A revaluation of the rotational speed of the upper atmosphere

In this paper the rotational speed of the upper atmosphere, mainly at heights of 200–300 km, is evaluated from the changes in the orbital inclinations of thirteen satellites. The values obtained represent the mean rotational speed over the latitudes covered by the satellites, at dates between late 1962 and early 1966, i.e. when solar activity was low.

If the angular velocity of the atmosphere is taken as Λ times that of the Earth, the values of Λ found are mostly between 1.0 and 1.6 with estimated S.D. between 0.1 and 0.25. If we exclude two values at heights above 300 km and one anomalous value, the mean of the remaining ten values of Λ obtained is 1.27, with r.m.s. scatter 0.18: this would correspond to an average west-to-east wind of about 100 m/sec in mid-latitudes.     

Upper-atmosphere zonal winds: Variation with height and local time

The average rotation rate of the upper atmosphere can be found by analysis of the changes in the orbital inclinations of satellites, and results previously obtained have indicated that the atmospheric rotation rate appreciably exceeds the Earth's rotation rate at heights between 200 and 400 km.We have examined all such results previously published in the light of current standards of accuracy: some are accepted, some revised, and some rejected as inadequate in accuracy. We also analyse a number of fresh orbits and, adding these to the accepted and revised previous results, we derive the variation of zonal wind speed with height and local time. The rotation rate (rev/day) averaged over all local times increases from near 1.0 at 150 km height to 1.3 near 350 km (corresponding to an average west-to-east wind of 120 m/s), and then decreases to 1.0 at 400 km and probably to about 0.8 at greater heights. The maximum west-to-east winds occur in the evening hours, 18–24 h local time: these evening winds increase to a maximum of about 150 m/s at heights near 350 km and decline to near zero around 600 km. In the morning, 4–12 h local time, the winds are east to west, with speeds of 50–100 m/s above 200 km. We also tentatively conclude that, at heights above 350 km, the average rotation rate is greater in equatorial latitudes (0–25°) than at higher latitudes.     

Features of the upper atmosphere revealed by analysis of the orbit of cosmos 1009 rocket, 1978-50B

COSMOS 1009 rocket was launched on 19 May 1978 into an orbit with initial perigee height 150 km and apogee 1100 km: its lifetime was only 17 days. The orbit has been determined daily during the final 14 days of its life, using the RAE orbit refinement program PROP6,with about 1100 observations supplied by NORAD. An average accuracy of about 60 m, radial and cross-track, was achieved.The orbits were analysed to reveal three features of the upper atmosphere at heights between 125 and 175 km. From the decrease in perigee height, five values of density scale height, accurate to ±4%, were obtained. The first three were within 10% of those from CIRA 1972; the fourth, after a magnetic storm, was higher than expected; the fifth gave evidence of the decrease in drag coefficient at heights below 130 km.Atmospheric oblateness produced a change of 4° in perigee position during the last four days of the life. Analysis showed that the ellipticity of the upper atmosphere was approximately equal to that of the Earth, f, for the first two of the four days, and about $\text{1}\text{2}\text{f}$ in the last two.The orbital inclination decreased during the 14 days by about 50 times its standard deviation, and the observed variation was analysed to determine zonal winds at heights of 150–160 km at latitudes near 47° north. The zonal wind was very weak (0±30 m/s) for 23–28 May at local times near 03h; and 90±30 m/s east-to-west for 29 May to 4 June at local times near 01 h.     

The formation of Mg i 4571 Å in the solar atmosphere

An analysis of the 4571 Å line of neutral magnesium is presented in which one-dimensional macroscopic velocity fields are included. It is shown that gradients over restricted heights in the vertical and horizontal components of the velocity field of order -0.005 s^–1 and -0.004 s^–1 (such that velocity towards the observer decreases as height increases), respectively, result in asymmetries in the computed line profile similar to those observed. The heights in the solar atmosphere at which these velocity gradients exist are shown to be very critical in reproducing the observations. It was found that the best results were obtained when the gradients existed in the height range from 200 km to 300 km below the temperature minimum. The results indicate that for the Mg i 4571 Å line model calculations that do not include one-dimensional flow velocities may safely be compared with frequency-averaged observations.     

Analysis of the orbit of 1966-51C

The satellite 1966-51C was launched in June 1966 into a polar orbit with perigee height 180 km, apogee height 3600 km, and orbital period 125 min. The orbit contracted rapidly under the influence of air drag, and the satellite decayed in March 1967. The only available observations are from the NASA Minitrack system, and 825 of these have been used with PROP6 orbit refinement program, to determine orbital parameters at 20 epochs. For most of these orbits the standard deviations in inclination and right ascension of the node are less than 0.002° (corresponding to about 200 m cross-track) and the standard deviations in eccentricity are less than 0.00002 (150 m in height).The variation in inclination is analysed to determine upper-atmosphere zonal wind speeds, with excellent resolution in local time. The results, for heights near 210 km and a representative latitude near 30°, indicate west-to-east winds of 100 ± 40 m/s for local time 18–21 h, and east-to-west winds of 80 ± 25 m/s for 02–04 h and 09–12 h local time. The values of the right ascension of the node are also analysed, and provide independent confirmation of the wind speeds obtained from the inclination. Analysis of the decrease in perigree distance indicates values of density scale height within 5% of those predicted by the COSPAR International Reference Atmosphere 1972, for the conditions experienced by 1966-51C.     

Systematic winds at heights between 350 and 675 km from analysis of the orbits of four balloon satellites

Six values of the rate of rotation of the Earth's upper atmosphere have been obtained by analysis of the orbital inclinations of four balloon satellites in the intervals just before the final decay of their orbits. The effective heights of these results range from about 350 to about 675 km. The values themselves range from 0·8 to 1·4 times the Earth's rotation and correspond to zonal wind speeds between 100 m/sec westward and 200 m/sec eastward. All the results correspond to fairly specific local times and are consistent with a diurnal wind pattern in low latitudes having a strong eastward maximum near local midnight and a lesser westward maximum near 10:00 LT. They argue against the contention of a sharp decrease in the rate with respect to that of the Earth, which is supposed to begin at about 360 km. The factors involved in the determination of these values and the method used are discussed in considerable detail.     

Variations in air density at heights near 200 km during 1967–1969, from the orbit of 1967-31A

Air density at a height of 180–200 km from July 1967 to September 1969 has been determined from analysis of the high eccentricity orbit of satellite 1967-31A. The data show good correlation between sudden density increase and geomagnetic disturbance. The increases for disturbances of equal strength are approximately 40% greater during night-time than daytime hours. The day-night influence is also observed in the changes in density with changes in the solar flux index, F₁₀. The 27-day density variation is predominant mainly during night-time, although the atmospheric response to F₁₀ variations is quite variable regardless of local time. A semi-annual variation of approx. 40% is observed. Also found is a 25% diurnal variation for heights near 170–180 km, which is in good agreement with the CIRA 1972 atmosphere.     

Superrotation of the thermosphere by global deposition of meteoroids?

Mitra has suggested that the Superrotation of the upper atmosphere is caused by a deposition of meteoroids. The meteoroids are assumed to impart to the atmosphere the excess of their orbital angular momentum per unit mass over the Earth's angular momentum per unit mass. The process is to take place in the height region above 150 km. Only above this height is a Superrotation of the atmosphere observed. In this report the forces that tend to make the atmosphere corotate with the Earth are analysed. It is shown that the most important of these forces is ion drag, and not viscous drag as postulated by Mitra. As the net angular spin momentum imparted by the meteoroids seems to be less than Mitra's estimate and its main part is applied to the atmosphere at altitudes much lower than 150 km, the hypothesis that meteoroids provide a significant contribution to the Superrotation is rejected.     

Analysis of the orbit of 1965-11D (COSMOS 54 rocket)

The satellite 1965-11D was the final-stage rocket used to launch Cosmos 54, 55 and 56 into orbit on 21 February 1965. The orbit of 1965-11D was inclined at 56° to the Equator, with an initial perigee height of 280 km; the lifetime was nearly 5 yr, with decay on 23 December 1969. The orbit has been determined at 75 epochs during the life, using the RAE orbit determination program PROP with over 4000 observations, photographic, visual and radar. Observations from the Hewitt camera at Malvern were available for 34 of the 75 orbits and typical accuracies for these orbits are 0.0005° in inclination and 100 m in perigee height.The variations in perigee height have been analyzed to determine reliable values of density scale height, at heights between 240 and 360 km. The analysis also revealed a rapid decrease of 5 km in perigee distance early in 1966, attributed to the escape of residual propellants.The variations in orbital inclination have been analyzed to determine upper-atmosphere zonal winds and 15th-order harmonics in the geopotential. The region of the upper atmosphere traversed by 1965-11D near its perigee is found to have had an average rotation rate of 1.10 ± 0.05 rev/day in 1966–1967, and 1.00 ± 0.03 rev/day between March 1968 and May 1969. In late 1969 there were probably wide variations in zonal winds, with east-to-west winds of order 100 m/s followed by west-to-east winds of order 200 m/s. The changes in inclination at the 15th-order resonance in July 1969 have been analyzed to give the first accurate values of lumped 15th-order harmonics obtained from a high-drag satellite. This success points the way towards similar analyses of the many other high-drag satellites that pass through 15th-order resonance, to evaluate individual geopotential coefficients of order 15 and even degree.     

Annual and semi-annual zonal wind components and corresponding temperature and density variations, 60–130 km

From rocket and radar-meteor wind observations, annual and semi-annual components of the zonal flow are derived for latitudes N at heights between 60 and 130 km. Height regions of maximum and minimum amplitude are described with reference to changes in phase. The annual components decrease with height throughout the mesosphere and, after a reversal of phase, enhance to 25 m/sec at 100 ± 5 km. The semi-annual components have maximum amplitudes of 25 m/sec over a wide range of latitude in two height regions at 90 and 120 km and in a limited range of latitude (near 50°) at 65 km.

Calculated temperatures and log densities are discussed in terms of amplitude and phase as functions of height and latitude. Below 100 km a comparison is made with temperature amplitudes derived from independent temperature data. Above 100 km the annual temperature variation maximizes at 115 km and is particularly large at high latitudes (exceeding 50°K). On the other hand, the semi-annual component increases rapidly with height between 110 and 120 km at all latitudes maximizing at the 120 km level, where amplitudes exceed 25°K at high and low latitudes and 10°K at mid-latitudes. The annual component of log density, like the temperature variation, is largest at high latitudes up to 125 km. The semi-annual variation has a minimum at 110–115 km, above which amplitudes increase with height, reaching 5–12 per cent at 130 km according to latitude. The phases at and near 130 km for the annual and semi-annual density variations are very close to those found at greater heights from satellite orbits and amplitudes could be readily extrapolated to agree with those in the satellite region.     

Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements

The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe i 6173.3 Å line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection-simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30?–?40 km above (line center) and 30?–?40 km below (average wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic-cutoff frequency.     

Analysis of the orbit of 1970-114F in its last 20 days

The satellite 1970-114F, the final-stage rocket of the Molniya 1S communications satellite, decayed in the atmosphere on 3 March 1973. During the last 20 days of its life the orbit suffered exceptionally rapid decay, with the apogee height decreasing from 7000 to 1000 km while the perigee height remained near 110 km. About 650 observations, made by visual observers in Britain and by U.S. Navy sensors, have been used with the PROP6 orbit refinement program to determine orbits at 14 epochs. Although the decay rate was more than ten times greater than in any previous orbit determination with PROP, good orbits were obtained, the standard deviation in inclination being less than 0.002° on eight orbits.The combination of high drag and good accuracy allows three techniques in orbital analysis to be successfully applied for the first time. Since zonal winds have little effect on the orbit, the changes in inclination are analysed to determine meridional winds near perigee, at heights of 110–120 km, latitudes of 63–65°S, and 6–12 hr LT. The changes in right ascension of the node are also successfully analysed for the same purpose. The two methods agree in indicating a south-to-north wind of 40 ± 30 m/sec from 11 to 21 February, a geomagnetically quiet period, and a south-to-north wind averaging 150 ± 30 m/sec from 22 February to 3 March, a geomagnetically disturbed period. Thirdly, the changes in the argument of perigee are analysed to determine atmospheric oblateness, which is found to be equal to the Earth's oblateness, to within ±20%. Lastly, the drag coefficient in transition flow is evaluated and found to be 0.85 ± 0.20.     

The rate of small impacts on Earth

Abstract— Asteroids tens to hundreds of meters in diameter constitute the most immediate impact hazard to human populations, yet the rate at which they arrive at Earth's surface is poorly known. Astronomic observations are still incomplete in this size range; impactors are subjected to disruption in Earth's atmosphere, and unlike the Moon, small craters on Earth are rapidly eroded. In this paper, we first model the atmospheric behavior of iron and stony bodies over the mass range 1–10¹² kg (size range 6 cm‐1 km) taking into account deceleration, ablation, and fragmentation. Previous models in meteoritics deal with rather small masses (<10⁵–10⁶ kg) with the aim of interpreting registered fireballs in atmosphere, or with substantially larger objects without taking into account asteroid disruption to model cratering processes. A few earlier attempts to model terrestrial crater strewn fields did not take into account possible cascade fragmentation. We have performed large numbers of simulations in a wide mass range, using both the earlier “pancake” models and also the separated fragments model to develop a statistical picture of atmosphere‐bolide interaction for both iron and stony impactors with initial diameters up to ?1 km. Second, using a compilation of data for the flux at the upper atmosphere, we have derived a cumulative size‐frequency distribution (SFD) for upper atmosphere impactors. This curve is a close fit to virtually all of the upper atmosphere data over 16 orders of magnitude. Third, we have applied our model results to scale the upper atmosphere curve to a flux at the Earth's surface, elucidating the impact rate of objects <1 km diameter on Earth. We find that iron meteorites >5 times 10⁴ kg (2.5 m) arrive at the Earth's surface approximately once every 50 years. Iron bodies a few meters in diameter (10⁵–10⁶ kg), which form craters ?100 m in diameter, will strike the Earth's land area every 500 years. Larger bodies will form craters 0.5 km in diameter every 20,000 years, and craters 1 km in diameter will be formed on the Earth's land area every 50,000 years. Tunguska events (low‐level atmospheric disruption of stony bolides >10⁸ kg) may occur every 500 years. Bodies capable of producing hazardous tsunami (?200 m diameter projectiles) should strike the Earth's surface every ?100,000 years. This data also allows us to assess the completeness of the terrestrial crater record for a given area over a given time interval.     

The Solar granulation in different heights

Intensity images and Doppler-velocity maps of the quiet sun in different heights are obtained from simultaneously recorded spectra of different lines. A relation between the intensity images is recognizable up to formation heights of 900 km above continuum, but the correlation coefficient changes sign above 400 km. The core of H_α shows a different pattern without any correlation to the continuum layer. Extreme Doppler velocities as well as the rms-velocities have minima at a height of 400 km, values of about 2 km/s occur in deep photospheric layers and 2.5 km/s in a height of 900 km. The velocities in the lower and in the upper photosphere are well correlated indicating that the pattern of the velocity field is preserved up to higher layers than the intensity pattern. H_α-velocities reach values up to 10 km/s and more, they show no correlation with the continuum intensities and almost no with the line core intensities.     

Radarclinometry of the sand seas of Africa’s Namibia and Saturn’s moon Titan

Radarclinometry is a powerful technique for estimating heights of landforms in synthetic aperture radar (SAR) images of planetary surfaces. In particular, it has been used to estimate heights of dunes in the sand seas of Saturn’s moon Titan (Lorenz, R.D., and 39 colleagues [2006]. Science 312, 724-727). In this work, we verify the technique by comparing dune heights derived from radarclinometry to known topography of dune fields in the Namib sand sea of western Africa. We compared results from three different image grid spacings, and found that 350 m/pixel (the same spacing at which the Cassini RADAR data was processed) is sufficient to determine dune height for dunes of similar morphometry to those of the Namib sand sea. At this grid spacing, height estimates derived from radarclinometry are largely representative of, though may underestimate by as much as 30%, or overestimate by as much as 40%, true dune height. Applying the technique to three regions on Titan, we estimate dune heights of 45-180 m, and dune spacings of 2.3-3.3 km. Obtaining accurate heights of Titan’s dunes will help to constrain the total organic inventory on Titan.     

Remarks concerning the diffusion of ion clouds in the earth's upper atmosphere

The diffusive motion of initially ellipsoidal plasma irregularities or ion clouds in the Earth's upper atmosphere is studied theoretically using a model similar to that described by Pickering (1972) for an initially spherical cloud. The work presented here concerns irregularities with major to minor axis ratio between 10:1 and 200:1 at each of the altitudes 97.5 km, 102 km and 114 km (where the ionization could be produced by meteors) and between approximately 200:1 and 1000:1 for altitudes 210 km and 300 km. In particular the effect of the space-charge electric field on the nature of the diffusion process is discussed. The possible effects of ionospheric electric fields and possible relevance to artificial Ba⁺ clouds released in the upper atmosphere are discussed in the second section.     

Impacts into oceans and seas

Impacts of cosmic bodies into oceans and seas lead to the formation of very high waves. Numerical simulations of 3-km and 1-km comets impacting into a 4 km depth ocean with a velocity of 20 km/sec have been conducted. For a 1-km body, depth of the interim crater in the sea bed is about 8 km below ocean level, and the height of the water wave is 10 m at a distance of 2000 km from the impact point. As the water wave runs into shallows, a huge tsunami hits the coast. The height of the wave strongly depends on the coastal and sea bed topography.If the impact occurred near the shore, the huge mass of water strikes the cliffs and the near shore mountain ridges and can cause displacement of the rocks, initiate landslides, and change the relief. Thus, impact into oceans and seas is an important geological factor.Cosmic bodies of small sizes are disrupted by aerodynamic forces. Fragments of a 100-m radius comet striking the water surface create an unstable cavity in the water of about 1 km radius. Its collapse also creates tsunami.A simple estimate has been made using the light curves from recent atmosphere explosions detected by satellites. The results of our assessment of the characteristics of meteoroids which caused these intense light flashes suggests that fragments of a 25-m stony body with initial impact velocity 15 to 20 km/sec will hit the surface. For a 75-m iron body striking the sea with a depth of 600 m, the height of the wave is 10 m at 200–300 km distance from the impact.     

Upper air density derived from the orbits of Discoverer satellites and its variation with latitude

Observations on artificial satellites have been used to investigate how the air density at heights between 190 and 260 km varies with latitude The Discoverer series of satellites was used because the position of their perigees moved over the latitude range from 80°S to 80°N.

It is concluded that the air density at a fixed height is a function of latitude and is about 30 per cent smaller at the poles than at the equator. This result is applicable to a local time of 14^h in the years 1959–1960: it is different from that obtained by Groves who concluded that the density is independent of latitude.     

Residual mass from ablation of meteoroid grains detached during atmospheric flight

Previous studies of the residual masses resulting from ablation of small meteoroid grains have been concerned with the ablation of particles which enter the atmosphere independently. There is widespread evidence that fragmentation is a common occurrence for meteors ranging from bright fireballs to the smallest meteors recorded with optical techniques. According to a widely accepted model, meteoroids can be considered to be a collection of tiny grains, with these grains being detached from the meteoroid during atmospheric flight. This investigation numerically solves the differential equations governing ablation of grains detached at different heights. Initial velocities from 12 to 70km s⁻¹, and initial masses from 10⁻⁵ to 10⁻¹³kg, are considered. The ablation equations allow for thermal heating prior to the onset of intensive evaporation, and thermal reradiation throughout. The atmospheric density profile used is one based on the U.S. Standard Atmosphere (1962, U.S. Government Printing Office, Washington). Calculations were completed for grains detached at 120, 100, 95, 90, 85, 80 and 75km height. For the purposes of the ablation model it is assumed that grains are ejected with an initial temperature of 1300 K, and that intensive grain evaporation begins at 2100 K. These values are consistent with grains emitted according to the model of Hawkes and Jones (1975a, Mon. Not. R. astr. Soc. 173, 339; Mon. Not. R. astr. Soc. 185, 727). For comparison purposes, calculations were also completed for grains entering the atmosphere independently (initial height 140km and beginning temperature 280 K assumed).

It is found that particles ejected at heights of 100km and above behave essentially as independent particles incident from infinity. Hence the results of earlier studies (e.g. Nicol et al., 1985, Planet. Space Sci.33, 315) can be applied. For ejection at lower heights the resultant residual mass is somewhat less than that corresponding to grains of the same initial mass and velocity. The difference is greatest for high velocity, low mass meteors. For initial masses near 10⁻⁵kg, residual mass is almost independent of ejection height, at least down to an ejection height of 75km. The significant finding of Nicol et al. (1985, Planet. Space Sci.33, 315) that residual mass is almost independent of initial mass for a fairly wide range of initial masses is only loosely followed when in-flight ejection of particles at heights below about 95 km is considered.

Typical calculations are presented to show that in-flight fragmentation of dustballs can be an important source of macroscopic ablation product micrometeorites. The astronomical and atmospheric implications of this finding are briefly discussed.     

Ionosphere disturbances accompanying the flight of the Chelyabinsk body

Data received from a network of ionosondes located at distances of 1500–3100 km from the Chelyabinsk meteorite site are used to analyze ionospheric disturbances at a height of approximately 300 km following the flight and explosion of the space body. The fall of the meteoroid is believed to be accompanied by the generation of gravitational waves in the neutral atmosphere and traveling ionospheric disturbances. The velocity and period of the latter are 600–700 m/s and 70–135 min, respectively; the amplitude of relative electron concentration disturbances is 10–20%. There is evidence of the 6–7 h ionospheric presence of wave electron concentration disturbances with relative amplitude of 10–20%, which could have been caused by long-living whirlwinds in the upper atmosphere.