lack of definitive evidence, the origin of Phobos and Deimos is under debate between the two leading hypotheses: the capture of volatile-rich primordial asteroid(s) and the in-situ formation from a debris disk that generated by a giant impact onto early Mars. Whichever theory is correct, the Martian moons likely preserve key records on the evolution of the early solar system and the formation of Mars. Through close-up observations of both moons and sample return from Phobos, MMX will settle the controversy of their origin, reveal their evolution, and elucidate the early solar system evolution around the region near the snow line. Global circulation and escape of the Martian atmosphere will also be monitored to reveal basic processes that have shaped and altered the Martian surface environment. The MMX spacecraft consists of three modules with chemical propulsion systems. By releasing used modules at appropriate timings, the spacecraft mass is reduced to allow orbital tuning to quasi-satellite orbits around Phobos, landings on Phobos surface, and the escape from the Martian gravity to return to the Earth. MMX will arrive at the Martian system in 2025 and start close-up observations of Phobos from quasi-satellite orbits. Among the total of 7 mounted instruments for scientific observations, TENGOO (telescope camera) and LIDAR will conduct high-resolution topography mapping and OROCHI (multi-band visible camera), MIRS (infra-red spectrometer provided by CNES), MEGANE (gamma-ray and neutron spectrometer provided by NASA), and MSA (ion mass spectrum analyzer) will survey surface composition and its heterogeneity. Hydrous minerals and interior ice are important observational targets because they, if identified, strongly support the capture hypothesis. Data taken by these instruments will be also useful for the landing site selection and characterization. Before the first landing, a rover (provided by CNES/DLR) will be released near the sampling site to collect data on surface regolith properties to be referred for the mothership landing operation. The rover will carry cameras, miniRAD (thermal mapper), and RAX (laser Raman spectrometer) to collect data on the physical and mineralogical characteristics of the Phobos surface around the sampling site. In early 2027, Mars will come to its closest approach to the Earth which minimizes the communication delay between the spacecraft and the Earth station. Together with the timing relatively far from Sun-Mars conjunctions and the Martian equinoxes, this period is the most favorable for landing operations that need real-time communication with the ground station and solar illumination undisturbed by eclipses. MMX will use two sampling systems, the C-sampler using a coring mechanism equipped on the tip of a manipulator and the P-sampler (provided by NASA) using a pneumatic mechanism equipped on a landing leg. After the stay near Phobos, the MMX spacecraft will be transferred to Deimos-flyby orbits to conduct Deimos observations, and then the return module will depart the Martian system in 2028. During the stay in the Martian system, MMX will also conduct wide-area observations of the Martian atmosphere using imagers (OROCHI, MIRS, and TENGOO) to study the atmospheric dynamics and the water vapor and dust transport. Simultanenousely, MSA will survey ions not only released and sputtered from Phobos's surface but also escaped from the Martian upper atmosphere. CMDM (dust monitor) will continuously survey the dust flux around the moons to assess the processes of space weathering by micrometeoroid bombardments and the possible formation of dust rings along the moons&amp;#8217; orbits. The sample capsule will come back to the Earth in 2029. Complimentarily with remote sensing studies, returned samples will provide us strong cosmo-chemical constraints for the origin of Phobos as well as those for early solar system processes. &amp;#160;&amp;#160;&lt;/p&gt;


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