The effect of atmospheric rotation on the orbital plane of a near-earth satellite

1960 ◽  
Vol 258 (1295) ◽  
pp. 516-528 ◽  
Keyword(s):  
Gravitational Field ◽  
Orbital Plane ◽  
Earth Satellite ◽  
Theoretical Curve ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Earth’S Atmosphere ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Good Agreement

Besides the perturbations due to the gravitational field of the earth, the rotation of the earth’s atmosphere produces a perturbing force on a satellite which affects the motion of its orbital plane. Theoretical formulae are derived for the rotation of the orbital plane about the earth’s axis and the change in orbital inclination of a near-earth satellite of small eccentricity (< 0.2) due to the influence of the atmosphere. It is assumed that the atmosphere is spherically symmetrical and has a density which varies exponentially with altitude. Comparison of the theoretical changes in orbital inclination show reasonably good agreement with those estimated from kinetheodolite observations, although the need for a slightly steeper theoretical curve is indicated. Although the rotation of the orbital plane is small, allowance must be made for it when making estimates of the harmonics of the earth's gravitational field.

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.

scholarly journals The motion of a geosynchronous satellite

1986 ◽  
Vol 114 ◽  
pp. 293-295
Author(s):  
K. B. Bhatnagar
Keyword(s):  
Angular Velocity ◽  
Solar Radiation ◽  
Radiation Pressure ◽  
Angular Position ◽  
Orbital Plane ◽  
Solar Radiation Pressure ◽  
Orbital Inclination ◽  
Geosynchronous Satellite ◽  
The Earth ◽  
Earth’S Equatorial Ellipticity

The motion of a geosynchronous satellite has been studied under the combined gravitational effects of the oblate Earth (including its equatorial ellipticity), the Sun, the Moon and the solar-radiation pressure. It is observed that the orbital plane rotates with an angular velocity the maximum value of which is 0.058°/yr. and regresses with a period which increases both as the orbital inclination and the altitude increase. The effect of earth's equatorial ellipticity on the regression period is oscillatory whereas that of Solar-radiation pressure is to decrease it.The synchronism is achieved when the angular velocity of the satellite is equal to the difference between the spin-rate of the Earth and the regression rate of the orbital plane. With this angular velocity of the satellite, the ground trace is in the shape of figure eight, though its size and position relative to the Earth change as the time elapses. The major effect of earth's equatorial ellipticity is to produce a change in the relative angular position of the satellite as seen from the Earth. If the satellite is allowed to execute large angle oscillations the mid-point of oscillation would be at the position of the minor axis of the earth's equatorial section. The oscillatory period T has been determined in terms of the amplitude Γ and the tesseral harmonic J2(2). From this result we can determine the value of J2(2) as T and Γ can be observed accurately.

scholarly journals Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

2021 ◽  
pp. 44-53
Author(s):  
A. Ebaid ◽  
Shorouq M. S. Al-Qahtani ◽  
Afaf A. A. Al-Jaber ◽  
Wejdan S. S. Alatwai ◽  
Wafaa T. M. Alharbi
Keyword(s):  
Gravitational Field ◽  
Real Life ◽  
Vertical Motion ◽  
Exact Form ◽  
Potential Danger ◽  
Accurate Calculation ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Celestial Bodies ◽  
Newton’S Laws

The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.

Gravitational acceleration of a weakly relativistic electron in a conducting drift tube

2018 ◽  
Vol 33 (33) ◽  
pp. 1850192 ◽  
Author(s):  
V. I. Denisov ◽  
I. P. Denisova ◽  
M. G. Gapochka ◽  
A. F. Korolev ◽  
N. N. Koshelev
Keyword(s):  
Gravitational Field ◽  
Relativistic Electron ◽  
Horizontal Plane ◽  
Drift Tube ◽  
Gravitational Force ◽  
Vertical Direction ◽  
Gravitational Acceleration ◽  
The Earth ◽  
Earth’S Gravitational Field

We propose the idea of method for observing the effect of the Earth’s gravitational field on the motion of an electron. Earlier attempts to measure such an effect proved unsuccessful due to the fact that under the conductive sheath, the gravitational force acting on the non-relativistic electron is completely compensated by Barnhill–Schiff force. Therefore, experiments of this kind were unable to measure the effect of the Earth’s gravitational field on the motion of electrons. In this paper, we propose to use electrons moving with relativistic speeds in the horizontal plane, and with non-relativistic speeds in the vertical direction, in which case the gravitational force on these electrons is not fully compensated by the Barnhill–Schiff force. Calculations showed that in this case, it is possible to measure the force exerted on an electron by the gravitational field of the Earth.

scholarly journals Satellite Gravimetry: A Review of Its Realization

2021 ◽  
Author(s):  
Frank Flechtner ◽  
Christoph Reigber ◽  
Reiner Rummel ◽  
Georges Balmino
Keyword(s):  
Gravitational Field ◽  
Gravity Field ◽  
Water Cycle ◽  
Temporal Changes ◽  
Sensor Technology ◽  
Satellite Gravimetry ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Gravity Field Determination ◽  
Space Age

AbstractSince Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstacles and the Earth as a whole could be observed and measured in consistent series of measurements. Of particular interest is the determination of the spatial structures and finally the temporal changes of the Earth's gravitational field. The knowledge of the gravitational field represents the natural bridge to the study of the physics of the Earth's interior, the circulation of our oceans and, more recently, the climate. Today, key findings on climate change are derived from the temporal changes in the gravitational field: on ice mass loss in Greenland and Antarctica, sea level rise and generally on changes in the global water cycle. This has only become possible with dedicated gravity satellite missions opening a method known as satellite gravimetry. In the first forty years of space age, satellite gravimetry was based on the analysis of the orbital motion of satellites. Due to the uneven distribution of observatories over the globe, the initially inaccurate measuring methods and the inadequacies of the evaluation models, the reconstruction of global models of the Earth's gravitational field was a great challenge. The transition from passive satellites for gravity field determination to satellites equipped with special sensor technology, which was initiated in the last decade of the twentieth century, brought decisive progress. In the chronological sequence of the launch of such new satellites, the history, mission objectives and measuring principles of the missions CHAMP, GRACE and GOCE flown since 2000 are outlined and essential scientific results of the individual missions are highlighted. The special features of the GRACE Follow-On Mission, which was launched in 2018, and the plans for a next generation of gravity field missions are also discussed.

scholarly journals Constants related to the Earth and Moon

1965 ◽  
Vol 21 ◽  
pp. 67-79
Author(s):  
Harold Jeffreys
Keyword(s):  
Gravitational Field ◽  
The Moon ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Tesseral Harmonics

The author discusses various determinations of zonal and tesseral harmonics of the Earth's gravitational field, the values of the solar parallax, and the constants related to the figure of the Moon and its motion.

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 .

scholarly journals Orbital Perigee Deviation under Inclination Window for Sun Synchronized Low Earth Orbits

2019 ◽  
Vol 4 (10) ◽  
pp. 127-130
Author(s):  
Shkelzen Cakaj ◽  
Bexhet Kamo
Keyword(s):  
Orbital Plane ◽  
Earth Observation ◽  
Gas Content ◽  
The Sun ◽  
Orbital Inclination ◽  
The Earth ◽  
Low Earth Orbits ◽  
Earth Observation Satellites ◽  
Earth Orbits ◽  
Earth’S Oblateness

Data processing related to the Earth’s changes, gathered from different platforms and sensors implemented worldwide and monitoring the environment and structure represents Earth observation (EO). Environmental monitoring includes changes in Earth’s vegetation, atmospheric gas content, ocean state, melting level in the ice fields, etc. This process is mainly performed by satellites. The Earth observation satellites use Low Earth Orbits (LEO) for their missions. These missions are accomplished mainly based on photo imagery. Thus, the relative Sun’s position related to the observed area, it is very important for the photo imagery, in order the observed area from the satellite to be treated under the same lighting (illumination) conditions. This could be achieved by keeping a constant Sun position related to the orbital plane due to the Earth’s motion around the Sun. This is called Sun synchronization for low Earth orbits, the feature which is applied for satellites dedicated for the Earth observation. Nodal regression is the phenomenon which is utilized for low circular orbits providing to them the Sun synchronization. Nodal regression refers to the shift of the orbit’s line of nodes over time as Earth revolves around the Sun,  caused due to the Earth’s oblateness. Nodal regression depends on orbital altitude and orbital inclination angle. For the in advance defined range of altitudes stems the inclination window for the satellite low Earth orbits to be Sun synchronized. For analytical and simulation purposes, the altitudes from 600km to 1200km are considered. Further for the determined inclination window of the Sun synchronization it is simulated the orbital perigee deviation for the above considered altitudes and the eventual impact on the satellite’s mission.

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