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.

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.

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.

Air Density in the Upper Atmosphere from Satellite Orbit Observations

Nature ◽  
1959 ◽  
Vol 184 (4681) ◽  
pp. 178-179 ◽  
Author(s):  
G. V. GROVES
Keyword(s):  
Satellite Orbit ◽  
Upper Atmosphere ◽  
Air Density

scholarly journals Analytical Study of Earth Tides on Low Orbits Satellites

2020 ◽  
pp. 453-461
Author(s):  
Ahmed K. Izzet ◽  
Mayada J. Hamwdi ◽  
Abed T. Jasim
Keyword(s):  
Analytical Study ◽  
Satellite Orbit ◽  
Major Axis ◽  
Earth Tides ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Tidal Perturbation ◽  
Right Ascension ◽  
Tide Effect

     The main objective of this paper is to calculate the perturbations of tide effect on LEO's satellites . In order to achieve this goal, the changes in the orbital elements which include the semi major axis (a) eccentricity (e) inclination , right ascension of ascending nodes ( ), and fifth element argument of perigee ( ) must be employed. In the absence of perturbations, these element remain constant. The results show that the effect of tidal perturbation on the orbital elements depends on the inclination of the satellite orbit. The variation in the ratio  decreases with increasing the inclination of satellite, while it increases with increasing the time.

scholarly journals Correspondances Entre Une Theorie Generale Planetaire En Variables Elliptiques Et La Theorie Classique De Le Verrier

1978 ◽  
Vol 41 ◽  
pp. 15-32 ◽  
Author(s):  
L. Duriez
Keyword(s):  
General Theory ◽  
Classical Theory ◽  
Major Axis ◽  
Second Order ◽  
Semi Major Axis ◽  
First Order ◽  
Short Period ◽  
The Masses ◽  
Secular Terms

AbstractIn order to improve the determination of the mixed terms in classical theories, we show how these terms may be derived from a general theory developed with the same variables (of a keplerian nature). We find that the general theory of the first order in the masses already allows us to develop the mixed terms which appear at the second order in the classical theory. We also show that a part of the constant perturbation of the semi-major axis introduced in the classical theory is present in the general theory as very long-period terms; by developing these terms in powers of time, they would be equivalent to the appearance of very small secular terms (in t, t2, …) in the perturbation of the semi-major axes from the second order in the masses. The short period terms of the classical theory are found the same in the general theory, but without the numerical substitution of the values of the variables.

scholarly journals Orbital Parameters of the PSR B1620–26 Triple System

1996 ◽  
Vol 160 ◽  
pp. 525-530 ◽  
Author(s):  
Z. Arzoumanian ◽  
K. Joshi ◽  
F. A. Rasio ◽  
S. E. Thorsett
Keyword(s):  
Proper Motion ◽  
Time Derivative ◽  
Major Axis ◽  
Mass Range ◽  
Pulse Frequency ◽  
Rate Of Change ◽  
Semi Major Axis ◽  
Orbital Parameters ◽  
Error Bar ◽  
Stellar Masses

AbstractPrevious timing data for PSR B1620–26 were consistent with a second companion mass m2anywhere in the range ∼ 10−3– 1M⊙, i.e., from a Jupiter-type planet to a star. We present the latest timing parameters for the system, including a significant change in the projected semi-major axis of the inner binary, a marginal detection of the fourth time derivative of the pulse frequency, and the pulsar proper motion (which is in agreement with published values for the proper motion of M4), and use them to further constrain the mass m2and the orbital parameters. Using the observed value of, we obtain a one-parameter family of solutions, all with m2≲ 10−2M⊙, i.e., excluding stellar masses. Varyingwithin its formal 1σ error bar does not affect the mass range significantly. However, if we varywithin a 4σ error bar, we find that stellar-mass solutions are still possible. We also calculate the predicted rate of change of the projected semi-major axis of the inner binary and show that it agrees with the measured value.

DETERMINATION OF THE ELEMENTS OF METEOR PATHS FROM RADAR OBSERVATIONS

1949 ◽  
Vol 27a (3) ◽  
pp. 53-67 ◽  
Author(s):  
D. W. R. McKinley ◽  
Peter M. Millman
Keyword(s):  
Sea Level ◽  
Path Length ◽  
Major Axis ◽  
Radar Data ◽  
Semi Major Axis ◽  
Radar Observations ◽  
Short Period ◽  
Single Station

Methods of determining meteor velocities from single-station observations are discussed. Where three-station observations are available both the velocity and the elements of the meteor's path through the atmosphere can be computed in favorable cases. These methods are applied to a selected daytime meteor, recorded by the three radar stations at 17h 59m 48s E.S.T., Aug. 4, 1948. The following elements of the meteor's path have been obtained from the radar data:—Apparent geocentric velocity    35.0 ± 0.4 km. per sec.True bearing of apparent radiant    074° ± 2°Elevation of apparent radiant    2° ± 2°Total radar path length    270 km.Height above sea level    108 − 104 km.These values lead to an orbit similar to one of the short-period comets, with these elements:—Semi-major axis    a    2.66Eccentricity    e    0.87Angle node to perihelion    ω    294°.9Longitude of node        132°.4Inclination    i    33°.6Period    P    4.33 years

Effect of an oblate rotating atmosphere on the orientation of a satellite orbit

1961 ◽  
Vol 261 (1305) ◽  
pp. 246-258 ◽  
Keyword(s):  
Orbital Plane ◽  
Satellite Orbit ◽  
Major Axis ◽  
Earth Satellite ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Earth Satellite Orbit ◽  
The Right ◽  
Right Ascension

For an earth satellite orbit of small eccentricity ( e < 0·2) formulae are derived for the changes per revolution produced by the atmosphere in the argument of perigee, in the right ascension of the ascending node, and in the orbital inclination. These changes are then expressed in terms of the change in length of the semi-major axis, and numerical values are obtained for satellite 1957 β . It is found that the rotation of the major axis in the orbital plane due to the atmosphere is significant, being most important for inclinations between 60 and 70°. The total rotation, due both to the gravitational potential and to the atmosphere, agrees reasonably well with the observed values. The oblateness of the atmosphere is found to have only a small effect on the changes in the orbital inclination and the right ascension of the ascending node.

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 *

scholarly journals The influence of starspots activity on the determination of planetary transit parameters

2009 ◽  
Vol 5 (S264) ◽  
pp. 440-442 ◽  
Author(s):  
Adriana Silva-Válio
Keyword(s):  
Light Curve ◽  
Major Axis ◽  
The Other ◽  
Semi Major Axis ◽  
Active Star ◽  
Orbital Parameters ◽  
Correct Determination ◽  
The Times ◽  
Parent Star

AbstractAs a planet eclipses its parent star, dark spots on the surface of the star may be occulted, causing a detectable variation in the transit light curve. There are basically two effects caused by the presence of spots on the surface of the star which can alter the shape of the light curve during transits and thus preclude the correct determination of the planet physical and orbital parameters. The first one is that the presence of many spots within the latitude band occulted by the planet will cause the depth of the transit in the light curve to be shallower. This will erroneously result in a smaller radius for the planet. The other effect is that generated by spots located close to the limb of the star. In this case, the spots will interfere in the light curve during the times of ingress or egress of the planet, causing a decrease in the transit duration. This in turn will provide a larger value for the semi-major axis of the planetary orbit. Qualitative estimates of both effects are discussed and an example provided for a very active star, such as CoRoTo-2.

Sign in / Sign up

Export Citation Format

Share Document