Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds

Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients J_n for n ? 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients J_n in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter’s gravity coefficients J₂, J₄, J₆, … , J₁₂ taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ₂, ΔJ₄, ΔJ₆, … , ΔJ₁₂ caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJ_n/J_n∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ? 8.     

On the existence of the relative equilibria of a rigid body in the J 2 problem

The motion of a point mass in the J ₂ problem has been generalized to that of a rigid body in a J ₂ gravity field for new high-precision applications in the celestial mechanics and astrodynamics. Unlike the original J ₂ problem, the gravitational orbit-rotation coupling of the rigid body is considered in the generalized problem. The existence and properties of both the classical and non-classical relative equilibria of the rigid body are investigated in more details in the present paper based on our previous results. We nondimensionalize the system by the characteristic time and length to make the study more general. Through the study, it is found that the classical relative equilibria can always exist in the real physical situation. Numerical results suggest that the non-classical relative equilibria only can exist in the case of a negative J ₂, i.e., the central body is elongated; they cannot exist in the case of a positive J ₂ when the central body is oblate. In the case of a negative J ₂, the effect of the orbit-rotation coupling of the rigid body on the existence of the non-classical relative equilibria can be positive or negative, which depends on the values of J ₂ and the angular velocity Ω _e . The bifurcation from the classical relative equilibria, at which the non-classical relative equilibria appear, has been shown with different parameters of the system. Our results here have given more details of the relative equilibria than our previous paper, in which the existence conditions of the relative equilibria are derived and primarily studied. Our results have also extended the previous results on the relative equilibria of a rigid body in a central gravity field by taking into account the oblateness of the central body.     

Artificial Martian frozen orbits and Sun-Synchronous orbits using continuous low-thrust control

This paper analyses three types of artificial orbits around Mars pushed by continuous low-thrust control: artificial frozen orbits, artificial Sun-Synchronous orbits and artificial Sun-Synchronous frozen orbits. These artificial orbits have similar characteristics to natural frozen orbits and Sun-Synchronous orbits, and their orbital parameters can be selected arbitrarily by using continuous low-thrust control. One control strategy to achieve the artificial frozen orbit is using both the transverse and radial continuous low-thrust control, and another to achieve the artificial Sun-Synchronous orbit is using the normal continuous low-thrust control. These continuous low-thrust control strategies consider J ₂, J ₃, and J ₄ perturbations of Mars. It is proved that both control strategies can minimize characteristic velocity. Relevant formulas are derived, and numerical results are presented. Given the same initial orbital parameters, the control acceleration and characteristic velocity taking into account J ₂, J ₃, and J ₄ perturbations are similar to those taking into account J ₂ perturbations for both Mars and the Earth. The control thrust of the orbit around Mars is smaller than that around the Earth. The magnitude of the control acceleration of ASFOM-4 (named as Artificial Sun-Synchronous Frozen Orbit Method 4) is the lowest among these strategies and the characteristic velocity within one orbital period is only 0.5219 m/s for the artificial Sun-Synchronous frozen orbit around Mars. It is evident that the relationship among the control thrusts and the primary orbital parameters of Martian artificial orbits is always similar to that of the Earth. Simulation shows that the control scheme extends the orbital parameters’ selection range of three types of orbits around Mars, compared with the natural frozen orbit and Sun-Synchronous orbit.     

An analytic solution for theJ 2 perturbed equatorial orbit

An analytic solution for theJ ₂ perturbed equatorial orbit is obtained in terms of elliptic functions and integrals. The necessary equations for computing the position and velocity vectors, and the time are given in terms of known functions. The perturbed periapsis and apoapsis distances are determined from the roots of a characteristic cubic.     

The effect of dense cores on the structure and evolution of Jupiter and Saturn

We have calculated evolutionary and static models of Jupiter and Saturn with homogeneous solar composition mantles and dense cores of material consisting of solar abundances of SiO₂, MgO, Fe, and Ni. Evolutionary sequences for Jupiter were calculated with cores of mass 2, 4, 6, and 8% of the Jovian mass. Evolutionary sequences for Saturn were calculated with cores of mass 16, 18, 20, and 22% of total mass. Two envelope mixtures, representative of the solar abundances were used: X (mass fraction of hydrogen) = 0.74, Y (mass fraction of helium) = 0.24 and X = 0.77 and Y = 0.21. For Jupiter, the observations of the temperature at 1 bar pressure (T_1bar), radius and internal luminosity were best fit by evolutionary models with a core mass of ～6.5% and chemical composition of X = 0.77, Y = 0.21. The calculated cooling time for Jupiter is approximately 4.9 × 10⁹ years, which is consistent, within our error bars, with the known age of the solar system. For Saturn, the observations of the radius, internal luminosity and T_1BAR can be best fit by evolutionary models with a core mass of ～21% and chemical composition of X = 0.77, Y = 0.21. The cooling time calculated for Saturn is approximately 2.6 × 10⁹ years, almost a factor 2 less than the present age of the solar system. Static models of Jupiter and Saturn were calculated for the above chemical compositions in order to investigate the sensitivity of the calculated gravitational moments, J₂ and J₄, to the mass of the dense core, T_1BAR and hydrogen/helium ratio. We find for Jupiter that a model having a core mass of approximately 7% gives values of J₂, J₄, and T_1BAR that are within observational limits, for the mixture X = 0.77, Y = 0.21. The static Jupiter models are completely consistent with the evolutionary results. For Saturn, the quantities J₂, J₄, and J₆ determined from the static models with the most probable T_1BAR of 140°K, using modeling procedures which result in consistent models for Jupiter, are considerably below the observed values.     

Analytical Solution of Coupled Perturbation of Tesseral Harmonic Terms of Mars's Non-Spherical Gravitational Potential

The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J_2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J₂. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10⁻⁴ in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.     

Regularization and linearization of the equations of motion in central force-fields

Within the framework of linear and regular celestial mechanics, a wide class of central force field problems are considered. We take as potential function a polynomial whose variable is the reciprocal of the distance from the origin, and, as regularizing function the square root of a certain reciprocal polynomial, related to the potential function. The relations between the coefficients of both functions, in order to arrive to linear equations, are given. In particular, the case of a quintic polynomial is analyzed, and an application is made to artificial earth satellites considering harmonicsJ ₂,J ₃,J ₄.     

Molecular and low excitation emission in high mass post-main-sequence nebulae

We have undertaken mapping and spectroscopy of a broad range of type I post-Main-Sequence nebulae in COJ=1→0,J=2→1, andJ=3→2, using the 12 m antenna at Kitt Peak, and the 45 m facility of the Nobeyama Radio Observatory. As a consequence, we find COJ=2→1 emission associated with NGC 3132 and NGC 6445, determine the location of COJ=1→0 emission in the nucleus of NGC 6302, and obtain (for the first time) COJ=3→2 spectroscopy for a substantial cross-section of type I sources. LVG analysis of the results suggests densitiesn(H₂) ～ 10⁴ cm^?3, and velocity gradients dv/dr ～ 2×10² in both NGC 7027 and CRL 618, commensurate with uniform expansion of a constant velocity outflow, whilst for the case of NGC 2346 these values probably exceedn(H₂) ～ 4.0×10⁵ cm^?3. dv/dr ～ 2.6×10³ km s^?1 andT _k ～10² K, implying appreciable compression (and shock heating?) of the CO excitation zone. Hi masses extend over a typical range 0.01<M(Hi)/M _⊙<1, whilst corresponding estimates of the progenitor mass imply 0.7<M _prog/M _⊙<2.3; values significantly in excess of those pertinent for normal PN, although somewhat at the lower end of the type I mass range. COJ=3→2 profiles for CRL 2688 confirm the presence of an extended plateau with width Δv～85 km s^?1, whilst modestJ=3→2 enhancement is also observed for the high-velocity components in NGC 7027. TheJ=3→2 spectrum for NGC 2346 appears to mimic lower-frequency results reasonably closely, confirming the presence of a double-peaked structure towards the core, and predominantly unitary profiles to the north and south, whilst there is also evidence to suggest appreciableJ=3→2 asymmetry in CRL 618 compared to lower-frequency measures. The status of an extended cloud near HB 5 remains uncertain, although this clearly represents a remarkably complex region with velocity span ΔV～50 km s^?1. Our presentJ=3→2 results appear to track lower frequency measures extremely closely, implying local densitiesn(H₂)>3×10³ cm^?3—although temperatures close to theV _lsr of HB 5 are relatively weak, and of orderT _MB (J=3→2)≤0.9 K. Finally, as a result of both this, and previous investigations we find that of type I sources so far observed in CO, some ～42% appear to possess detectable levels of emissionT _r ^* >0.1 K. Similarly, in cross-correlating this data with other results, we note a closely linear relation betweenJ=2→1 antenna temperaturesT _MB, and the surface brightness of H₂ S(1) quadrupole emissionS(H₂)—a trend which appears also to be reflected betweenS(H₂) and corresponding parameters for [Oi], [Oii], [Ni], [Nii], and [Sii]. Such relations almost certainly arise from comparable secular variations in line intensities, although the CO, H₂, and optical emission components are likely to derive from disparate line excitation zones. As a consequence, it is clear that whilst H₂ S(1) emission is probably enhanced as a result of local shock activity, the evidence for post-shock excitation of the CO and optical forbidden lines is at best marginal. Similarly, although it seems likely that CO emission derives from circum-nebular Hi shells with kinetic temperatureT _k ～ 30 K or greater, the predominant fraction of low-excitation emission arises from a mix of charge exchange reactions, nebular stratification and, probably most importantly, the influence of UV shadow zones and associated neutral inclusions.     

Integrable approximation of J 2-perturbed relative orbits

Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J ₂ perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J ₂ Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J ₂ problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator.     

Cooling of neutron stars: Two types of triplet neutron superfluidity

We consider the cooling of neutron stars with superfluid cores composed of neutrons, protons, and electrons (for singlet proton pairing and triplet neutron pairing). The emphasis is on triplet neutron pairing with the component of the total moment of neutron pairs along the quantization axis |m _J | = 2. This case stands out in that it leads to power-law rather than exponential suppression of the main neutrino processes by neutron superfluidity. For the chosen critical neutron temperatures T _cn, the cooling with |m _J | = 2 proceeds either almost in the same way as the commonly considered cooling with m _J =0 or appreciably faster. The cooling with variable (over the core) critical temperatures T _cn(ρ) and T _cp(ρ) can generally be described by the cooling with some effective constant temperatures T _cn and T _cp. The hypothesis of strong neutron superfluidity with |m _J | = 2 is in conflict with the observational data on the thermal radiation from isolated neutron stars; the hypothesis of weak neutron superfluidity of any type is consistent with the observations.     

Effects of zonal harmonics and a circular cluster of material points on the stability of triangular equilibrium points in the R3BP

We have studied a modified version of the classical restricted three-body problem (CR3BP) where both primaries are considered as oblate spheroids and are surrounded by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effects of oblateness of both primaries up to zonal harmonic J ₄; together with gravitational potential from the circular cluster of material points on the existence and linear stability of the triangular equilibrium points. It is found that, the triangular points are stable for 0<μ<μ _c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ _c is the critical mass ratio affected by the oblateness up to J ₄ of the primaries and potential from the circular cluster of material points. The coefficient J ₄ has stabilizing tendency, while J ₂ and the potential from the circular cluster of material points have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near oblate bodies surrounded by a circular cluster of material points.     

Frost grain size metamorphism: Implications for remote sensing of planetary surfaces

An understanding of the rates of frost grain growth is essential to the goal of relating spectral data on surface mineralogy to the physical history of a planetary surface. Models of grain growth kinetics have been constructed for various frosts based on their individual thermodynamic properties and on the difference in binding energy between molecules on plane vs curved faces. A steady state situation can occur on planetary surfaces in which thermal elimination of small grains competes with their creation, usually by meteorite impact. We utilize predicted grain growth rates to explain telescopic spectral data on condensate surfaces throughout the solar system. On Pluto, predicted CH₄ ice grain growth rates are very high despite the low temperature, resulting in a multicentimeter optical path. This explains the strong CH₄ absorption band depths, which otherwise would require large amounts of CH₄ gas. On the Uranian and Saturnian satellites, extremely slow grain growth rates are predicted because of the low vapor pressure of H₂O at the existing average surface temperatures. This may explain evidence for fine grain size and peculiar microstructure. On Io, ordinary thermal exchange is more effective than sputtering in promoting grain growth because of the properties of SO₂. Over much of Io's disk, submicron size grains of SO₂ could plausibly reconfigure into a surface glaze on a timescale comparable to the resurfacing rate. This may explain the relatively strong SO₂ signature in Io's infrared absorption spectrum as opposed to its weaker manifestation in the visible spectrum. In spite of lower sputtering fluxes, sputtering plays a more important role in grain growth for Europa, Ganymede, and Callisto than on Io. This is a result of high rates of thermally activated grain growth and resurfacing on Io. The sequence of H₂O-ice absorption band depths (related to the mean grain size) is J₂(T) ～ J₃(T) > J₂(L) > J₃(L) ～ J₄(T) ～ J₄(L), where L = leading and T = trailing. This is to be expected if sputtering were dominant. The calculations show, however, that neither thermalized exchange fluxes nor sputtering exchange fluxes can produce the implied grain growth or the ordering by ice absorption band depths of the six satellite hemispheres. Only sputtering control by simple ejection of H₂O from the satellites, as the dominant cause of shorter mean lifetimes for smaller exposed grains, can satisfactorily explain the data. Some observations, which suggest that there are vertical grain size gradients, may result from a steady state balance between intense near surface production of fine frost by comminution, coupled with ongoing ubiquitous grain growth in the vertical column. In certain cases, e.g., Europa and Enceladus, the possibility exists that endogenic activity as well as comminution could affect grain size—at least locally. It is concluded that not only ice identification and mapping, but ice grain size mapping is an important experiment to be conducted on future missions.     

Second-order solution of Lindstedt's equation with constant coefficients

The Hori-Lie transformation for a non-conservative system is applied to the Lindstedt's equation with constant coefficients. A second-order solution when the right hand is a quartic polynomial is derived explicity. We made two applications of our solution. We obtained a new form of the trajectorv of a test particle moving in a Schwarzschild field. The radius of the particle is a periodic funciton of the polar angle with a period slightly different from 2π. The deviation is the relativistic precession. We also considered the solution of the coordinates ρ and η in Vinti's problem containing J₃. They are expressed as periodic functions of O'Mathuna's regularization argument.     

Effects of axis-symmetric body,zonal harmonic and potential from a belt on the stability of triangular libration points in the CR3BP

Within the frame work of the circular restricted three-body problem (CR3BP) we have examined the effect of axis-symmetric of the bigger primary, oblateness up to the zonal harmonic J ₄ of the smaller primary and gravitational potential from a belt (circular cluster of material points) on the linear stability of the triangular libration points. It is found that the positions of triangular libration points and their linear stability are affected by axis-symmetric of the bigger primary, oblateness up to J ₄ of the smaller primary and the potential created by the belt. The axis-symmetric of the bigger primary and the coefficient J ₂ of the smaller primary have destabilizing tendency, while the coefficient J ₄ of the smaller primary and the potential from the belt have stabilizing tendency. The overall effect of these perturbations has destabilizing tendency. This study can be useful in the investigation of motion of a particle near axis-symmetric—oblate bodies surrounded by a belt.     

Satellite orbital precessions caused by the first odd zonal J 3 multipole of a non-spherical body arbitrarily oriented in space

An astronomical body of mass M and radius R which is non-spherically symmetric generates a free space potential U which can be expanded in multipoles. As such, the trajectory of a test particle orbiting it is not a Keplerian ellipse fixed in the inertial space. The zonal harmonic coefficients J ₂,J ₃,… of the multipolar expansion of the potential cause cumulative orbital perturbations which can be either harmonic or secular over time scales larger than the unperturbed Keplerian orbital period T. Here, I calculate the averaged rates of change of the osculating Keplerian orbital elements due to the odd zonal harmonic J ₃ by assuming an arbitrary orientation of the body’s spin axis \(\hat{\boldsymbol{k}}\) . I use the Lagrange planetary equations, and I make a first-order calculation in J ₃. I do not make a-priori assumptions concerning the eccentricity e and the inclination i of the satellite’s orbit.     

Editorial

The Galilean satellites Io, Europa, and Ganymede interact through several stable orbital resonances where $\text{λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_1\text{= 0, λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_2\text{= 180°, λ}{}_2\text{? 2λ}{}_3\text{+}\text{ω}{}_2\text{= 0}$ and λ₁ ? 3λ₂ + 2λ₃ = 180°, with λ_i being the mean longitude of the ith satellite and $\text{ω}{}_{\mathrm{i}}$ the longitude of the pericenter. The last relation involving all three bodies is known as the Laplace relation. A theory of origin and subsequent evolution of these resonances outlined earlier (C. F. Yoder, 1979b, Nature279, 747–770) is described in detail. From an initially quasi-random distribution of the orbits the resonances are assembled through differential tidal expansion of the orbits. Io is driven out most rapidly and the first two resonance variables above are captured into libration about 0 and 180° respectively with unit probability. The orbits of Io and Europa expand together maintaining the 2:1 orbital commensurability and Europa's mean angular velocity approaches a value which is twice that of Ganymede. The third resonance variable and simultaneously the Laplace angle are captured into libration with probability ～0.9. The tidal dissipation in Io is vital for the rapid damping of the libration amplitudes and for the establishment of a quasi-stationary orbital configuration. Here the eccentricity of Io's orbit is determined by a balance between the effects of tidal dissipation in Io and that in Jupiter, and its measured value leads to the relation $\text{k}{}_1\text{?}{}_1\text{/Q}{}_1\text{≈ 900k}{}_{\mathrm{<mtext>J</mtext>}}\text{/Q}{}_{\mathrm{<mtext>J</mtext>}}$ with the k's being Love numbers, the Q's dissipation factors, and f a factor to account for a molten core in Io. This relation and an upper bound on Q₁ deduced from Io's observed thermal activity establishes the bounds 6 × 10⁴ < Q_J < 2 × 10⁶, where the lower bound follows from the limited expansion of the satellite orbits. The damping time for the Laplace libration and therefore a minimum lifetime of the resonance is 1600 Q_J years. Passage of the system through nearby three-body resonances excites free eccentricities. The remnant free eccentricity of Europa leads to the relation $\text{Q}{}_2\text{/?}{}_2\text{? 2 × 10}{}^{\mathrm{?4}}\text{Q}{}_{\mathrm{<mtext>J</mtext>}}$ for rigidity μ₂ = 5 × 10¹¹ dynes/cm². Probable capture into any of several stable 3:1 two-body resonances implies that the ratio of the orbital mean motions of any adjacent pair of satellites was never this large.A generalized Hamiltonian theory of the resonances in which third-order terms in eccentricity are retained is developed to evaluate the hypothesis that the resonances were of primordial origin. The Laplace relation is unstable for values of Io's eccentricity e₁ > 0.012 showing that the theory which retains only the linear terms in e₁ is not valid for values of e₁ larger than about twice the current value. Processes by which the resonances can be established at the time of satellite formation are undefined, but even if primordial formation is conjectured, the bounds established above for Q_J cannot be relaxed. Electromagnetic torques on Io are also not sufficient to relax the bounds on Q_J. Some ideas on processes for the dissipation of ideal energy in Jupiter yield values of Q_J within the dynamical bounds, but no theory has produced a Q_J small enough to be compatible with the measurements of heat flow from Io given the above relation between Q₁ and Q_J. Tentative observational bounds on the secular acceleration of Io's mean motion are also shown not to be consistent with such low values of Q_J. Io's heat flow may therefore be episodic. Q_J may actually be determined from improved analysis of 300 years of eclipse data.     

Combined effect of oblateness,radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP

This paper studies the motion of an infinitesimal mass in the framework of the restricted three-body problem (R3BP) under the assumption that the primaries of the system are radiating-oblate spheroids, enclosed by a circular cluster of material points. It examines the effects of radiation and oblateness up to J ₄ of the primaries and the potential created by the circular cluster, on the linear stability of the liberation locations of the infinitesimal mass. The liberation points are found to be stable for 0<μ<μ _c and unstable for $\mu_{c}\le\mu\le\frac{1}{2}$ , where μ _c is the critical mass value depending on terms which involve parameters that characterize the oblateness, radiation forces and the circular cluster of material points. The oblateness up to J ₄ of the primaries and the gravitational potential from the circular cluster of material points have stabilizing propensities, while the radiation of the primaries and the oblateness up to J ₂ of the primaries have destabilizing tendencies. The combined effect of these perturbations on the stability of the triangular liberation points is that, it has stabilizing propensity.     

Possible H2staggered+ ultraviolet spectrum of Jupiter

An ultraviolet spectral probe for a hydrogen-rich planetary atmosphere, such as that of Jupiter, is suggested, utilizing discrete lines in the H₂^staggered+ 2pπ_u?1sσ_g electronic transition. For the Jovian atmosphere, the dominant mechanism for exciting H₂⁺ to its 2pπ_u state appears to be photoexcitation, principally through absorption of the solar Lyman-α line. We estimate that the Jovian column emission rate of the H₂⁺ 2pπ_u(ν′ = 2, J′ = 1) →1sσ_g(ν″ = 18,J″ = 0) fluorescent line at 1236.6 Å is if1 photon cmsu-2 secsu-1; i.e., that if1 photon secsu-1 of this radiation would strike a 15-cm diameter mirror in a Jupiter fly-by at an impact parameter of 3 × 10⁵km. The critical role of corrections to the Born-Oppenheimer approximation in the use of an H₂⁺ probe is discussed.     

Longitudinal variation of equatorial electrojet parameters derived from POGO satellite observations

A method of analysis has been developed making it possible to obtain electrojet parameters from vertical profiles of the POGO electrojet data. This has provided an unprecedented quantity of electrojet parameters—about 500 each of its peak eastward current intensity J₀, its total eastward current I₊, and its half width w—spanning through 360° longitude round the Earth, 5 h of daytime and September equinoctial months of the years 1967, 1968 and 1969. The daytime all-longitude averages of the parameters for the 3 years are 235 ± 14 km for w, 232 ± 63A km^?1 for J₀ and (54 ± 11) × 10³A for I₊. This first coverage round the globe shows that J₀ and I₊ vary considerably with longitude unlike w. While confirming the expected maximum of J₀ and I₊ at about 280°E longitude, we find that each of them also has an unexpected major maximum at about 100°E and a subsidiary maximum at 190°E longitude. The major maxima are found to be prominent only at hours near local noon. It is argued that the surprising longitudinal variations of J₀ and I₊ cannot be explained satisfactorily by variations in the upper mantle conductivity along the dip equator but possibly by longitudinal variations of wind systems and gradients at electrojet altitudes.     

An analytic satellite theory using gravity and a dynamic atmosphere

An analytical solution is given for the motion of an artifical Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational effects of the zonal harmonicsJ ₂,J ₃, andJ ₄ are included, and the drag effects of any arbitrary dynamic atmosphere are included. By a dynamic atmosphere, we mean any of the modern empirical models which use various observed solar and geophysical parameters as inputs to produce a dynamically varying atmosphere model. The subtleties of using such an atmosphere model with an analytic theory are explored, and real world data is used to determine the optimum implementation. Performance is measured by predictions against real world satellites. As a point of reference, predictions against a special perturbations model are also given.