Perturbations of a geo-centric synchronous satellite with resonance

We have investigated the resonances due to the perturbations of a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity. The resonances at the points resulting from (i) the commensurability between \(\dot{\theta}_{0}\) (steady-state orbital angular rate of the satellite) and \(\dot{\theta}_{m}\) (angular velocity of the moon around the earth) and (ii) the commensurability between \(\dot{\theta}_{0}\) and \(\dot{\psi}_{0}\) (steady-state regression rate of the synchronous satellite) are analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure as given in Brown and Shook (Planetary Theory, Cambridge University Press, Cambridge, 1933). We have observed that as θ _m (0^°≤θ _m ≤45^°) and ψ (0^°≤ψ≤135^°) increase, the amplitude decreases and the time period also decreases. We have also shown the effect of ψ on amplitude and time period for 0^°≤Γ≤45^°, where Γ is the angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the satellite on the plane of the equator.     

The geometry of impacts on a synchronous planetary satellite

We consider a satellite in a circular orbit about a planet that, in turn, is in a circular orbit about the Sun; we further assume that the plane of the planetocentric orbit of the satellite is the same as that of the heliocentric orbit of the planet. The pair planet–satellite is encountered by a population of small bodies on planet-crossing, inclined orbits. With this setup, and using the extension of Öpik’s theory by Valsecchi et al. (Astron Astrophys 408:1179–1196, 2003), we analytically compute the velocity, the elongation from the apex and the impact point coordinates of the bodies impacting the satellite, as simple functions of the heliocentric orbital elements of the impactor and of the longitude of the satellite at impact. The relationships so derived are of interest for satellites in synchronous rotation, since they can shed light on the degree of apex–antapex cratering asymmetry that some of these satellites show. We test these relationships on two different subsets of the known population of Near Earth Asteroids.     

Cratering rate over the surface of a synchronous satellite

Equations have been derived for the asymmetries of crater frequency over the surface of a synchronously rotating satellite, when the orbital velocities of projectiles about the parent planet are always larger than the satellite's circular orbital velocity. If the projectiles orbit the planet in moderately eccentric ellipses, no marked apex-antapex asymmetries of crater frequency distribution are expected. Theoretical values of apex-antapex asymmetries are presented for the Earth, the Moon, and some Jovian and Saturnian satellites, and are compared with available observational and theoretical results.     

Geomagnetic field variation during winter storm at localized southern and northern high latitude

This paper presents the effect of geomagnetic storm on geomagnetic field components at Southern (Maitri) and Northern (Kiruna) Hemispheres. The Indian Antarctic Station Maitri is located at geom. long. 66.03° S; 53.21° E whereas Kiruna is located at geom. long. 67.52° N; 23.38° E. We have studied all the geomagnetic storms that occurred during winter season of the year 2004–2005. We observed that at Southern Hemisphere the variation is large as compared to the Northern Hemisphere. Geomagnetic field components vary when the interplanetary magnetic field is oriented in southward direction. Geomagnetic field components vary in the main phase of the ring current. Due to southward orientation of vertical component of IMF reconnection takes place all across the dayside that transports plasma and magnetic flux which create the geomagnetic field variation.     

Orbital variation of the synchronous satellite and its calculation

This paper investigates the orbital variation of the 24-hour synchronous satellite and gives a method for calculating the variation. The results provide a theoretical basis for the design and calculation of the orbit of the communication satellites.     

On the existence of a long range correlation in the Geomagnetic Disturbance storm time (Dst) index

The Dst (Disturbance storm time) index is a measurement of earth geomagnetic activity and is widely used to characterize the geomagnetic storm. It is calculated on the basis of the average value of the horizontal component of the earth’s magnetic field at four observatories, namely, Hermanus (33.3° south, 80.3° in magnetic dipole latitude and longitude), Kakioka (26.0° north, 206.0°), Honolulu (21.0° north, 266.4°), and San Juan (29.9° north, 3.2°) and is expressed in nano-Teslas. The strength of the low-latitude surface magnetic field is inversely proportional to the energy content of the ring current around earth caused by solar protons and electrons, which increases during geomagnetic storms. Thus a negative Dst index value indicates that the earth’s magnetic field is weakened which is specifically the case during solar storms. Predicting Dst index is a difficult task due to its structural complexity involving a variety of underlying plasma mechanism. For characterizing and forecasting this complex time series, a formal model must be established to identify the specific pattern of the series. Persistent demand for a fool proof model of Geomagnetic Dst index prompted us to investigate the Dst Time Series mechanism with a very recent technique called Visibility Algorithm and it is observed that the Dst time series follows the same model that of a Stochastic Fractional Brownian motion having long range correlation.     

Eclipsing binaries in the MOST satellite fields

Sixteen new eclipsing binaries have been discovered by the MOST satellite among guide stars used to point its telescope in various fields. Several previously known eclipsing binaries were also observed by MOST with unprecedented quality. Among the objects we discuss in more detail are short‐period eclipsing binaries with eccentric orbits in young open clusters: V578 Mon in NGC 2244 and HD 47934 in NGC 2264. Long nearly‐continuous photometric runs made it possible to discover three long‐period eclipsing binaries with orbits seen almost edge‐on: HD 45972 with P = 28.1 days and two systems (GSC 154 1247 and GSC 2141 526) with P > 25 days. The high precision of the satellite data led to discoveries of binaries with very shallow eclipses (e.g., HD 46180 with A = 0.016 mag, and HD 47934 with A = 0.025 mag). Ground‐based spectroscopy to support the space‐based photometry was used to refine the models of several of the systems (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Motion near frozen orbits as a means for mitigating satellite relative drift

Generally, any initially-close satellites—chief and deputy—moving on orbits with slightly different orbital elements, will depart each other on locally unbounded relative trajectories. Thus, constraints on the initial conditions must be imposed to mitigate the chief-deputy mutual departure. In this paper, it is analytically proven that choosing the chief’s orbit to be a frozen orbit can mitigate the natural relative drift of the satellites. Using mean orbital element variations, it is proven that if the chief’s orbit is frozen, then the mean differential eccentricity is periodic, leading to a periodic variation of the differential mean argument of latitude. On the other hand, if the chief’s orbit is non-frozen, a secular growth in the differential mean argument of latitude leads to a concomitant along-track separation of the deputy from the chief, thereby considerably increasing the relative distance evolution over time. Long-term orbital simulation results indicate that the effect of choosing a frozen orbit vis-à-vis a non-frozen orbit can reduce the relative distance drift by hundreds of meters per day.     

On the analytic lunar and solar perturbations of a near Earth satellite

The disturbing function of the Moon (Sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the Moon (Sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elementsl, l′, F, D and Γ of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements ω and Ω of the satellite so that analytic integration is simple and the results accurate over a long period of time.     

Geomagnetic storm effects on the thermosphere and the ionosphere revealed by in situ measurements from OGO 6

The temporal response of ion and neutral densities to a geomagnetic storm has been investigated on a global scale with data from consecutive orbits of OGO-6 (>400km) for 4 days covering both magnetically quiet and disturbed conditions. The first response of the neutral atmosphere to the storm takes place in the H and He densities which start to decrease near the time of the storm sudden commencement. The maximum decreases in H and He were more than 40% of the normal density at high latitudes. A subsequent increase in O and N₂ densities occurs about 8 hours later than the change in H and He densities, while the relative O and N₂ density changes indicate a depletion of atomic oxygen in the lower thermosphere by more than a factor of two. The overall features of the change in the neutral atmosphere, especially the patterns of change for individual species, strongly support the physical picture that energy is deposited primarily at high latitudes during the storm, and the thermosphere structure changes through (1) heating of the lower thermosphere and (2) generation of large scale circulation in the atmosphere with upwelling at high latitudes and subsidence at the equator. The storm-time response of H⁺ occurs in two distinct regions separated by the low latitude boundary of the light ion trough. While on the poleward side of the boundary the H⁺ density decreases in a similar manner to the decrease in H density, on the equatorward side of the boundary the H⁺ decrease occurs about half a day later. It is shown that the decrease of H⁺ density is principally caused by the decrease in H density for both regions. The difference in H⁺ response between the two regions is interpreted as the difference in H⁺ dynamics outside and inside the plasmasphere. The O⁺ density shows an increase, the pattern of which is rather similar to that for O. Two possibilities for explaining the observed change in O⁺ density are suggested. One attributes the observed increase in O⁺ density to an increase in the plasma temperature during the storm. The other possibility is that the increase in the production rate of O⁺ due to an increase in O density exceeds the increase in the loss rate of O⁺ due to an increase in N₂ density, especially around the time of sunrise. Hence the change in O⁺ density in the F-region may actually be controlled by the change in O density.     

Rotational shear near the solar surface as a probe for subphotospheric magnetic fields

Helioseismology revealed an increase in the rotation rate with depth just beneath the solar surface. The relative magnitude of the radial shear is almost constant with latitude. This rotational state can be interpreted as a consequence of two conditions characteristic of the near-surface convection: the smallness of convective turnover time in comparison with the rotation period and absence of a horizontal preferred direction of convection anisotropy. The latter condition is violated in the presence of a magnetic field. This raises the question of whether the subphotospheric fields can be probed with measurements of near-surface rotational shear. The shear is shown to be weakly sensitive to magnetic fields but can serve as a probe for sufficiently strong fields of the order of one kilogauss. It is suggested that the radial differential rotation in extended convective envelopes of red giants is of the same origin as the near-surface rotational shear of the Sun.     

On the asymmetric development of magnetic storm fields in low and middle latitudes

By a detailed analysis of the disturbance field of certain magnetic storms, including that of 13 September 1957, it is shown that there must be a fairly steady current system, partly external and partly ionospheric, which contributes a substantial portion of the asymmetry in the low and middle latitude storm field, independent of the growth and decay of auroral electrojets. A new model electric current system is presented to account for such an asymmetry. It is suggested that there is a gap in the ring current belt on the night side, and that the ring current is closed through the ionosphere.     

Line profile analysis of a coronal formation observed near a quiescent prominence: Intensities,temperatures and velocity fields

A technique developed for analysing line profiles with both speed and high accuracy was used to study the physical conditions of a coronal formation near a quiescent prominence. Detailed analyses of five coronal lines (Fe xiv λ 5303, Fe x λ 6374, Ni xv λ 6702, Fe xv λ 7059, and Fe xi λ 7892) provided total intensities, Doppler width temperatures, ionization temperatures, and velocities. Dissimilar spatial fluctuations in intensity are obvious for ions grouped according to (low vs high) ionization potentials. The intensity of the green line shows a local minimum around the observed quiescent prominence; a corresponding but much more diffuse pattern is visible in the red line intensity. Large differences are observed in temperatures derived by different means. In particular, , while , and . The differences between and are taken as direct evidence of temperature inhomogeneity. One can thus put little significance in T _e (xi/x). T _D(λ5303) and T _e (xv/xiv) fluctuate nearly in parallel at each slit height, with a weak local minimum evident around the prominence. The discrepancy between these two can be removed if a non-thermal turbulent motion of 6–16 km s⁻¹ is assumed. Variations with height of both T _D(λ5303) and T _e (xv/xiv) suggest that the coronal temperature maximum is located no more than 15000 km above the top of spicules. A negative gradient of about 6 deg km⁻¹ is found in the height variation of T _D(λ5303). The height variation of the green line wavelength shows that the majority of coronal material in this region is flowing from west to east on the Sun, with the highest velocity of 12 km s⁻¹ found at the lowest heights. This motion is in the same sense as that of the nearby coronal rain, as determined both from the spectra and wavelength-shifted Hα filtergrams. Superposed on the above flow is a systematic velocity field of up to ±5 km s⁻¹. This field similarly reaches maximum amplitudes at lowest heights showing a local maximum around the prominence. On leave from Institute of Earth Science and Astrophysics, Shiga University, Ohtsu 520, Japan, as 1973–75 National Academy of Science/National Research Council Senior Post-Doctoral Research Associate at Sacramento Peak Observatory.     

Comparison of two methods for determining the magnetic fields near black holes

We compare two methods for estimating the magnetic field near a black hole—based on a statistical formula that relates the magnetic field on the horizon of the black hole to its mass and on a direct magnetic field determination from optical polarimetric observations. An optically thick magnetized accretion disk is usually formed around the black hole in active galactic nuclei. The linear polarization of the radiation emerging from the disk is related to the local magnetic field and the polarization in Milne’s classical problem. The magnetic field in the region from where the radiation with the observed wavelength comes can be estimated by measuring this polarization. On the other hand, this field can be estimated from the above statistical formula if the field near the black hole is extrapolated into the accretion disk using a standard power law. Comparison of the magnetic field obtained from the observed polarization with the extrapolated field can serve to estimate the accuracy of the latter and the exponent in the adopted extrapolation law. As an example, we compare these two methods for the source NGC 4258.     

Pc 1–2 observations of heavy ion effects by synchronous satellite ATS-6

Ion cyclotron waves generated in the magnetosphere by the ion cyclotron instability of protons are thought to be the origin of Pc 1–2 geomagnetic pulsations. Propagation characteristics of these waves have been measured using ATS-6 synchronous satellite magnetometer wave data. Of particular interest are the wave spectra, polarization properties, and wave diagnostics; all are characteristic of propagation in a cool ambient magnetospheric plasma containing He⁺ and O⁺ heavy ions.     

A method to determine regional lunar gravity fields from earth-based satellite tracking data

A method to determine regional gravity fields of the Moon from Earth-based Doppler and range satellite tracking data residuals of a low Moon-orbiting satellite has been developed and thoroughly tested in a controlled simulation environment. A short-arc approach, where one arc consists of the time it takes the satellite to cross the grid of interest on the lunar surface, is used in order to filter out most long-wavelength signal that can still be present in the residuals. Simulation results where the data are contaminated with either typical systematic or stochastic noise show that recovery of the local gravity field down to the level of several mGal is possible. The inclusion of extremely low-altitude data also means that regularisation in the sense of including a priori information in the form of a regularisation matrix is not necessary in order to obtain a good solution at high resolution.     

Wind estimates near 150 km from the variation in inclination of low-perigee satellite orbits

Precise orbit determinations of five Air Force low-altitude satellites are used to estimate winds near 150 km from variations in the satellite orbital inclinations. Zonal winds determined by this method range from 25 to 200 m/sec during quiet to moderately disturbed geomagnetic conditions, to winds on the order of 300–600 m/sec during active geomagnetic conditions. Comparisons are made with other wind data and appropriate theories.     

Variations in exospheric density at heights near 1100km, derived from satellite orbits

In an earlier paper, values of exospheric density were obtained from the orbit of Echo 2 for the years 1964–1965. The results indicated a semi-annual variation in density by a factor of between 2 and 3, considerably larger than predicted by existing atmospheric models.

These studies have now been extended to the beginning of 1967, using both Echo 2 and Calsphere 1, to show how the density is responding to increasing solar activity. Variations in density during 1964 have been analysed in more detail. The long-term variation associated with the solar cycle and the short-term variations associated with magnetic and solar disturbances agree with the variations expected on the basis of current models. The semi-annual variation is persisting to higher levels of solar activity, and although its amplitude is diminishing the factor of variation was still 1.6 in 1966.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

Predicting Solar Cycle 24 Using a Geomagnetic Precursor Pair

We describe using Ap and F_10.7 as a geomagnetic-precursor pair to predict the amplitude of Solar Cycle 24. The precursor is created by using F_10.7 to remove the direct solar-activity component of Ap. Four peaks are seen in the precursor function during the decline of Solar Cycle 23. A recurrence index that is generated by a local correlation of Ap is then used to determine which peak is the correct precursor. The earliest peak is the most prominent but coincides with high levels of non-recurrent solar activity associated with the intense solar activity of October and November 2003. The second and third peaks coincide with some recurrent activity on the Sun and show that a weak cycle precursor closely following a period of strong solar activity may be difficult to resolve. A fourth peak, which appears in early 2008 and has recurrent activity similar to precursors of earlier solar cycles, appears to be the “true” precursor peak for Solar Cycle 24 and predicts the smallest amplitude for Solar Cycle 24. To determine the timing of peak activity it is noted that the average time between the precursor peak and the following maximum is ≈?6.4 years. Hence, Solar Cycle 24 would peak during 2014. Several effects contribute to the smaller prediction when compared with other geomagnetic-precursor predictions. During Solar Cycle 23 the correlation between sunspot number and F_10.7 shows that F_10.7 is higher than the equivalent sunspot number over most of the cycle, implying that the sunspot number underestimates the solar-activity component described by F_10.7. During 2003 the correlation between aa and Ap shows that aa is 10 % higher than the value predicted from Ap, leading to an overestimate of the aa precursor for that year. However, the most important difference is the lack of recurrent activity in the first three peaks and the presence of significant recurrent activity in the fourth. While the prediction is for an amplitude of Solar Cycle 24 of 65±20 in smoothed sunspot number, a below-average amplitude for Solar Cycle 24, with maximum at 2014.5±0.5, we conclude that Solar Cycle 24 will be no stronger than average and could be much weaker than average.