Variations in air density at heights near 150 km, from the orbit of the satellite 1966-101G

The satellite 1966-101G was launched on 2 November 1966 into an orbit with an initial perigee height of 140 km. A satellite with such a low perigee usually decays within a few days, but 1966-101G was exceptionally dense and remained in orbit until 6 May 1967. Analysis of the changes in its orbital period provides an unique opportunity for studying continuously for six months the variations in air density at a height near 150 km.

This paper records the results of such an analysis, applicable for the (medium) level of solar activity prevailing early in 1967. It is shown that at a height of 155 km the air density is greater by day than by night, with the maximum daytime density exceeding the minimum night-time density by a factor of 1.7: in contrast the COSPAR International Reference Atmosphere 1965 predicts that the density should be slightly greater by night than by day. It is also found that the night-time density increases as solar activity increases, and that the density scale height given by CIRA 1965 at heights near 150 km is too low, perhaps by about 20%.     

Upper-atmosphere rotation rate,from analysis of the orbit of 1970-43B

The orbit of Cosmos 347 rocket (1970-43B) has been determined in the form of 23 sets of orbital elements at intervals during its 8-month life, with the aid of the RAE orbit improvement program PROP, using about 850 observations from 47 observing stations. The values of orbital inclination obtained, which had standard deviations between 0.7 and 10 sec of arc, were analysed to give a mean atmospheric rotation rate of 1.40 ± 0.05 rev/day at a mean height near 240 km, for dates between July and December 1970, and local times ranging from 1800 hr to midnight to 0900 hr. This value is higher than those obtained from other satellites at similar heights.     

Variations of the thermal accommodation coefficient from the analysis of the atmospheric lift effects on the satellite 1974-70 A

The changes of the orbital inclination of the satellite 1974-70 A show some peculiarities which cannot be explained by the usual disturbing effects (odd zonal harmonics, lunisolar perturbations, rotation of the atmosphere). The effect of a lift force normal to the orbital plane explains the residual inclination variations if a changing value of the thermal accommodation coefficient is introduced. The theory agrees well with the observations if the coefficient rises from a low value (～0.1) corresponding to a quasi-specular reflection of the molecules incident to the satellite surface to higher values (>0.9) characterizing a diffuse reflection.     

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.     

Geopotential coefficients of order 29, from analysis of the orbit of satellite 1967-104B

The orbit of the satellite 1967-104B has been analysed as it passed through 29:2 resonance with the Earth's gravitational field between January 1977 and September 1978. From the changes in inclination and eccentricity the following lumped 29th-order geopotential harmonic coefficients were obtained: $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{0.2}\text{= 4.1 ± 0.8}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{0.2}\text{= 10.3 ± 2.4}$, $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{1.1}\text{= ? 160 ± 19}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{1.1}\text{= 79 ± 10}$, $\text{10}{}^9\text{C}\text{?}{}_{29}{}^{\mathrm{?1.3}}\text{= 38 ± 14}$, $\text{10}{}^9\text{S}\text{?}{}_{29}{}^{\mathrm{?1.3}}\text{= 19 ± 5}$. These values have been compared with existing comprehensive geopotential models: the best agreement is with the model of Rapp (1981).     

Geopotential harmonics of order 15 and 30, from analysis of the orbit of satellite 1971-10B

The satellite 1971-10B passed through exact 15th-order resonance on 30 March 1981 and orbital parameters have been determined at 52 epochs from some 3500 observations using the RAE orbit refinement program, PROP, between September 1980 and October 1981. The variations in inclination and eccentricity during this time have been analysed, and six lumped 15th-order harmonic coefficients and two 30th-order coefficients have been evaluated. The 15th-order coefficients are the best yet obtained for an orbital inclination near 65°; and previously there were no 30th-order coefficients available at this inclination. The lumped coefficients have been used to test the Goddard Earth Model GEM 10B: there is good agreement for seven of the eight coefficients.     

Air density at heights near 200km from the orbit of 1970-65D

Cosmos 359 rocket, 1970-65D, entered orbit on 22 August 1970, with an initial perigee height of 209 km and inclination 51·2°, and decayed on 6 October 1971. Using the values of perigee height from RAE orbits and decay rates from USAF Spacetrack bulletins, 146 values of air density have been calculated between August 1970 and September 1971, mainly at heights between 180 and 230 km.On ten occasions in 1971 when there were substantial geomagnetic disturbances there were sudden increases in density, the largest being about 32 per cent.When the density was corrected to a fixed height and allowance was made for the day-tonight variation and the effects of solar activity, the dominant feature was a semi-annual variation, with maxima in density centred at 6 November 1970 and 7 April 1971, and minima centred at 5 January and 28 July 1971. The maxima in density are nearly equal and exceed the minima by about 50 per cent.     

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.     

Variations in the solar rotation rate derived from Ca+ K plage areas

Daily calcium plage areas for the period 1951–1981 (which include the solar cycle 19 and 20) have been used to derive the rotation period of the Sun at latitude belts 10–15 ° N, 15–20 ° N, 10–15 ° S, and 15–20 ° S and also for the entire visible solar disk. The mean rotation periods derived from 10–20 ° S and N, total active area and sunspot numbers were 27.5, 27.9, and 27.8 days (synodic), respectively. A power spectral analysis of the derived rotation rate as a function of time indicates that the rotation rate in each latitude belt varies over time scales ranging from the solar activity cycle, down to about 2 years. Variations in adjacent latitude belts are in phase, whereas those in different hemispheres are not correlated. The rotation rates derived from sunspot numbers also behave similarly though the dependence over the solar cycle are not very apparent. The total plage areas, integrated over the entire visible hemisphere of the Sun shows a dominant periodicity of 7 years in rotation rate, while the other time scales are also discernible.     

The semi-annual variation in air density for 1974–1978 from the orbit of 1972-05B

Values of air density at 712 epochs between August 1973 and September 1978 have been determined using orbital elements of 1972-05B with orbital decay rates from NORAD bulletins. Normalised to a series of fixed heights and cleared of the effects of solar activity, geomagnetic activity and the diurnal variation, the residual air density was analysed for the semi-annual variation. This variation exhibited maxima usually in April and October and minima usually in January and July.

For 1974–1978, this study revealed near-identical values of the April and October maxima and a July minimum 12% stronger than the January minimum. Further, the shape and phase of the variation exhibited an irregular pattern from year-to-year. Overall the amplitude of the variation was considerably greater than that given in the atmospheric models (CIRA, 1972; Jacchia, 1977). Other observations included the presence of subsidiary minima and maxima in late May and June respectively during 1977 and 1978 and a general increase in air density from mid 1977 onwards, relative to the atmospheric models.     

Atmospheric density from the low altitude satellite 1970-48A: Comparison of orbital decay measurements,accelerometer measurements and atmospheric models

Atmospheric densities have been deduced from high resolution radar-determined orbital decay data and from data obtained from a uniaxial accelerometer flown onboard the low altitude satellite 1970-48A. Data were obtained during late June and early July, 1970. The orbital decay-deduced densities, having an effective 6 hr temporal resolution, were determined at an altitude of 143 km, essentially one-half scale height above perigee. The accelerometer deduced densities at the same altitude were obtained on both the approaching-perigee and leaving-perigee portions of each of fifty-nine orbits. A detailed comparison of the densities derived from both types of data is presented. In general, agreement is very good. A comparison of both types of data has also been made with the Jacchia 1970 and 1971 atmospheric models as well as the new OGO-6 atmospheric model. The Jacchia models display reasonable agreement with the data, but the OGO-6 model is unsuitable as a representation of atmospheric density at this altitude.     

The determination and analysis of the orbit of NIMBUS 1 rocket, 1964-52B: Variations in orbital inclination

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the orbital inclination combining the effects of air drag with those of the Earth's gravitational field is given.The 310 observed values of inclination are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure, low-order long-periodic tesseral harmonic perturbations and changes due to precession. The method of removal of these effects is given in some detail.The variations in inclination due to drag are analysed to give four values of the average atmospheric rotation rate at heights of 296–476 km at latitude 0–54°. These values are as expected from previous analyses.The analysis of the change in inclination due to solar radiation pressure shows that this rapidly tumbling cylindrical satellite may be considered as equivalent to a spherical satellite of a given area-to-mass ratio.Analysis of the inclination near 15:1 resonance with the geopotential yields values of lumped geopotential harmonics of order 15 and 30, namely, $\text{10}{}^9\text{C}\text{?}{}^{0.1}{}_{15}\text{= ?31.2 ± 2.3 10}{}^9\text{S}\text{?}{}^{0.1}{}_{15}\text{= ?4.4 ± 3.2 10}{}^9\text{C}\text{?}{}^{0.2}{}_{30}\text{= 39.0 ± 10.7 10}{}^9\text{S}\text{?}{}^{0.2}{}_{30}\text{= 51.8 ± 10.0}$     

Air density at heights near 300 km,from analysis of the orbit of China 2 rocket (1971-18b)

China 2 rocket, 1971-18B, was launched on 3rd March 1971 into an orbit inclined at 69.9° to the Equator, with an initial perigee height of 265 km. Analysis of its orbit has yielded values of air density at average intervals of 6 days between July 1971 and January 1972. When corrected to a fixed height, the density exhibits a correlation with the geomagnetic index A_p and the solar 10.7-cm radiation. With values of density extending over seven months it is possible to examine a complete cycle of the semi-annual variation at a height near 300 km. The values of density, corrected for the day-to-night variation and for solar and geomagnetic activity, reveal minima in mid-August and late January; at the intervening maximum, in early November, the density is almost 40% higher than at the minima.     

Upper-atmosphere rotation rate from analysis of the orbital inclination of explorer 1

Explorer 1, 1958α, ths first U.S. artificial satellite, was launched on 1 February 1958 and remained in orbit for 12 years. In this paper theoretical curves have been fitted to the values of inclination, giving three values of the average atmospheric rotation rate at heights of 350–400 km, and latitudes 0–20°:

     

17.

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 2: Variations in orbital eccentricity     

W.J. Boulton 《Planetary and Space Science》1985,33(6):735-756

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the eccentricity, e, combining the effects of air drag with those of the Earth's gravitational field is given. This is solved numerically using as initial conditions 310 computed orbits of 1964-52B.The observed values of eccentricity are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure and low-order long-periodic tesseral harmonic perturbations. The method of removal of these effects is given in some detail. The behaviour of the orbital eccentricity predicted by the numerical solution is compared with the modified observed eccentricity to obtain values of atmospheric parameters at heights between 310 and 430 km. The daytime maximum of air density is found to be at 14.5 hours local time. Analysis of the eccentricity near 15th order resonance with the geopotential yielded values of four lumped geopotential harmonics of order 15, namely: $\text{10}{}^9\text{C}{}^{\mathrm{1,0}}{}_{15}\text{= ?78.8 ± 7.0}$, $\text{10}{}^9\text{S}{}^{\mathrm{1,0}}{}_{15}\text{= ?69.4 ± 5.3}$, $\text{10}{}^9\text{C}{}^{\mathrm{?1,2}}{}_{15}\text{= ?41.6 ± 3.5}$$\text{10}{}^9\text{S}{}^{\mathrm{?1,2}}{}_{15}\text{= ?26.1 ± 8.9}$, at inclination 98.68°.     

18.

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

G.G. Swinerd 《Planetary and Space Science》1982,30(9):909-921

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.     

19.

Air density at heights near 200 km from the orbit of 1969-20B     

Doreen M. C. Walker 《Planetary and Space Science》1972,20(12):2165-2173

The rocket of Cosmos 268, 1969-20B, entered orbit on 5 March 1969, with an initial perigee height of 230 km and inclination of 48.40°. Accurate orbits were computed at RAE from all available observations. Using the values of perigee height from the RAE orbit and decay rates from Spacetrack bulletins, 103 values of density have been calculated between July 1969 and February 1970. On three occasions when geomagnetic activity was strong there were sudden increases in density. When the density was corrected to a fixed height, the semi-annual variation was apparent. There was a strong minimum in July 1969, a maximum in October–November 1969 and a weak minimum in January 1970.     

20.

Mass and density of Asteroid 121 Hermione from an analysis of its companion orbit     

F. Marchis  D. Hestroffer  J. Berthier  I. de Pater 《Icarus》2005,178(2):450-464

We report on Adaptive Optics observations of the satellite of Asteroid 121 Hermione with the ESO-Paranal UT4 VLT and the Keck AO telescopes. The binary system, belonging to the Cybele family, was observed during two observing campaigns in January 2003 and January 2004 aiming to confirm its trajectory and accurately determine its orbital elements. A precessing Keplerian model was used to describe the motion of S/2002 (121) 1. We find that the satellite of Hermione revolves at a=768±11 km from the primary in P=2.582±0.002 days with a roughly circular and prograde orbit (e=0.001±0.001, i=3±2° w.r.t. equator primary). These extensive astrometric measurements enable us to determine the mass of Hermione to be 0.54±0.03×¹⁰¹⁹ kg and its pole solution (λ₀=1.5°±2.00, β₀=10°±2.0 in ecliptic J2000). Additional Keck AO observations taken close to the asteroid opposition in December 2003 give us direct insight into the structure of the primary which presents a bilobated shape. Since the angular resolution is limited to the theoretical angular resolution of the telescope (43 mas corresponding to a spatial resolution of 80 km), two shape models (called snowman and peanut) are proposed based on the images which were deconvolved with MISTRAL deconvolution process. Assuming a purely synchronous orbit and knowing the mass of the primary, the peanut shape composed of two separated components is quite unlikely. Additionally the J₂ calculated from the analysis of the secondary orbit is not in agreement with the peanut model, but close to the snowman shape. The bulk density of the primary as derived from the observed size of the snowman shape is estimated to ρ∼1.8±0.2 g/cm³ implying a porosity ∼14% for this C-type asteroid, corresponding to a fractured asteroid. Considering the IRAS diameter, the density is lower (ρ=1.1±0.3 g/cm³) leading to a high porosity (p=30-60%) with a nominal value of p=48%, which indicates a completely loose rubble-pile structure for the primary. Further work is necessary to better constrain the size, shape, and then internal structure of Hermione's primary.     

Feb 1958 to mid 1960	1.5 rev/day
Mid 1960 to Dec 1967	1.2 rev/day
Jan 1968 to Mar 1970	1.3 rev/day

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 2: Variations in orbital eccentricity

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the eccentricity, e, combining the effects of air drag with those of the Earth's gravitational field is given. This is solved numerically using as initial conditions 310 computed orbits of 1964-52B.The observed values of eccentricity are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure and low-order long-periodic tesseral harmonic perturbations. The method of removal of these effects is given in some detail. The behaviour of the orbital eccentricity predicted by the numerical solution is compared with the modified observed eccentricity to obtain values of atmospheric parameters at heights between 310 and 430 km. The daytime maximum of air density is found to be at 14.5 hours local time. Analysis of the eccentricity near 15th order resonance with the geopotential yielded values of four lumped geopotential harmonics of order 15, namely: $\text{10}{}^9\text{C}{}^{\mathrm{1,0}}{}_{15}\text{= ?78.8 ± 7.0}$, $\text{10}{}^9\text{S}{}^{\mathrm{1,0}}{}_{15}\text{= ?69.4 ± 5.3}$, $\text{10}{}^9\text{C}{}^{\mathrm{?1,2}}{}_{15}\text{= ?41.6 ± 3.5}$$\text{10}{}^9\text{S}{}^{\mathrm{?1,2}}{}_{15}\text{= ?26.1 ± 8.9}$, at inclination 98.68°.     

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.     

Air density at heights near 200 km from the orbit of 1969-20B

The rocket of Cosmos 268, 1969-20B, entered orbit on 5 March 1969, with an initial perigee height of 230 km and inclination of 48.40°. Accurate orbits were computed at RAE from all available observations. Using the values of perigee height from the RAE orbit and decay rates from Spacetrack bulletins, 103 values of density have been calculated between July 1969 and February 1970. On three occasions when geomagnetic activity was strong there were sudden increases in density. When the density was corrected to a fixed height, the semi-annual variation was apparent. There was a strong minimum in July 1969, a maximum in October–November 1969 and a weak minimum in January 1970.     

Mass and density of Asteroid 121 Hermione from an analysis of its companion orbit

We report on Adaptive Optics observations of the satellite of Asteroid 121 Hermione with the ESO-Paranal UT4 VLT and the Keck AO telescopes. The binary system, belonging to the Cybele family, was observed during two observing campaigns in January 2003 and January 2004 aiming to confirm its trajectory and accurately determine its orbital elements. A precessing Keplerian model was used to describe the motion of S/2002 (121) 1. We find that the satellite of Hermione revolves at a=768±11 km from the primary in P=2.582±0.002 days with a roughly circular and prograde orbit (e=0.001±0.001, i=3±2° w.r.t. equator primary). These extensive astrometric measurements enable us to determine the mass of Hermione to be 0.54±0.03×¹⁰¹⁹ kg and its pole solution (λ₀=1.5°±2.00, β₀=10°±2.0 in ecliptic J2000). Additional Keck AO observations taken close to the asteroid opposition in December 2003 give us direct insight into the structure of the primary which presents a bilobated shape. Since the angular resolution is limited to the theoretical angular resolution of the telescope (43 mas corresponding to a spatial resolution of 80 km), two shape models (called snowman and peanut) are proposed based on the images which were deconvolved with MISTRAL deconvolution process. Assuming a purely synchronous orbit and knowing the mass of the primary, the peanut shape composed of two separated components is quite unlikely. Additionally the J₂ calculated from the analysis of the secondary orbit is not in agreement with the peanut model, but close to the snowman shape. The bulk density of the primary as derived from the observed size of the snowman shape is estimated to ρ∼1.8±0.2 g/cm³ implying a porosity ∼14% for this C-type asteroid, corresponding to a fractured asteroid. Considering the IRAS diameter, the density is lower (ρ=1.1±0.3 g/cm³) leading to a high porosity (p=30-60%) with a nominal value of p=48%, which indicates a completely loose rubble-pile structure for the primary. Further work is necessary to better constrain the size, shape, and then internal structure of Hermione's primary.