Secular Acceleration Research Articles

Geomagnetic Secular Variation, 1962.5 to 1967.5

Summary Mean values of observatory geomagnetic data for the intervals 1960.0 to 1965.0 and 1965.0 to 1970.0 are subjected to spherical harmonic analysis to obtain coefficients of the main magnetic field. Since the same set of 118 observatories was used for each interval, the difference between the two sets of coefficients gives a reliable measure of secular change. Westward drift and movements of the centred and eccentric dipole are discussed, and the value of secular acceleration as an aid to prediction is assessed. The correlation between changes in westward drift and in the length of the day is re-examined and found to be of doubtful significance.

Observations of Mars from Earth between 1965 and 1969

Since the 1965 Symposium on Planetary Atmospheres and Surfaces, groundbased observations of Mars have added significantly to our knowledge of that planet. Martian topography and surface properties have been mapped by radar, surface temperatures and thermal properties have been determined by microwave and infrared radiometry, and the spectral reflectivity of surface regions has been measured over a wide range of wavelengths at different Martian seasons. Topographic features have been detected by spectroscopy of the CO 2 atmosphere, and a re-analysis of observations of Mars' satellites has shown that any secular acceleration must be quite small.

Dynamical characteristics of Phobos and Deimos

The orbital properties of the two small Martian satellites, Phobos and Deimos, are discussed, as well as those dynamical constants of Mars that can be determined from the satellite orbits. A secular acceleration of the mean motion of Phobos was once thought to exist, but now, on the basis of the recent work of G. A. Wilkins, the acceleration is shown to be very small. Of mechanisms that could cause any such acceleration, only tidal friction appears to be important. From the orbital evolution of the Martian satellites under tidal forces, Phobos and Deimos seem to have originated in nearly circular orbits of low inclination fairly close to the distance at which a satellite's orbital period is the planet's rotation period. It is proposed that the Martian satellites were born at the same time as Mars from equatorial dust clouds. The satellites are predicted to be locked in synchronous rotation, with their axes of minimum moment of inertia pointing on the average toward Mars, whereas their maximum axes are approximately normal to their orbit planes. Moderate amplitude physical librations may be observed by Mariner 9 because of resonance effects produced by forcing torques that have roughly the satellite free‐libration period. Observations of the rotational motion of the satellites will permit an evaluation of the ratios of differences in the satellite principal moments of inertia and thus will place constraints on density models.

Creep in the earth and planets

Evidence of imperfectly elastic behaviour in the earth and planets is provided by the following phenomena: 1. (1) damping of the earth's free nutation; 2. (2) damping of elastic waves passing through the earth; 3. (3)secular acceleration of the moon; 4. (4) figure of the moon; 5. (5) figure of the earth; 6. (6) rotations of satellites of the planets; 7. (7) free oscillations of the directions of the moon's axes; 8. (8) eigenfrequencies of the earth; and 9. (9) damping of the S wave as a function of frequency. Darwin attempted to explain the secular acceleration of the moon by viscosity in the body of the earth. This was shown to be unsatisfactory in 1915. A logarithmic law of creep, containing one relevant constant, agrees with some laboratory tests and approximately with a large quantity of seismological data. But it was found that if the constant is chosen to fit the damping of the free nutation (Eulerian nutation or Chandler wobble) the beginning of a transverse seismic wave at distance 80° would be spread over about 70 sec and be unreadable. I propose a law of creep by which for a constant shearing stress P the response is a shearing strain ϵ given by: ϵ = P μ [1 + q α {(1 + at) α − 1 ]} where t is time and μ, q, a, α are constants. This is a particular case of imperfection of elasticity. In it, for disturbances lasting a second or more, there are essentially only two creep parameters to be fixed, α and qa α . These may be determined by the two data: 1. (1) that the relaxation time of the free nutation is 30 ± 20 yyears; 2. (2) that S at 80° reaches half its ultimate value in 2 sec. We obtain α as probably between 0.14 and 0.21, with 0.19 as the most probable value. We then proceed to show that this law of creep, with α = 0.19, can account for approximately the right amount of damping (or internal friction) in all the other phenomena listed above. Laws with α = 1 (elastico-viscous law) and α = 0 (logarithmic law) fail to do so. A consequence of this law of creep is that where it holds convection cannot take place.

Diffusion of Comets from Parabolic into Nearly Parabolic Orbits

It is assumed that the accumulation of small, independent, random perturbations in the reciprocal semimajor axis of the orbit of a comet follows a normal distribution law whose standard deviation is a function of the inclination and perihelion distance and that for nongravitational forces it is a function of perihelion distances only; it is also assumed that secular accelerations do not change into decelerations, and vice versa. The standard deviations given by diffusion theory are in good agreement with the mean values of nongravitational impulses obtained from calculations from short overlapping arcs. The mean lifetime of a comet is found to be one hundred revolutions. To explain why many more near-parabolic comets are actually discovered than are theoretically expected the existence of comets of very short lifetimes must be accepted.

An Investigation of the Motion of Periodic Comet Borrelly from 1904 to 1967

The motion of P/Borrelly has been investigated using all precise published positions and taking into account the perturbations by Venus to Pluto. Nongravitational forces have been found to influence the motion of the comet considerably, formerly as a secular deceleration, more recently as a secular acceleration. By linking the seven apparitions 1904–1960, with allowance for the nongravitational effects, we have obtained a set of elements which represents 802 observations with a mean error of 1′.89.

The Role of Occultations in the Improvement of the Lunar Ephemeris

Analyses of occultation timings show that periodic correction terms with semi-amplitude as great as 0.″18 arise from corrections required to the empirical constants of the Brown/Eckert theory. Using the atomic time-scale, some of the occultation data have been used to determine a correction of – 30 ± 16″/cy2 to Spencer Jones' value for the secular acceleration of the Moon. In the light of this correction, and previous determinations, attention is drawn to the possible weakness of Spencer Jones' value, which is not reflected in his quoted error of ± 1″/cy2. Further analyses of 50000 occultations observed since 1943 promise to reveal more accurately-determined corrections.

A Non-Newtonian Orbit for Periodic Comet Borrelly

A non-Newtonian orbit has been determined for P/Borrelly which successfully represents all eight apparitions. Although this comet has a substantial secular acceleration in its mean motion, the transverse nongravitational force is time independent over the 64-yr observed interval.

The secular accelerations of the moon's orbital motion and the earth's rotation

The results and methods of determining the secular accelerations of the Moon's orbital motion and the Earth's rotation from astronomical observations are critically reviewed. In particular, the effect on these results is considered should Spencer Jones' value for the secular acceleration of the Moon be revised. General relationships are deduced between these accelerations, the rate of dissipation of energy in the Earth and the fractional change in the rate of rotation of the Earth. It is shown that the theory of tidal torques alone does not completely account forany of the wide range of results for the retardation of the Earth deduced from astronomical observations.

The Value of Photoelectric Occultation Timings in Lunar Motion Studies

AbstractThe two most important advantages of photoelectric timings of occultations over visual timings are accuracy and freedom from systematic error. The observational error is so small compared with uncertainties in the lunar ephemeris, star positions, limb corrections, and such, that the value of the observations will continue to increase as time goes on and the other error sources are eliminated.A recent result made possible largely by the availability of photoelectric timings over the last 20 yr is a new value for the secular acceleration of the Moon, with corresponding consequences for the Ephemeris Time scale.An important current application for simultaneous photoelectric and visual observations is the determination of ‘personal equation’ for the visual observers. Experiments so far indicate the visual observers require a minimum of 0.1 sec to detect that an event has occurred, plus additional time to react to it; hence, typical personal equations are around 0.4 sec.

Secular Accelerations of the Earth and Moon

Secular Accelerations of the Earth and Moon

Motion of Phobos

THERE have been several attempts to explain the large secular acceleration of the motion of Phobos (the closer of the two satellites of Mars) that was derived by Sharpless1 by fitting a quadratic expression for the mean longitude to five selected groups of orbital elements covering the period 1879 to 1941. An analysis2 of all suitable visual observations made during the period 1877–1929 failed, however, to confirm this secular acceleration. The orbital elements obtained in this analysis, taking the secular acceleration as zero, were subsequently3 shown to fit these visual observations and also positions obtained by Sharpless in 1941 and, photographically, by Kuiper in 1956 to within about ±2° in the value of the constant term in the linear expression for the mean longitude. This uncertainty is believed to be due partly to the errors of the observations and partly to the approximations in the orbital model used to fit the observations.

Geomagnetic Secular Variation and its Changes, 1942.5 to 1962.5

A uniform set of geomagnetic data from observatories has been analysed to determine secular variation of the geomagnetic field for the interval 1942.5 to 1962.5 and to reveal any changes in secular variation during this time. The epoch to epoch changes are much smoother than have been previously found, and permit an examination of the movements of the centred and eccentric dipoles and changes in westward drift. The secular variation has also been used to determine surface motions of the Earth's core. Changes in secular variation are presented in the form of charts of secular acceleration.

Note on the paper by G. F. Schilling, ‘On exospheric drag as the cause of the supposed secular accelerations of phobos’

In his recent paper, Schilling [1964] postulated that the exosphere of Mars may exert a drag on Phobos of sufficient magnitude to account for the secular acceleration in longitude of this satellite as given by Sharpless [1945]. In his examination of the problem, Schilling cited the results of Kerr and Whipple [1954], which indicated that the tide in the mantle of Mars would be about 800 times too small to account for Phobos' secular acceleration. Schilling, consequently, did not consider the tidal effect as a significant contributor to the secular acceleration. F. F. Fish and I [Redmond and Fish, 1964] have re-examined the possibility of a tidal effect being responsible for Phobos' secular acceleration. We have calculated the minimum and the maximum values for the lunitidal interval in Mars that are required to account for the secular acceleration of Phobos; these are 1.1° and 4.4°, respectively. The uncertainty of the result is due to the uncertainties in the physical constants involved in the Mars-Phobos system.

Reply [to “Comments on the paper by G, F. Schilling, ‘On exospheric drag as the cause of the supposed secular accelerations of phobos’”

Reply [to “Comments on the paper by G, F. Schilling, ‘On exospheric drag as the cause of the supposed secular accelerations of phobos’”

Comments on the paper by G.F. Schilling, ‘On exospheric drag as the cause of the supposed secular accelerations of phobos’

Comments on the paper by G.F. Schilling, ‘On exospheric drag as the cause of the supposed secular accelerations of phobos’

Quantitatives zur Diracschen Schwerkraft-Hypothese

§1. Discussion of the fundamental constants of physics. The constants of atomic and nuclear physics are proven to be real constants by empirical facts, with thepossible exception of the Fermi constant of beta decay. Neither theoretical nor empirical arguments prove that the gravitational constantκ is really constant. §2. Geological and geophysical evidence shows a marked expansion of the Earth in performance. It can be used to gain some quantitative information. §3. (Written together with my coworkersEhlers andKundt). The recent refutation of Jeffreys theory of tidal friction necessitates a new discussion of the Moons secular acceleration, the idea of bodily internal tidal friction leading to difficulties. This discussion gives a new interpretation at the basis ofDirac's hypothesis, and further quantitative information about\(\dot \kappa \). §4. Roche limit and tidal friction. §5. The results of satellite precision measurements of the Earth's oblateness are in greement with our conclusions. §6. The result concerning\(\dot \kappa \) seems also to give the interpretation of diluvial glaciations.

The luni-tidal interval in Mars and the secular acceleration of Phobos

Phobos, the inner satellite of Mars, appears to perform a secular acceleration in longitude. The cause of this acceleration has not, as yet, been satisfactorily explained. The possibility of tidal friction in the solid body of Mars appears to be the most reasonable process; however, some authors dispute this contention. In this paper, a range of the luni-tidal interval required to account for the observed acceleration is calculated and found to be 1.1 to 4.4 degrees.

On exospheric drag as the cause of the supposed secular accelerations of Phobos

A recent theory by Shklovskiy explained the supposed orbital accelerations of Phobos by suggesting that it is an artificial satellite of Mars. Reasonable assumptions about the physical state of the equatorial exosphere of Mars, however, lead to values of atmospheric density that could exert observable drag effects on Phobos without its being a hollow sphere. It is further shown that a required correlation may exist between solar activity and reported values of the accelerations over a period of some 60 years. As long as reliable observational evidence remains scarce, the actual existence of orbital accelerations remains in doubt. Yet, because of the potential importance of the phenomenon to the study of planetary exospheres, future observations and analyses are emphatically necessary.

Radiation Pressure Effects on Earth Satellite Orbits.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Radiation Pressure Effects on Earth Satellite Orbits. Sehorn, Ronald A. Abstract Wyatt, Jr.). -The effects of electromagnetic radiation pressure on the orbital elements of artificial earth satellites are of interest in their own right, and they must be assessed independently for the accurate determination of quantities such as the atmospheric density at great heights and the characteristics of the earth's gravitational field. Wyatt has developed an analytical method for determining the secular change in anomalistic period of a satellite due to solar radiation pressure. The expression obtained has the form of a power series in the eccentricity, and permits computations to be done easily with a desk calculator. The present work has extended the series for period change to a higher order to examine its convergence, and has also applied the method to variations in the eccentricity. The resultant series converge rapidly enough to be useful for most earth satellites launched to date. As is well known, when the orbit is entirely in sunlight the secular change of period is zero, but the secular change of eccentricity is finite, even for e--0. Under these conditions, the satellite neither gains nor loses energy, but its perigee distance varies. When a satellite spends a finite fraction of its time in the earth's shadow, the secular changes of period and eccentricity are both finite, and the energy of the satellite changes. If e=0, the secular acceleration is zero even if the satellite enters the shadow. But the eccentricity is changing at e=0, and as soon as the orbit has a nonzero eccentricity the period begins to change secularly. The effect of radiation emitted by the earth has also been considered. Expressions for the rates of change of the period and eccentricity have been developed, utilizing a series of models of increasing complexity to describe the earth's radiating characteristics. Preliminary results suggest that a typical value of the secular acceleration due to this effect is about 10% of that due to solar radiation pressure. This work has been carried out under a contract from the U. S. Air Force. Publication: The Astronomical Journal Pub Date: June 1962 DOI: 10.1086/108861 Bibcode: 1962AJ.....67R.282S full text sources ADS |