Contraction of satellite orbits in an oblate atmosphere with a diurnal density variation

1982 ◽  
Vol 383 (1784) ◽  
pp. 127-145 ◽  
Keyword(s):  
Major Axis ◽  
Density Variation ◽  
Scale Height ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Third Order ◽  
Small Eccentricity ◽  
Air Density ◽  
The Mean ◽  
Density Scale

The effect of air drag on satellite orbits of small eccentricity, e < 0.2, is considered. A model of the atmosphere that allows for oblateness is adopted, in which the density behaviour approximates to the observed diurnal variation. The equations governing the changes due to drag in the semi-major axis a , and in x = ae , during one revolution of the satellite are integrated, the density scale-height H being assumed constant. The resulting expressions for ∆ a and ∆ x are presented to third order in e . Compact expressions for the gradient d a /d x , and for the mean air density at perigee altitude ρ 1 are obtained, when H is allowed to vary with altitude. An equivalence between the variable- H and the constant- H equations is demonstrated, provided that the value of H used in the latter is chosen appropriately.

The change in satellite mean anomaly due to a rotating oblate atmosphere with a diurnal variation in density

1984 ◽  
Vol 391 (1800) ◽  
pp. 201-214
Keyword(s):  
Atmospheric Model ◽  
Scale Height ◽  
Satellite Orbits ◽  
Atmospheric Drag ◽  
Linear Variation ◽  
Small Eccentricity ◽  
Anomalistic Period ◽  
Compact Expression ◽  
The Mean ◽  
Density Scale

The effect of atmospheric drag on satellite orbits of small eccentricity e ≲ 0.2, is considered. The atmospheric model allows for oblateness, and has a density profile that approximates to the observed day-to-night variation. The equation governing the changes due to drag in the mean anomaly M , during one revolution of the satellite is integrated, assuming that H , the density scale height is constant. Two particular cases are detailed. In the first, the change ∆ M in M over one anomalistic period is given for eccentricity e in the range 0.01 ≲ e ≲ 0.2, and in the second the change in ( M + ω) over one draconic period, ∆( M + ω) is given for eccentricity e in the range 0 ≼ e ≲ 0.01, where ω is the argument of perigee. Finally a compact expression for e ∆ M is derived for an atmosphere with a linear variation of H with altitude, if 0.01 ≲ e ≲ 0.2. This is the final paper in a series describing the secular and long-periodic effects of drag on the six Keplerian elements that determine the orbit of a satellite.

The advance of the perigee of a satellite in a rotating oblate atmosphere with a diurnal variation in density

1983 ◽  
Vol 389 (1797) ◽  
pp. 433-444 ◽  
Keyword(s):  
Diurnal Variation ◽  
Scale Height ◽  
Satellite Orbits ◽  
Third Order ◽  
Air Drag ◽  
Small Eccentricity ◽  
Density Scale

The effect of air drag on satellite orbits of small eccentricity, 0.01 ≾ е ≾ 0.2, is considered. A model of the atmosphere that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation, is adopted. The equation governing the changes due to drag in the argument of perigee ω , during one revolution of the satellite, is integrated with the assumption that the density scale height H is constant. The resulting expression for e ∆ ω is presented to third order in e . Compact expressions for e ∆ ω and e ∆ ω / ∆ T D , where ∆ T D is the corresponding change in the period, are obtained when H is allowed to vary with altitude. It is shown that there is an equivalence between the variable- H and the constant- H equations, provided that the value of H used in the latter is chosen appropriately.

Scale height in the upper atmosphere, derived from changes in satellite orbits

1962 ◽  
Vol 270 (1343) ◽  
pp. 562-587 ◽  
Keyword(s):  
Molecular Weight ◽  
Solar Activity ◽  
Air Temperature ◽  
Scale Height ◽  
Upper Atmosphere ◽  
Satellite Orbits ◽  
Small Eccentricity ◽  
Air Density ◽  
Density Scale ◽  
Eccentricity Orbit

The 'density scale height’ H in the upper atmosphere is a measure of the rate at which air density ρ varies with height y , being given by H = — ρ/(dρ/d y ). The value of H , although important because (with the molecular weight of the air) it determines the air temperature, has not as yet been well determined at heights above 200 km. This paper develops methods for finding H from the decrease in a satellite’s perigee height and from the decrease in the orbital period of a satellite in a small-eccentricity orbit. These methods are then applied to all the 14 satellites found suitable for the purpose. The 44 values of H obtained, for heights of 200 to 450 km, represent an average over day and night and probably have errors (s.d.) of 5 to 10 %. It is found that, as solar activity declined between 1957 and 1961, H decreased greatly: e.g. at height 275 km, H decreased from 60 km in early 1958 to 40 km in 1960-61. The results also show that the increase of H with height becomes much less rapid above 350 km, and are consistent with the supposition that H had low values, near 35 km, at heights near 250 km, for 1959-61, The results could be greatly extended in scope and improved in accuracy if more accurate orbits were available for short-lifetime satellites.

Determination of upper-atmosphere air density and scale height from satellite observations

1959 ◽  
Vol 252 (1268) ◽  
pp. 16-27 ◽  
Keyword(s):  
Satellite Orbit ◽  
Major Axis ◽  
Scale Height ◽  
Rate Of Change ◽  
Satellite Observations ◽  
Upper Atmosphere ◽  
Semi Major Axis ◽  
Air Density ◽  
Standard Deviations

A solution is obtained for the rate of change of semi-major axis and perigee distance of a satellite orbit with time due to the resistance of the atmosphere. The logarithm of air density is assumed to vary quadratically with height, and the oblateness of the atmosphere is taken into account. The calculation of perigee air density in terms of the rate of change of satellite period is dealt with; and the method is applied to data at present available on six different satellites. The variation of air density with height is obtained as ln ρ = -28·59(±0·15) - ( h - 200 )/46(±5) + 0·028(±0·013) ( h - 200) 2 /(46) 2 for h in the range of approximately 170 to 700 km, where ρ is in grams/cm 3 , h is in kilometres and standard deviations are given in brackets.

The contraction of satellite orbits under the influence of air drag IV. With scale height dependent on altitude

1963 ◽  
Vol 275 (1362) ◽  
pp. 357-390 ◽  
Keyword(s):  
Orbital Period ◽  
Scale Height ◽  
Rate Of Change ◽  
Time Interval ◽  
Satellite Orbits ◽  
Air Drag ◽  
Small Eccentricity ◽  
Best Constant ◽  
Air Density ◽  
Linear Manner

The effect of air drag on satellite orbits of small eccentricity e (< 0.2) was studied in part I on the assumption that atmospheric density p varies exponentially with distance r from the earth’s centre, so that the ‘density scale height’ H , defined as — p /(d p /d r ), is constant. In practice H varies with height in an approximately linear manner, and in the present paper the theory is developed for an atmosphere in which H varies linearly with r . Equations are derived which show how perigee distance and orbital period vary with eccentricity, and how eccentricity varies with time. Expressions are also obtained for the lifetime and air density at perigee in terms of the rate of change of orbital period. The main results are presented graphically. The results are formulated in two ways. The first is to specify the extra terms to be added to the constant- H equations of part I. The second (and usually better) method is to obtain the best constant value of H for use with the equations of part I. For example, it is found that the constant- H equations connecting perigee distance (or orbital period) and eccentricity can be used unchanged without loss in accuracy, if H is taken as the value of the variable H at a height y H above the mean perigee height during the time interval being considered, where y — 3/2 for e > 0.02, and y decreases from § towards zero as e decreases from 0.02 towards 0. Similarly the constant- H equations for air density at perigee can still be used if H is evaluated at a height above perigee, where £ = 3/4 for e >0.01, and £ decreases towards zero as e decreases from 0.01 towards 0. For circular orbits the constant- H equations for radius in terms of time can still be used if H is evaluated at one scale height below the initial height. Variation of H with altitude has a small effect on the lifetime—about 3 %— and on the curve of e against time. 1 *

Determination of upper-atmosphere air-density profile from satellite observations

1959 ◽  
Vol 252 (1268) ◽  
pp. 28-34 ◽  
Keyword(s):  
Density Profile ◽  
Satellite Orbit ◽  
Major Axis ◽  
Scale Height ◽  
Semi Major Axis ◽  
Relative Variation ◽  
Air Density ◽  
The Earth ◽  
Point Data

The theory previously developed for the changes in the perigee distance and semi-major axis of a satellite orbit due to air drag is extended to enable the air-density profile (i. e. its relative variation with height) to be derived from the motion of the orbit’s perigee. The solution is first obtained in terms of the change in perigee distance and then in terms of the change in the radius of the earth at the sub-perigee point. Data are analyzed by the two methods, leading to 39 (± 9) and 36 (± 15) km for the scale height in the 180 and 220 km altitude regions.

The change in satellite orbital inclination due to a rotating oblate atmosphere with a diurnal variation in density

1983 ◽  
Vol 386 (1790) ◽  
pp. 55-75 ◽  
Keyword(s):  
Orbital Plane ◽  
Atmospheric Model ◽  
Scale Height ◽  
Satellite Orbits ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Zonal Winds ◽  
Meridional Winds ◽  
Anomalistic Period ◽  
Density Scale

The effect of the motion of the upper atmosphere on satellite orbits of small eccentricity, e < 0.2, is considered. The atmospheric model allows for oblateness, and has a density profile that approximates to the observed day-to-night variation. The equations governing the changes due to zonal (west to east) and meridional (south to north) winds in the inclination of the orbital plane i during one anomalistic period of the satellite are integrated, with H , the density scale height, assumed to be constant. The resulting expressions for ∆ i w , due to zonal winds, and ∆ i ϕ , due to meridional winds, are given. Compact expressions for ∆ i and the ratio ∆ i /∆ T D , where ∆ T D is the corresponding change in orbital period, are given when H varies linearly with height. An equivalence between the variable- H equation and the constant- H equation is demonstrated for ∆ i w , when the value of H used in the latter is appropriately chosen. It is shown that there is no such equivalence for ∆ i ϕ and ∆ i /∆ T D .

The contraction of satellite orbits under the influence of air drag. VII. Orbits of high eccentricity, with scale height dependent on altitude

1987 ◽  
Vol 411 (1840) ◽  
pp. 1-17 ◽  
Keyword(s):  
Major Part ◽  
Atmospheric Model ◽  
Scale Height ◽  
Satellite Orbits ◽  
High Eccentricity ◽  
Air Drag ◽  
Air Density ◽  
Exponential Variation ◽  
Constant Part ◽  
Density Scale

Part III of this series of papers developed the theory of high-eccentricity orbits ( e > 0.2) in an atmosphere having an exponential variation of air density with height, that is, with the density scale height H taken as constant. Part IV derived the appropriate theory for low-eccentricity orbits ( e < 0.2) in a more realistic atmosphere where H varies linearly with height y (and μ = d H /d y < 0.2). The present paper treats the orbits of part III when they meet the air drag specified by the atmospheric model of part IV. Equations are derived showing how the perigee height varies with eccentricity, and the eccentricity varies with time, over the major part of the satellite’s life. It is shown that the theory of part III remains valid, to order μ 2 , if H is evaluated at a specific height above perigee.

scholarly journals Some Special Types of Orbits around Jupiter

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 183
Author(s):  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li ◽  
Hui Zhang
Keyword(s):  
Gravity Model ◽  
Small Perturbation ◽  
Equilibrium Points ◽  
Major Axis ◽  
Semi Major Axis ◽  
Ground Track ◽  
The Earth ◽  
Degenerate Equilibrium ◽  
The Mean ◽  
Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

scholarly journals Creation/destruction of ultra-wide binaries in tidal streams

2020 ◽  
Author(s):  
Jorge Peñarrubia
Keyword(s):  
Globular Clusters ◽  
Galactic Halo ◽  
Local Density ◽  
Formation Rate ◽  
Semimajor Axis ◽  
Major Axis ◽  
Binding Energies ◽  
Semi Major Axis ◽  
The Mean ◽  
Tidal Streams

Abstract This paper uses statistical and N-body methods to explore a new mechanism to form binary stars with extremely large separations (≳ 0.1 pc), whose origin is poorly understood. Here, ultra-wide binaries arise via chance entrapment of unrelated stars in tidal streams of disrupting clusters. It is shown that (i) the formation of ultra-wide binaries is not limited to the lifetime of a cluster, but continues after the progenitor is fully disrupted, (ii) the formation rate is proportional to the local phase-space density of the tidal tails, (iii) the semimajor axis distribution scales as p(a)da ∼ a1/2da at a ≪ D, where D is the mean interstellar distance, and (vi) the eccentricity distribution is close to thermal, p(e)de = 2ede. Owing to their low binding energies, ultra-wide binaries can be disrupted by both the smooth tidal field and passing substructures. The time-scale on which tidal fluctuations dominate over the mean field is inversely proportional to the local density of compact substructures. Monte-Carlo experiments show that binaries subject to tidal evaporation follow p(a)da ∼ a−1da at a ≳ apeak, known as Öpik’s law, with a peak semi-major axis that contracts with time as apeak ∼ t−3/4. In contrast, a smooth Galactic potential introduces a sharp truncation at the tidal radius, p(a) ∼ 0 at a ≳ rt. The scaling relations of young clusters suggest that most ultra-wide binaries arise from the disruption of low-mass systems. Streams of globular clusters may be the birthplace of hundreds of ultra-wide binaries, making them ideal laboratories to probe clumpiness in the Galactic halo.

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