Mean Solar Day Research Articles

On the variability of the Chandler frequency

We have estimated the Chandler frequency from a variety of polar motion time series derived from optical and space geodetic data which span various time periods from 1846 through the early 1990s. Estimates of F vary, depending upon which time series is employed, but the variation is not significant when associated intervals of confidence are considered; thus there is no evidence that the true Chandler frequency has varied. Using a maximum likelihood method, our preferred estimate of F is 0.8433 cycles per tropical year (cpy), ±0.003 cpy, or equivalently a period of 433.1 mean solar days (msd), ±1.7 msd. Estimates are given on the condition that the Gaussian statistical model of the excitation process is valid, and new approaches which employ observations of the polar motion excitation process should eventually provide better estimates, which may differ from those determined here.

Estimates of the Chandler wobble frequency and Q

The Chandler wobble frequency F and quality factor Q are estimated by least squares using polar motion data in combination with proxy excitations derived from atmospheric data. Monte Carlo tests show that this approach can provide useful improvements over traditional maximum likelihood methods, which use only observed polar motion. With less than a decade of good simultaneous polar motion and atmospheric data there is no new information about Q, but 90% confidence intervals for F are near ±0.004 cycles per year (cpy), making them comparable to maximum likelihood results based on nearly a century of historical polar motion data. Using our preferred proxy excitation, we obtain an estimate of F near 0.831 cpy (a period of 439.5 mean solar days), which is significantly different from the maximum likelihood value near 0.843 cpy (433 days). This difference can be understood in light of differences in assumptions underlying the two methods.

Comprehensive Model Simulation of Thermal Tides in the Martian Atmosphere

Abstract This paper discusses the thermotidal oscillations in simulations performed with a newly developed comprehensive general circulation model of the Martian atmosphere. With reasonable assumptions about the effective thermal inertia of the planetary surface and about the distribution of radiatively active atmospheric aerosol, the model produces both realistic zonal-mean temperature distributions and a diurnal surface pressure oscillation of at least roughly realistic amplitude. With any reasonable aerosol distribution, the simulated diurnal pressure oscillation has a very strong zonal variation, in particular a very pronounced zonal wavenumber-2 modulation. This results from a combination of the prominent wave-2 component in the important boundary forcings (topography and surface thermal inertia) and from the fact that the eastward-propagating zonal wave-1 Kelvin normal mode has a period near 1 sol (a Martian mean solar day of 88 775 s). The importance of global resonance is explicitly demonstrated w...

Time Scales for Theory and Practice

Very early human experience has suggested a practical definition for the measurement of time: We define a unit of time by defining a standard (cyclical) process. Whenever this process completes its cycle identically, a unit of time has elapsed. This is the origin for the various measures of time in classical astronomy. Nature suggests strongly that we use as such standard processes the year (defined as a complete revolution of the earth around the Sun), the month (the completion of a revolution of the moon around the earth), and the day which again can be measured in several different ways. While the sidereal day is measured by a rotation in respect to the vernal equinox, the mean solar day is measured in respect to the mean. Sun. More recently, we have distinguished many more different ways of defining measures of time, partly in response to perceived needs of the applications, but in part also from purely aesthetic principles.

The Half-Inertial Flow in the Eastern Equatorial Pacific: A Case Study

Abstract We address the problem of the oscillatory periods of two observed phenomena in the instability zone in the eastern equatorial Pacific. The first case concerns two high-speed anticyclonic flow with periods of approximately 12 and 15 mean solar days. The second concerns the long waves with an average period of about 25 days. The problem is that, in terms of their respective mean latitudes, these periods are about twice as large as those of the inertial period of one-half pendulum day. As a solution we offer the hypothesis of the half-inertial flow with its period of one pendulum day. The inertial flow is governed by KV = −f, where K is the path curvature, V the speed of the flow, and f the Coriolis parameter. In contrast, the half-inertial flow is governed by KV = −f/2 with a speed that is the maximum for a given curvature and latitude and approaches twice that of the geostrophic speed. In terms of the half-inertial flow, the average lone-wave period of 25 days would correspond to a plausible mean ...

The Chandlerian Period of minimum excitation

Up to the present, the Chandlerian Period has been defined as the mean period of the revolution of the pole around its mean position. However, as the motion of the excitation pole does not contain the Chandlerian component, we can determine the length of the Chandlerian Period under the condition that the motion of the excitation pole attains a minimum after elimination of the Chandlerian component. It is calculated as 416 (mean solar) days. It means the period deduced from the angular velocity of the pole around the instantaneous excitation pole, and is able to match better those deduced from the theory of the internal constitution of the Earth. The calculated results using the recent data of ERP with a high precision show that the Chandlerian Period in this sense seems to have a reality.The main results are shown in the Figure on the next pape.This paper was published in full form in the Journal of the Geodetic Society of Japan, 33 (1987) pp.97–100.

Astronomical records from Ancient Babylon

Because of its calendrical and prognosticatory significance astronomical observation was assiduously practised in many of the ancient civilisations. Of the surviving records by far the greatest number are from Babylon, covering effectively the period 731 BC-AD 75, but it is only comparatively recently that these have been systematically deciphered and interpreted. Apart from their great historic interest, the remarkable accuracy of many of the observations makes them of value to modern astronomers, in such contexts as the variation in length of the mean solar day.

The rotation of the earth between 1955.5 and 1976.5

The difference between the rotational time UT1 and atomic time scale AT was analysed in order to find the secular and periodic variations in the rotational velocity of the Earth. It was found that the length of the mean solar day was increasing by 12.8 ms per century in the interval discussed. As a whole, eleven periodic terms were found, the most significant having the periods of 0.5, 1.0, 6.7 and 11.9 y. The correlation between the long period changes in the Earth's rotation and relative sunspot numbers is shown.

Determination ofM2ocean tide parameters from satellite orbit perturbations

A sequence of 80 mean inclinations obtained from successive 2-day orbital arcs of a U.S. Navy navigation satellite (1967-92A) has been used to obtain M2 ocean tide parameters. By assuming solid tide parameters of k2 = 0.30 and δ2 = 0° the implied observation equation on terms of order 2 and degree 2, 4, 6, …, is (3.8″±0.60) × 10−2 sin [wt + (331°±10°)] = (0.99″/cm) × 10−2 C22+ sin (wt + e22+) + (0.94″/cm) × 10−2 C42+ sin (wt + e42+) + …, where w = 1 cycle/13.58 days and t is the time in mean solar days from 1900.0. This observation agrees well with published numerical solutions of Laplace's tidal equation.

Period, Qp and Amplitude of the Pole Tide

Summary The maximum entropy method (MEM) of Burg has been applied to monthly mean values of tide gauge records from 126 stations. Principal results are: (1) the Chandlerian induced pole tide signal is detected on a world-wide basis, (2) the spectral character of the signal is a single broad peak, (3) the mean and standard error of the period is 433-16+0.41 mean solar days, (4) the mean and standard deviation of the pole tide Q, is 22+ 12, and (5) in agreement with Miller evidence is found for an enhanced pole tide in certain locations outside the shallow seas of North Europe.

Period and Qw of The Chandler Wobble

A splined ILS/IPMS data set (1900–1973) from the most homogeneous values available has been analysed by the maximum entropy method of Burg. Principal conclusions are: (1) the spectral character of the Chandler wobble is a single broad peak, (2) the period is 432·95 ± 1·02 mean solar days and, (3) the Qw is 36±10. Measurements indicate that Qw is non- stationary in time.

The Variation of Latitude

The 14-monthly variation of the Earth's axis is a free oscillation, and like others it is damped, and must be maintained by some irregular disturbance. In addition there are complications from the annual variation and observational error. The method adopted is first to analyse the data from 1899 to 1967 over 7-yr intervals, to eliminate the free period as well as possible and leave a mean value of the annual terms. The mean displacements fluctuated considerably. With a unit 0·001″ l(=x) ranged from – 15 to + 53, m(= – y) from the start to 1947 from – 41 to + 3, in both cases quite irregularly, but m reached – 164 in 1955–61 and has reached – 225 in 1962–8. The apparent standard errors are mostly about 6. This behaviour is inconsistent with any hypothesis of a uniform rate of drift in either the pole or the observatories. A smooth formula for interpolating the means was adopted; this and the mean annual terms were subtracted, and the remainder was analysed for harmonic terms of 14-month period. Drift of phase gave a correction to this trial period. A model on Yule's lines was used to estimate the parameters in a disturbed system. The remaining observational error over 14-month intervals turned out to be very small. The final period was 433·15 ± 2·23 mean solar days. The damping factor e–k in 14 months gave k = 0·05 ± 0·034, suggesting a time of relaxation between 14 and 73 yr, with a most probable value of 23 yr.

The Variation of Latitude

The 14-monthly variation of the Earth's axis is a free oscillation, and like others it is damped, and must be maintained by some irregular disturbance. In addition there are complications from the annual variation and observational error. The method adopted is first to analyse the data from 1899 to 1967 over 7-yr intervals, to eliminate the free period as well as possible and leave a mean value of the annual terms. The mean displacements fluctuated considerably. With a unit 0·001″ l(=x) ranged from – 15 to + 53, m(= – y) from the start to 1947 from – 41 to + 3, in both cases quite irregularly, but m reached – 164 in 1955–61 and has reached – 225 in 1962–8. The apparent standard errors are mostly about 6. This behaviour is inconsistent with any hypothesis of a uniform rate of drift in either the pole or the observatories. A smooth formula for interpolating the means was adopted; this and the mean annual terms were subtracted, and the remainder was analysed for harmonic terms of 14-month period. Drift of phase gave a correction to this trial period. A model on Yule's lines was used to estimate the parameters in a disturbed system. The remaining observational error over 14-month intervals turned out to be very small. The final period was 433·15 ± 2·23 mean solar days. The damping factor e–k in 14 months gave k = 0·05 ± 0·034, suggesting a time of relaxation between 14 and 73 yr, with a most probable value of 23 yr.

Geodetic annual variation of the sidereal day

Synopsis Owing to the geodetic precession of parallel axes, effect of Einstein's theory of gravitation 1), the sidereal day will be shorter than the proper terrestrial day. The difference will amount to 3 2 m/r of the difference between mean solar day and sidereal day (237 sec), where m is the gravitation parameter of the sun, expressed as a length (1,47 km) and r the radius of the earth's orbit (1,5 · 108 km). The earth's orbit being an ellipse (1/r = (1 + e cos φa) with eccentricity e = 1/60, the geodetic fluctuation amplitude in the difference of sidereal and proper terrestrial day will amount to 237 sec e · 3 2 m/a = 6 nanosecond. In the spring the sidereal clock will be 3,44 μ sec fast, in the autumn as much slow. Recent data on the seasonal irregularities of the earth's rotation point to a fluctuation of about 27 millisec.

Time Determination and Time Keeping

The rotation of the Earth provides the ultimate standard of time. As the fundamental unit of time we can use either the mean solar day or the sidereal day; these two units are related in a definite manner, so that when one is determined, the other can be inferred. The purpose of any timepiece is to subdivide the day into shorter intervals, and so give the time at any instant. No timepiece will give exact time; the error of the timepiece at some definite instant and the rate of change of that error, or, briefly, the rate, must be determined in order to extrapolate for the correct time at some subsequent instant. The accuracy of the extrapolation will depend upon the uniformity of the rate of the timepiece. Radio time signals sent out from an observatory, which is responsible for the determination and distribution of time, provide the most convenient means for deriving the error and rate of a timepiece. For normal navigational purposes an accuracy of about 0·05 seconds is adequate. But for the purpose of frequency control a very much higher precision is needed—but a precision in time interval rather than in absolute time. Some of the radio-aids to navigation depend upon the accuracy in standardization of frequency, so that high accuracy in time interval has become, indirectly, a navigational requirement.

4. Commission des Éphémérides

The agenda for the meeting in Stockholm are:(1)Report on the progress of the FK3 catalogue, and the volume of apparent places of the stars in this catalogue.(2)At the meeting in Paris it was suggested that the value of the Gaussian constant k should be fixed, and the President was asked to consult people known to be interested. As complete agreement appears to have been reached, the following resolution will be moved: “That the value of the Gaussian constant k shall be taken as 0-01720 20989 50000, the unit of time being the mean solar day for 1900·0”

The Navy's Primary Frequency Standard

In this paper is described a constant frequency source which is used as the Navy's primary working standard of frequency. This frequency source is a crystal-controlled oscillator of special design which was developed at the U.S. Naval Research Laboratory, Washington, D.C. This oscillator employs a type of circuit which is rich in harmonics, over 200 of which may be used as fixed standard frequencies. It also describes in detail the method employed to determine the fundamental frequency of this standard in terms of Naval Observatory time to an accuracy of about one part in 100,000. The ultimate standard of frequency is therefore the mean solar day.

VIII. On the intensity and direction of the force of gravity in India

Between 1865 and 1873 observations were taken at 31 stations in India by Captains Basevi and Heaviside with the Royal Society’s seconds pendulums. The results were published in Vol. V. of the ‘Account of the Operations of the Great Trigonometrical Survey of India,’ and have been subsequently discussed by many authorities. Captain Basevi expressed his results in terms of N, the number of vibrations of the mean pendulum observed in a mean solar day. The International Geodetic Association show their results in dynes, and it is desirable that we should follow their example. We have, therefore, to change the notation employed by our predecessors.

I. On an apparatus for facilitating the reduction of tidal observations

The tidal oscillation of the ocean may be represented as the sum of a number of simple harmonic waves which go through their periods approximately once, twice, thrice, four times in a mean solar day. But these simple harmonic waves may be regarded as being rigorously diurnal, semi-diurnal, ter-diurnal, and so forth, if the length of the day referred to be adapted to suit the particular wave under con­sideration.

The Star of Bethlehem

REFERRING to the hypothesis in your last week's issue, that the star of Bethlehem was Venus, I would point out that 1180 synodical periods of Venus (i.e. 1180 × 583.92 = 689,025 mean solar days) take us back from October 28, 1887—when Venus was at her maximum brilliancy as a morning star—to only May 3 of the year 1 A.D. instead of December 25 of the year 1 B.C. For the number of days from October 28, 1887, to December 25, 1 B.C., is 689,155 (viz. 1887 × 365.2425 = 689,213 - 64 + 6 = 689,155). This would appear to show, either that the birth of Christ took place about May 3, or that Venus at her maximum brilliancy as a morning star was not the star of Bethlehem. I should be glad of your remarks on this.