The contraction of satellite orbits under the influence of air drag V. With day-to-night variation in air density

1965 ◽  
Vol 259 (1096) ◽  
pp. 33-67 ◽  
Keyword(s):  
Orbital Period ◽  
Angular Distance ◽  
Maximum Density ◽  
Rate Of Change ◽  
Satellite Orbits ◽  
The Sun ◽  
Air Drag ◽  
Air Density ◽  
Main Geometrical Parameter ◽  
Long Term Effect

The effect of air drag on satellite orbits of small eccentricity (< 0-2) was studied in part I on the assumption that the atmosphere was spherically symmetrical. In reality the density of the upper atmosphere depends on the elevation of the Sun above the horizon and has a maximum when the Sun is almost overhead. In the present paper the theory is extended to an atmosphere in which the air density at a given height varies sinusoidally with the geocentric angular distance from the maximum-density direction. Equations are derived which show how perigee distance and orbital period vary with eccentricity throughout the satellite’s life, and how eccentricity varies with time. Expressions are also obtained for lifetime and air density at perigee in terms of the rate of change of orbital period. The main geometrical parameter determining the long-term effect of this day-to-night variation is the angular distance <f>p of perigee from the maximum-density direction. Results are obtained for <})pconstant and <j)pvarying linearly with time.

The contraction of satellite orbits under the influence of air drag. II. With oblate atmosphere

1961 ◽  
Vol 264 (1316) ◽  
pp. 88-121 ◽  
Keyword(s):  
Orbital Period ◽  
Rate Of Change ◽  
Satellite Orbits ◽  
Constant Density ◽  
Circular Orbits ◽  
Air Drag ◽  
Small Eccentricity ◽  
Separate Section ◽  
Air Density ◽  
Independent Parameters

The effect of air drag on satellite orbits of small eccentricity e (< 0.2) was studied in part I on the assumption that the atmosphere was spherically symmetrical. Here the theory is extended to an atmosphere in which the surfaces of constant density are spheroids of arbitrary small ellipticity. Equations are derived which show how perigee distance and orbital period vary with eccentricity, and how eccentricity is related to time. Expressions are also obtained which give lifetime and air density at perigee in terms of the rate of change of period. In most of the equations, terms of order e 4 and higher are neglected. The results take different forms according as the eccentricity is greater or less than about 0.025, while circular orbits are dealt with in a separate section. The influence of atmospheric oblateness is difficult to summarize fairly, because it depends on four independent parameters. If these simultaneously assume their ‘worst’ values, some of the spherical-atmosphere results can be altered by up to 30% as a result of oblateness. But usually the influence of atmospheric oblateness is much smaller, and 5 to 10% would be a more representative figure.

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 *

The contraction of satellite orbits under the influence of air drag, III. High-eccentricity orbits (0·2≤ e <1)

1962 ◽  
Vol 267 (1331) ◽  
pp. 541-557 ◽  
Keyword(s):  
Orbital Period ◽  
Rate Of Change ◽  
Satellite Orbits ◽  
High Eccentricity ◽  
Air Drag ◽  
Air Density

The effect of air drag on satellite orbits of eccentricity e less than 0·2 was studied in parts I and II. Here the theory for values of e between 0·2 and 1 is presented. Equations are derived which show how perigee distance and orbital period vary with eccentricity during the satellite’s life, and how eccentricity is related to time; and formulae are obtained for the lifetime and the air density at perigee, in terms of the rate of change of period. The results are also presented graphically and their implications and limitations are discussed.

The contraction of satellite orbits under the influence of air drag. I. With spherically symmetrical atmosphere

1960 ◽  
Vol 257 (1289) ◽  
pp. 224-249 ◽  
Keyword(s):  
Perturbation Method ◽  
Orbital Period ◽  
Satellite Orbits ◽  
Air Drag ◽  
Small Eccentricity

The effect of air drag on satellite orbits of small eccentricity e (< 0.2) is studied analytically by a perturbation method, on the assumption that the atmosphere is spherically symmetrical. Equations are derived which show (1) how perigee distance and orbital period vary with eccentricity as the orbit contracts, and (2) how each of these quantities varies with time. The equations of type (1) are nearly independent of the oblateness of the atmosphere. In all the equations, terms of order e 4 and higher are usually neglected. The results are also presented graphically, in a manner designed for practical use. The theory will be extended to an oblate atmosphere in part II, and will later be compared with observation.

The contraction of satellite orbits under the influence of air drag - VI. Near-circular orbits with day-to-night variation in air density

1968 ◽  
Vol 303 (1472) ◽  
pp. 17-35 ◽  
Keyword(s):  
Mathematical Theory ◽  
Angular Motion ◽  
Satellite Orbits ◽  
Orbital Eccentricity ◽  
Air Drag ◽  
Rates Of Change ◽  
Gravitational Forces ◽  
Air Density ◽  
Complicated Form ◽  
Time Variations

The theory for the effect of air drag on satellite orbits was developed in Parts I to V of this series of papers on the assumption that the angular motion of perigee is controlled by gravitational forces and is not affected by air drag. If the orbital eccentricity is less than about 0·01, however, and the atmosphere exhibits a substantial day-to-night variation in density, the air drag itself significantly affects the angular motion of perigee. In these circumstances the mathematical theory takes a different and more complicated form, which is developed in the present paper. General equations are derived for the rates of change of parameters specifying the eccentricity and argument of perigee. Complete analytical solutions for the time variations of these parameters are obtained when e is of order 0·001, in two different forms, for (1) high drag, i. e. short lifetime, and (2) low drag. The results are illustrated by numerical examples.

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.

Haul-out behaviour and densities of ringed seals (Phoca hispida) in the Barrow Strait area, N.W.T.

1979 ◽  
Vol 57 (10) ◽  
pp. 1985-1997 ◽  
Author(s):  
Kerwin J. Finley
Keyword(s):  
Wind Speed ◽  
Early Morning ◽  
Maximum Density ◽  
Stable Population ◽  
The Sun ◽  
High Wind ◽  
Phoca Hispida ◽  
High Wind Speed ◽  
Ringed Seals ◽  
Calm Weather

Numbers of ringed seals hauled out on the ice began to increase in early June. Numbers on the ice were highest from 0900 to 1500 hours Central Standard Time and lowest (average 40–50% of peak) in early morning. Seals commonly remained on the ice for several hours, and occasionally (during calm weather) for > 48 h. Numbers on the ice were reduced on windy days and possibly also on unusually warm, bright and calm days. Seals tended to face away from the wind (particularly with high wind speed) and oriented broadside to the sun. Seals usually occurred singly (60–70% of all groups) at their holes.Numbers of seals hauled out at Freemans Cove remained relatively constant during June (maximum density 4.86/km2), whereas at Aston Bay numbers increased dramatically to a maximum density of 10.44/km2 in late June. The increase was thought to be due to an influx of seals abandoning unstable ice. The density of seal holes at Freemans Cove (5.92/km2) was much higher than at Aston Bay (2.73/km2). The ratio of holes to the maximum numbers of seals (1.12:1) at Freemans Cove represents a first estimate of this relationship in an apparently stable population.

Longevity of moons around habitable planets

2014 ◽  
Vol 13 (4) ◽  
pp. 324-336 ◽  
Author(s):  
Takashi Sasaki ◽  
Jason W. Barnes
Keyword(s):  
Orbital Period ◽  
Extrasolar Planets ◽  
The Sun ◽  
Habitable Zone ◽  
Evolution Theory ◽  
Earth System ◽  
The Moon ◽  
Tidal Dissipation ◽  
Habitable Planets ◽  
Rocky Planets

AbstractWe consider tidal decay lifetimes for moons orbiting habitable extrasolar planets using the constant Q approach for tidal evolution theory. Large moons stabilize planetary obliquity in some cases, and it has been suggested that large moons are necessary for the evolution of complex life. We find that the Moon in the Sun–Earth system must have had an initial orbital period of not slower than 20 h rev−1 for the moon's lifetime to exceed a 5 Gyr lifetime. We assume that 5 Gyr is long enough for life on planets to evolve complex life. We show that moons of habitable planets cannot survive for more than 5 Gyr if the stellar mass is less than 0.55 and 0.42 M⊙ for Qp=10 and 100, respectively, where Qp is the planetary tidal dissipation quality factor. Kepler-62e and f are of particular interest because they are two actually known rocky planets in the habitable zone. Kepler-62e would need to be made of iron and have Qp=100 for its hypothetical moon to live for longer than 5 Gyr. A hypothetical moon of Kepler-62f, by contrast, may have a lifetime greater than 5 Gyr under several scenarios, and particularly for Qp=100.

POSITION FINDING BY RATE OF CHANGE OF ALTITUDE OF THE SUN

Survey Review ◽  
1978 ◽  
Vol 24 (189) ◽  
pp. 323-325
Author(s):  
R. F. Rish
Keyword(s):  
Rate Of Change ◽  
The Sun

scholarly journals Proxima’s orbit around α Centauri

2017 ◽  
Vol 598 ◽  
pp. L7 ◽  
Author(s):  
P. Kervella ◽  
F. Thévenin ◽  
C. Lovis
Keyword(s):  
Radial Velocity ◽  
High Precision ◽  
Orbital Period ◽  
Triple System ◽  
Orbital Motion ◽  
The Sun ◽  
Proper Motions ◽  
Velocity Measurements ◽  
Degree Of Confidence ◽  
High Degree

Proxima and α Centauri AB have almost identical distances and proper motions with respect to the Sun. Although the probability of such similar parameters is, in principle, very low, the question as to whether they actually form a single gravitationally bound triple system has been open since the discovery of Proxima one century ago. Owing to HARPS high-precision absolute radial velocity measurements and the recent revision of the parameters of the α Cen pair, we show that Proxima and α Cen are gravitationally bound with a high degree of confidence. The orbital period of Proxima is ≈ 550 000 yr. With an eccentricity of 0.50+0.08-0.09, Proxima comes within 4.3+1.1-0.9 kau of α Cen at periastron, and is currently close to apastron (13.0+0.3-0.1 kau). This orbital motion may have influenced the formation or evolution of the recently discovered planet orbiting Proxima, as well as circumbinary planet formation around α Cen.

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