Atmospheric Density Values Research Articles

Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed “HASDM-ML,” “CHAMP-ML,” and “MSIS-UQ” machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called “consider covariance sigma point (CCSP)” filter that can account for the density uncertainties during orbit propagation. As a test-bed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions.

Conductivity, electric field and electron drift velocity within the equatorial electrojet

Abstract Rocket-borne in-situ measurements of electron density and current density made from Thumba, India, on four occasions between 1966 and 1973 and on one flight from Peru in 1965 are studied along with the corresponding ground magnetometer data. The Cowling conductivity is computed using the yearly mean magnetic field values of 1965 and the atmospheric density values from the MSIS 1986 model. The rocket-borne measurements from Thumba cover different geophysical conditions of strong, moderate and partial counter-electrojet events. The vertical profiles of the measured current density and electron density are presented along with the computed Cowling conductivity, electron drift velocity and electric field. The peak current density occurred at 106–107 km over Thumba and at 109 km over Peru compared to 104 km over Brazil. Cowling conductivity peaks occurred at 102 km over Huancayo and 101 km over Thumba, while electron drift velocity and electric field peaks occurred at approximately 105–107 km over Thumba, 108 and 110 km over Huancayo and 104 km over Brazil, respectively. While the electron density near the level of peak current density shows some variability, electron drift velocity and electric field show large variability. We conclude that the local electric field plays an important role in the spatial and temporal variability of the strength of the electrojet.

Effects of Martian conditions on numerically modeled, cooling‐limited, channelized lava flows

We used the FLOWGO thermorheological model to examine the effects of Martian gravitational and environmental conditions on the cooling‐limited behavior of lava flowing in a channel. The largest effect is due to the lower gravity on Mars as compared to Earth, which causes lava to flow more slowly. The lower velocity means that heat loss per distance down a Mars channel is greater even though the lower velocity also produces a higher percentage cover of insulating crust. Gravity alone causes the Mars flow to be >65 km shorter than an Earth flow with an equivalent volumetric flow rate. The cooler ambient Mars atmosphere causes a slight increase in heat loss by forced convection. This slows the flow a bit more, resulting in a very slight increase in heat loss per distance by all mechanisms, and decreases the modeled flow length by ∼1 km, a difference well below our model uncertainty. Replacing terrestrial values of atmospheric density, viscosity, thermal conductivity, heat capacity, and cubic expansivity makes convection less efficient and increases flow length by ∼15 km. Nevertheless, at the same volumetric flow rate, lava flows ∼50 km less far under Martian conditions than under terrestrial conditions. Our specific model flow has a volumetric flow rate of ∼5000 m3 s−1 and traveled ∼190 km down a channel on a constant 7° slope. This volumetric flow rate is slightly less than the maximum rates during the 1783–1785 Laki eruption and is 5–10 times greater than those of typical Mauna Loa eruptions.

Atmospheric densities derived from CHAMP/STAR accelerometer observations

The satellite CHAMP carries the accelerometer STAR in its payload and thanks to the GPS and SLR tracking systems accurate orbit positions can be computed. Total atmospheric density values can be retrieved from the STAR measurements, with an absolute uncertainty of 10–15%, under the condition that an accurate radiative force model, satellite macro-model, and STAR instrumental calibration parameters are applied, and that the upper-atmosphere winds are less than 150 m/ s . The STAR calibration parameters (i.e. a bias and a scale factor) of the tangential acceleration were accurately determined using an iterative method, which required the estimation of the gravity field coefficients in several iterations, the first result of which was the EIGEN-1S (Geophys. Res. Lett. 29 (14) (2002) 10.1029) gravity field solution. The procedure to derive atmospheric density values is as follows: (1) a reduced-dynamic CHAMP orbit is computed, the positions of which are used as pseudo-observations, for reference purposes; (2) a dynamic CHAMP orbit is fitted to the pseudo-observations using calibrated STAR measurements, which are saved in a data file containing all necessary information to derive density values; (3) the data file is used to compute density values at each orbit integration step, for which accurate terrestrial coordinates are available. This procedure was applied to 415 days of data over a total period of 21 months, yielding 1.2 million useful observations. The model predictions of DTM-2000 (EGS XXV General Assembly, Nice, France), DTM-94 (J. Geod. 72 (1998) 161) and MSIS-86 (J. Geophys. Res. 92 (1987) 4649) were evaluated by analysing the density ratios (i.e. “observed” to “computed” ratio) globally, and as functions of solar activity, geographical position and season. The global mean of the density ratios showed that the models underestimate density by 10–20%, with an rms of 16–20%. The binning as a function of local time revealed that the diurnal and semi-diurnal components are too strong in the DTM models, while all three models model the latitudinal gradient inaccurately. Using DTM-2000 as a priori, certain model coefficients were re-estimated using the STAR-derived densities, yielding the DTM-STAR test model. The mean and rms of the global density ratios of this preliminary model are 1.00 and 15%, respectively, while the tidal and latitudinal modelling errors become small. This test model is only representative of high solar activity conditions, while the seasonal effect is probably not estimated accurately due to correlation with the solar activity effect. At least one more year of data is required to separate the seasonal effect from the solar activity effect, and data taken under low solar activity conditions must also be assimilated to construct a model representative under all circumstances.

Solar modulation of dose rate onboard the Mir station.

Models of the radiation belts that are currently used to estimate exposure for astronauts describe the environment at times of either solar minimum or solar maximum. Static models, constructed using data acquired prior to 1970 during a solar cycle with relatively low solar radio flux, have flux uncertainties of a factor of two to live and dose-rate uncertainties of a factor of about two. The inability of these static models to provide a dynamic description of the radiation belt environment limits our ability to predict radiation exposures for long-duration missions in low earth orbits. In an attempt to add some predictive capability of these models, we studied the measured daily absorbed dose rate on the Mir orbital station over roughly the complete 22nd solar cycle that saw some of the highest solar flux values in the last 40 y. We show that the daily trapped particle dose rate is an approximate power law function of daily atmospheric density. Atmospheric density values are in turn obtained from standard correlation with observed solar radio noise flux. This correlation improves, particularly during periods of high solar activity, if the density at roughly 400 days earlier time is used. This study suggests the possibility of a dose- and flux-predictive trapped-belt model based on atmospheric density.

Shuttle high resolution accelerometer package experiment results - Atmospheric density measurements between 60 and 160 km

Indirect or inferred values of atmospheric density encountered by the Shuttle Orbiter during reentry have been calculated from acceleration measurements made by the High Resolution Accelerometer Package (HiRAP) and the Orbiter Inertial Measurement Unit (IMU) liner accelerometers. The atmospheric density data developed from this study represent a significant gain with respect to the body of data collected to date by various techniques in the altitude range of 60 to 160 km. The data are unique in that they cover a very wide horizontal range during each flight and provide insight into the actual density variations encountered along the reentry flight path. The data, which were collected over about 3 years, are also characterized by variations in solar activity, geomagnetic index, and local solar time. Comparison of the flight-derived densities with various atmospheric models have been made, and analyses have attempted to characterize the data and to show correlation with selected physical variables.

The semi-annual variation in air density from June 1974 until September 1977 from the analysis of the orbit of Intercosmos 10 rocket (1973-82B)

Orbital decay rates of the satellite Intercosmos 10 rocket (1973-82B) have been calculated to obtain 591 values of atmospheric density at heights between 180 and 280 km for the period November 1973–September 1977. After allowing for changes due to solar activity, geomagnetic disturbances, and the day-to-night and seasonal-latitudinal variations, the residual semi-annual variation in exospheric density at a height of 250 km is revealed. It is shown that: (a) the amplitude of a particular maximum or minimum of the semi-annual variation varied by as much as 14% from year to year; (b) the October–November maximum was always higher than the corresponding March-April maximum; (c) the January–February minimum was always higher than the corresponding July-August minimum; (d) the minima occurred on average in the last weeks of January and July; and (e) the maxima occurred on average in the third week of April and the second week of November.

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: The semi-annual variation in air density from June 1968 to August 1974

Orbital decay rates of the satellite NIMBUS 1 ROCKET (1964-52B) have been calculated to obtain 619 values of atmospheric density at heights between 240 and 430 km for the period from June 1968–August 1974. After allowing for changes due to solar activity, geomagnetic disturbances, the day-to-night and seasonal-latitudinal variations the residual semi-annual variation in exospheric density is revealed. It is shown that : (a) the amplitude of a particular maximum or minimum of the semi-annual variation varied by as much as 20% from year to year ; (b) the October–November maximum was nearly always higher than the corresponding March–April maximum ; (c) the January–February minimum was always higher than the corresponding July–August minimum, and (d) the average dates of the maxima and minima agreed well with previous determinations.

Values of the Atmospheric Density at 280 km Obtained from Spin Drag Data of COSMOS 54 Rocket

AbstractA set of atmospheric density values at a height of 280 km between MJD 39675—39702 is determined by using the spin drag data of COSMOS 54 rocket. For this purpose photometric observations from five tracking stations and data about the satellite and its orbital evolution were used. The density values determined firstly at the perigee height were reduced at a standard height of 280 km and then compared with density values determined by using orbital drag data of this rocket at the same height and in the same time interval. The agreement between the two sets of densities (determined by using two different methods) is satisfactory.

Air density at heights near 400km from the orbit of 1963-27A

The Agena B upper-stage rocket 1963-27A was launched into a near-circular orbit, inclined at 82.3° to the Equator, on 29 June 1963. Its orbit is determined at 52 epochs over the 16 month interval prior to its decay on 26 October 1969. The resulting orbital elements are used to obtain 95 atmospheric density values, at heights near 400km. Corrected to fixed heights, and normalised to a common exospheric temperature, these values reveal the semi-annual variation in density. A comparison between the observed variation and that of a recent model atmosphere is made. Although agreement between the two is generally good, their principal differences are discussed.

A low‐order global gravity field of Venus and dynamical implications

An estimate of sixth‐degree and sixth‐order harmonic coefficients of the global gravity field of Venus has been obtained by processing the long periodic variations of the mean orbital elements of the Pioneer Venus orbiter. Approximately 220 days of data have been included in this reduction, which provides almost complete longitudinal coverage. Our estimate of oblateness (C20) is −5.97±3.2 × 10−6. The amplitudes of other coefficients are similar to the predicted coefficients using Kaula's rule under equal stress assumption. Atmospheric density values as a function of altitude have been obtained to help model drag perturbation. A radial acceleration map at 100 km above the Venus surface has been generated, and correlation between gravity anomalies and major topographic features is observed. Spectral analysis of the harmonic model suggests that the interior density anomalies are similar to those on earth. The orientation angles of the principal axes of the moments of inertia have been computed, and deviation of the maximum moment of inertia axis from the spin axis is observed to be small (<5°). The minimum moment of inertia axis passes through the Aphrodite and Beta regions.

Air density at a height of 128 km, form visual observations of 1972-25g

655 visual observations of 1972-25G, Molniya 1V Rocket, were made when its perigee height was below 130 km, and have been used to determine its orbit at 17 epochs between 5 November 1973 and 24 February 1974 and obtain almost daily values of its rate of decay. These give 52 values of atmospheric density with a relative accuracy of 1 % at a height of 128 km in latitudes 55–65°S. Day-to-day variations correlated with geomagnetic activity of up to 10% are found, plus an irregular semi-annual variation of amplitude 10%. The decrease in inclination has been measured accurately enough to enable the mean atmospheric rotation rate to be determined over the same time-span.

Density variations in the exosphere from june 1968 to december 1970

Two satellites, Calsphere (1964-63C) and Dodecapole (1965-16G), have been used to determine weekly mean values of atmospheric density at heights near 1070 and 900 km respectively, between June 1968 and December 1970. Both satellites have nearly circular orbits and are therefore ideal for studying long-term variations in the atmosphere. After correcting the values of density to both a fixed height and a fixed level of solar activity, it is possible to trace for the first time the progress of the semi-annual variation in the exosphere over 2 1 2 years of high solar activity. The semi-annual variation in density is large, with the average value for the ratio of the October maxima to the July minima being about 2. When the results are combined with earlier data from Echo 2 there is evidence of a strong oscillation in the amplitude with a periodicity of 3 years.

Corrections to Observed Beta-Ray Atmospheric Densitometer Values as Caused by Cosmic Rays

Abstract Theoretical and experimental studies have led to the development and fabrication of a rocketborne beta-ray densitometer for the direct determination of atmospheric density in the 30–65 km atmospheric interval. Comparison of atmospheric density profiles determined by the Betasonde densitometer with temperature-derived atmospheric density profiles showed excellent agreement to 35 km. Above 35 km, however, the two profiles gradually, diverged until at 50 km the Betasonde-determined density was 35–40%. greater than the temperature-derived density. This paper discusses the results of the cosmic ray count determination in the 0–50 km region with a cosmic ray detector, identical in configuration and sensitivity to the Betasonde, which served as a part of the instrument package on a high-altitude balloon flight from White Sands Missile Range, to 50 km on 22 September 1969. These results indicate that the differences in the comparison atmospheric density values can be attributed to cosmic rays which are d...

Variations in exospheric density during 1967–68, as revealed by Echo 2

Values of atmospheric density at heights near 1000 km nave been obtained from the orbit of Echo 2 during 1967 and 1968. The results clearly show the existence in the exosphere of 27-day variations associated with the rotation of the Sun and also correlation with geomagnetic disturbances. The semi-annual variation m the exosphere is again apparent, and has been traced from before solar minimum in 1964 up to and probably past the current solar maximum; the magnitude of the semi-annual density variation shows no definite dependence on the level of solar activity. The irregular year-to-year variations in the effect are similar to those at lower heights, being large at all heights at the same time. The variation in the exosphere exceeds the magnitude expected on the basis of variations at lower heights at dates before July 1966 and after April 1968, but is of the expected magnitude between these dates.

On the accuracy of measured values of upper-atmosphere density

In an interesting paper Newton et al. [1964] discussed values of atmospheric density obtained using ionization gages aboard the satellite Explorer 17. The gage densities were adjusted to magnetically quiet conditions and normalized to a height of 280 km on the basis of the model atmosphere of Harris and Priester [1962]. The values were then plotted against local time and compared with results from drag studies normalized to the same conditions. The drag values were taken from studies of the orbits of Injun 3 [Jacchia and Slowey, 1964] and Explorer 17 [Bryant, 1964] ; values given by the Harris and Priester model for a solar radiation energy flux S of 90 watts m−2 sec−1 (c/s)-1 on a wavelength of 10.7 cm were also shown.

On exospheric drag as the cause of the supposed secular accelerations of Phobos

A recent theory by Shklovskiy explained the supposed orbital accelerations of Phobos by suggesting that it is an artificial satellite of Mars. Reasonable assumptions about the physical state of the equatorial exosphere of Mars, however, lead to values of atmospheric density that could exert observable drag effects on Phobos without its being a hollow sphere. It is further shown that a required correlation may exist between solar activity and reported values of the accelerations over a period of some 60 years. As long as reliable observational evidence remains scarce, the actual existence of orbital accelerations remains in doubt. Yet, because of the potential importance of the phenomenon to the study of planetary exospheres, future observations and analyses are emphatically necessary.

A comparison of theory and observation of the Echo I satellite

Observations of the Echo I balloon satellite have been compared with a theory including the following perturbing effects: (1) solar radiation pressure; (2) lunar and solar gravitation; (3) second, third, and fourth harmonics of the earth's gravitational potential; and (4) atmospheric drag. With a set of orbital elements at the 26th day of the lifetime of the satellite, it was possible to match the observational data to 180 days with root mean square residuals as follows: Delta-a = 17.9 km, Delta-e = 0.0021, Delta-i = 0.0177 deg., Delta-omega = 1.1231 deg., Delta-Omega = 0.4821 deg., Delta-perigee height = 7.50 km. No differential correction has been applied as yet. Values of atmospheric density between 1500 and 930 km, assuming neutral drag effects only, have been inferred from the orbital data. The connection between solar activity and drag is also examined. As the Echo I perigee height continues to oscillate between 900 and 1500 km, more valuable orbital data will be obtained and atmospheric properties will be deduced. Further refinements in the mathematical model, especially in a time-dependent model atmosphere, should bring a substantial reduction in the residuals of the observations.

High-Altitude Atmospheric Density

Atmospheric density values obtained from the motion of artificial earth satellites, at altitudes between 186 and 656 kilometers, are discussed. There is some doubt about the reliability of densities from satellites because of the effects of ionization and, in the case of nonspherical satellites, because of their orientation. Densities inferred from satellites are higher than for the ARDC model of the atmosphere. These densities are about ten times higher than densities inferred from rocket-borne ionization gauges between 186 and 230 kilometers. The inference of atmospheric density from rocket-borne ionization gauges is discussed critically, and densities so obtained are considered to be inferior in reliability to the satellite densities. The satellite densities suggest molecular scale temperatures higher than those of the ARDC model in one or more regions of altitude above 80 kilometers.

Plastic boats turned out at the pugget sound naval shipyard

The satellite CHAMP carries the accelerometer STAR in its payload and thanks to the GPS and SLR tracking systems accurate orbit positions can be computed. Total atmospheric density values can be retrieved from the STAR measurements, with an absolute uncertainty of 10–15%, under the condition that an accurate radiative force model, satellite macro-model, and STAR instrumental calibration parameters are applied, and that the upper-atmosphere winds are less than 150m/s. The STAR calibration parameters (i.e. a bias and a scale factor) of the tangential acceleration were accurately determined using an iterative method, which required the estimation of the gravity field coefficients in several iterations, the first result of which was the EIGEN-1S (Geophys. Res. Lett. 29 (14) (2002) 10.1029) gravity field solution. The procedure to derive atmospheric density values is as follows: (1) a reduced-dynamic CHAMP orbit is computed, the positions of which are used as pseudo-observations, for reference purposes; (2) a dynamic CHAMP orbit is fitted to the pseudo-observations using calibrated STAR measurements, which are saved in a data file containing all necessary information to derive density values; (3) the data file is used to compute density values at each orbit integration step, for which accurate terrestrial coordinates are available. This procedure was applied to 415 days of data over a total period of 21 months, yielding 1.2 million useful observations. The model predictions of DTM-2000 (EGS XXV General Assembly, Nice, France), DTM-94 (J. Geod. 72 (1998) 161) and MSIS-86 (J. Geophys. Res. 92 (1987) 4649) were evaluated by analysing the density ratios (i.e. “observed” to “computed” ratio) globally, and as functions of solar activity, geographical position and season. The global mean of the density ratios showed that the models underestimate density by 10–20%, with an rms of 16–20%. The binning as a function of local time revealed that the diurnal and semi-diurnal components are too strong in the DTM models, while all three models model the latitudinal gradient inaccurately. Using DTM-2000 as a priori, certain model coefficients were re-estimated using the STAR-derived densities, yielding the DTM-STAR test model. The mean and rms of the global density ratios of this preliminary model are 1.00 and 15%, respectively, while the tidal and latitudinal modelling errors become small. This test model is only representative of high solar activity conditions, while the seasonal effect is probably not estimated accurately due to correlation with the solar activity effect. At least one more year of data is required to separate the seasonal effect from the solar activity effect, and data taken under low solar activity conditions must also be assimilated to construct a model representative under all circumstances.