A finite and exact expression for the refraction of an atmosphere nearly resembling that of the earth

1833 ◽  
Vol 2 ◽  
pp. 207-208
Keyword(s):  
Exact Expression ◽  
Square Root ◽  
Total Height ◽  
The Earth ◽  
Direct Equation ◽  
Astronomical Refraction ◽  
Nautical Almanac

Having shown that if the pressure of the .atmosphere he represented either by the square, or by the cube of the square root of the density, the astronomical refraction may be attained in a finite equation; and having adverted to Mr. Ivory’s computation of the refraction with the assistance of converging series, and several transformations from an equation which expresses the pressure in terms of the density and of its square, Dr. Young proceeds to observe, that if we substitute for the simple density the cube of its square root, we shall represent the constitution of the most important part of the atmosphere with equal accuracy, although this expression supposes the total height somewhat smaller than the truth; and that we shall thus obtain a direct equation for the refraction, which agrees very nearly with Mr. Ivory’s table, and still more accurately with that in the Nautical Almanac, and with the French tables. At the horizon the refraction is equal to 33' 49"· 5, which is only l''·5 less than the quantity assigned by the French tables and in the Nautical Almanac; while Mr. Ivory makes it 34' 17"·5. Again, for the altitude 5° 44' 21", we obtain 8' 49"'·5 for the refraction; while the Nautical Almanac gives us 8' 53", and Mr. Ivory’s table S' 49"·6. The author, however, observes that there is no reason for proceeding to compute a new table by this formula, since the method employed for that in the Nautical Almanac is in all common cases more compendious; and even if it were desired to represent Mr. Ivory’s table by the approximation there employed, we might obtain the same results, with an error scarcely exceeding a single second, from an equation of the same form.

VII. A finite and exact expression for the refraction of an atmosphere nearly resembling that of the earth

1824 ◽  
Vol 114 ◽  
pp. 159-161
Keyword(s):  
Royal Society ◽  
Exact Expression ◽  
Square Root ◽  
Total Height ◽  
The Earth ◽  
Royal Institution ◽  
Direct Equation ◽  
Astronomical Refraction ◽  
Nautical Almanac

It has lately been demonstrated, in the Journal of the Royal Institution, that if the pressure of the atmosphere, y , be represented either by the square or by the cube of the square root of the density, z , the astronomical refraction, r , may be obtained in a finite equation. Mr. Ivory, in a very ingenious and elaborate paper lately presented to the Royal Society, has computed the refraction, by means of several refined transformations, and with the assistance of converging series, from an equation which expresses the pressure in terms of the density and of its square: I have now to observe, that if we substitute, for the simple density, the cube of its square root, and make y = 3/2 z 3/2 — ½ z 2 , we shall represent the constitution of the most important part of the atmosphere with equal accuracy, although this expression supposes the total height somewhat smaller than the truth, and belongs to one of those hypotheses, which Mr. Ivory has considered as inadmissible: it has the advantage, however, of affording a direct equation for the refraction, which agrees very nearly with Mr. Ivory’s table, and still more accurately with the French table, and with that which has been published for some years in the Nautical Almanac.

The Calculation of Astronomical Refraction in Marine Navigation

1982 ◽  
Vol 35 (2) ◽  
pp. 255-259 ◽  
Author(s):  
G. G. Bennett
Keyword(s):  
Wide Range ◽  
Temperature And Pressure ◽  
Astronomical Refraction ◽  
Marine Navigation ◽  
Nautical Almanac

Since programmable electronic calculators were first employed in marine navigation, a variety of formulae has been used for calculating astronomical refraction. As the choice is wide, some formulae have been selected from commonly used reference sources and their accuracy and suitability examined. No attempt has been made to assess the validity of the selected formulae to represent astronomical refraction in practical circumstances. Accuracy comparisons have been made using the refraction algorithm proposed by Garfinkel – the standard adopted by the British and American Nautical Almanac Offices. New formulae are given that are simple and accurate, even over a wide range of temperature and pressure, and which for all practical purposes may be considered equivalent to the tables of refraction given in the Nautical Almanac.

scholarly journals Gravitational Weakening of Seismic Origin as a Driving Mechanism of Some Astronomical Anomalies

2018 ◽  
Author(s):  
Paul C. Rivera
Keyword(s):  
Structure Constant ◽  
Equatorial Region ◽  
Fine Structure Constant ◽  
Past Century ◽  
Driving Mechanism ◽  
Astronomical Unit ◽  
Anomalous Increase ◽  
The Earth ◽  
New Equation ◽  
Astronomical Refraction

The anomalous increase of the astronomical unit, the mysterious secular increase of the lunar eccentricity and the flyby anomaly are important issues of modern astronomy. This study aims to determine the effect of earthquakes on the origin of these anomalies. Based on conventional physics, we found the existence of earthquake-induced gravitational weakening within the earth-moon-sun system and beyond. New equations of gravitation, including time dilation, are introduced that can explain the anomalous increase of the astronomical unit and the lunar orbit. A modified equation that includes the effect of massive quakes also explains the anomalous increase of the lunar eccentricity. Furthermore, the results of the present study can explain the flyby and Pioneer anomalies experienced by spacecraft during gravity assisted maneuvers. A modification of the 3rd Law of Kepler is also presented. Implications on the elliptic orbit of the earth, its reduced velocity and the occurrence of leap years are also discussed. Using the seismic-induced gravitational weakening model, probable trigger mechanisms of the faint young sun paradox and the Allais effect are also presented. An estimate of the age of the earth based on the observed values of the Hubble parameter and the USGS earthquake data for the past century is also presented. A new model of the seismic-driven expanding universe and a new equation to determine the expansion rate of galaxies and the universe is also proposed. The sudden earth’s retreat due to gravitational weakening and its implication on anomalous astronomical refraction and flight risk at night especially near the equatorial region, and its effect on the abrupt satellite orbital decay, spin and drift are also discussed. This study may also shed light on the occurrence of sinkholes and massive landslides. Finally, this study proposes a new equation that can explain the observed changes in the fine structure constant.

A Device to Determine Position Rapidly Without Calculation

1956 ◽  
Vol 9 (1) ◽  
pp. 11-16
Author(s):  
Leo Randić
Keyword(s):  
Sidereal Time ◽  
Outer Circle ◽  
The Earth ◽  
Geographical Latitude ◽  
The Difference ◽  
Celestial Sphere ◽  
The Right ◽  
Right Ascension ◽  
Nautical Almanac

The problem of the determination of the observer's position on the Earth can be most easily solved in terms of the equatorial coordinates of the observer's zenith. From Fig. 1, in which the inner circle represents the Earth and the outer circle the celestial sphere, it can be seen that the zenithal point on the celestial sphere is its intersection with the prolongation of the radius to the observer's position. The geographical latitude of the observer is equal to the declination of the observer's zenith, and the geographical longitude is equal to the difference between Greenwich sidereal time (G.S.T.) and the right ascension of the observer's zenith. We can obtain G.S.T. by interpolation from a nautical almanac or directly from a separate watch or clock set to keep sidereal time.

scholarly journals III. On the corrections of Bouvard’s elements of Jupiter and Saturn (Paris, 1821)

1869 ◽  
Vol 17 ◽  
pp. 344-346
Keyword(s):  
Mean Error ◽  
The Earth ◽  
Royal Observatory ◽  
The Mean ◽  
The Difference ◽  
Nautical Almanac

The Tables of Jupiter and Saturn which have been used for some years past in the computations of the ‘Berliner Jahrbuch’ and ‘Nautical Almanac,’ differ more from observation than is consistent with the present requirements of astronomy; and, moreover, abundant means for the correction of Bouvard’s ‘Elements’ exist in the publication of the Greenwich Planetary Observations, 1750-1835, and the annual volumes issued from the Royal Observatory since 1836. The present work, which has been undertaken for this purpose, is based exclusively on the Greenwich Observations, 1750-1865. Each mean group of observations in the Greenwich Planetary Reductions &c. gives the mean error of the planet’s tabular geocentric place, with its equivalent in terms of the heliocentric errors of the earth and planet; but in the present investigation the places of Carlini’s Solar Tables, which have been used throughout the whole period (with the exception of 1864 and 1865), have been accepted without alteration; for Jupiter and Saturn the factors of the earth’s heliocentric errors are so small, that the difference of Carlini’s Solar Tables from the recent investigations of Leverrier rnay be neglected.

scholarly journals ‘The Metrication of Navigation’

1968 ◽  
Vol 21 (2) ◽  
pp. 236-237
Author(s):  
D. H. Sadler
Keyword(s):  
Universal Time ◽  
Time System ◽  
Precise Position ◽  
The Earth ◽  
Time Signals ◽  
Time Argument ◽  
Orbital Periods ◽  
Rotation Of The Earth ◽  
Mean Time ◽  
Nautical Almanac

In his note (Journal 21, 81) on this subject, Ronald Turner says ‘No longer will orbital periods of the rotation of the Earth on its axis be measures of time’. This is not so, either in general or in the particular, case of navigation.Universal Time (U.T.), which is the generally accepted name for Greenwich Mean Time (G.M.T.), continues to be essential for all purposes (in astronomy, geodesy, surveying and navigation) for which are required astronomical observations related to the precise position of the observer on the Earth's surface. The Nautical Almanac must continue to tabulate the positions of the Sun, Moon, planets and stars with G.M.T. as the time-argument; and observations should be timed in a time-system related to U.T., such as the broadcast time-signals of Coordinated Universal Time (U.T.C:).

The Square Root Approximation to the Dispersion Relation of the Axially-symmetric Electron Wave on a Cylindrical Plasma

1997 ◽  
Vol 52 (10) ◽  
pp. 709-712
Author(s):  
V.M. Babović ◽  
B.A. Aničin ◽  
D. M. Davidović
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Gravity Waves ◽  
Water Surface ◽  
Bessel Functions ◽  
Exact Expression ◽  
Square Root ◽  
Axially Symmetric ◽  
Electron Wave ◽  
Surface Gravity Waves

Abstract This paper suggests the use of a simple square root approximation to the dispersion relation of axially-symmetric electron surface waves on cylindrical plasmas. The point is not merely to substitute the exact expression for the dispersion relation which involves a number of Bessel functions with a more tractable analytical approximant, but to cast the dispersion relation in a form useful in the comparison with other waves, such as water surface gravity waves and the associated tide-rip effect. The square root form of the dispersion relation is also of help in the analysis of surfactron plasmas, as it directly predicts a linear roll-off of electron density in the discharge.

scholarly journals Remarks on the probabilities of error in physical observations, and on the density of the Earth, considered, especially with regard to the reduction of experiments on the pendulum. In a letter to Capt. Henry Kater, F. R. S. By Thomas Young, M. D. For. Sec. R. S

1833 ◽  
Vol 2 ◽  
pp. 106-108
Keyword(s):  
Joint Effect ◽  
Square Root ◽  
Black And White ◽  
Mean Error ◽  
The Earth ◽  
Natural Tendency ◽  
The Mean

In the first section of this letter, Dr. Young proceeds to examine in what manner the apparent constancy of many general results, subject to numerous causes of diversity, may be best explained; and shows that the combination of many independent causes of error, each liable to incessant fluctuation, has a natural tendency, dependent on their multiplicity and independence, to diminish the aggregate variation of their joint effect; a position illustrated by the simple case of supposing an equal large number of black and white balls to be thrown into a box, and 100 of them to be drawn out at once or in succession; when it is demonstrated that there is 1 chance in 12 1/2; that exactly 50 of each kind will be drawn, and an even chance that there will not be more than 53 of either; and that it is barely possible that 100 black, or 100 white, should be drawn in succession. From calculations contained in this paper, Dr. Young infers that the original conditions of the probability of different errors do not considerably modify the conclusions respecting the accuracy of the mean result, because their effect is comprehended in the magnitude of the mean error from which these conclusions are deduced. The author also shows that the error of the mean, on account of this limitation is never likely to be greater than six sevenths of the mean of all the errors divided by the square root of the number of observations.

POTENTIAL AND APPARENT RESISTIVITY OVER DIPPING BEDS

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 780-793 ◽  
Author(s):  
Jerome Chastenet De Gery ◽  
Geza Kunetz
Keyword(s):  
Point Source ◽  
Current Density ◽  
Potential Field ◽  
Apparent Resistivity ◽  
Exact Expression ◽  
Electrode Configuration ◽  
Vertical Profiles ◽  
The Earth ◽  
Electrode Separation

The potential field due to a point source of current, located on the surface of the earth near a dipping bed, is given in an exact expression and modified expressions are developed for computations. These expressions lead to graphs of the potential field and to apparent resistivity vertical profiles which are presented. The Schlumberger electrode configuration is used. This configuration consists of two current electrodes and two potential electrodes, the latter placed close enough together that the current density between them can be considered to be uniform. With this configuration oriented perpendicular to the strike of the dipping bed, the apparent resistivity is paradoxical in that it approaches either zero or infinity as the electrode separation increases without limit.

scholarly journals Gravitational Weakening of Seismic Origin as a Driving Mechanism of Some Astronomical Anomalies

2019 ◽  
Vol 11 (2) ◽  
pp. 10
Author(s):  
Paul C. Rivera
Keyword(s):  
Structure Constant ◽  
Equatorial Region ◽  
Fine Structure Constant ◽  
Past Century ◽  
Driving Mechanism ◽  
Astronomical Unit ◽  
Anomalous Increase ◽  
The Earth ◽  
New Equation ◽  
Astronomical Refraction

The anomalous increase of the astronomical unit, the mysterious secular increase of the lunar eccentricity and the flyby anomaly are important issues of modern astronomy. This study aims to determine the effect of earthquakes on the origin of these anomalies. Based on conventional physics, we found the existence of earthquake-induced gravitational weakening within the earth-moon-sun system and beyond. New equations of gravitation, including time dilation, are introduced that can explain the anomalous increase of the astronomical unit and the lunar orbit. A modified equation that includes the effect of massive quakes also explains the anomalous increase of the lunar eccentricity. Furthermore, the results of the present study can explain the flyby and Pioneer anomalies experienced by spacecraft during gravity assisted maneuvers. A modification of the 3rd Law of Kepler is also presented. Implications on the elliptic orbit of the earth, its reduced velocity and the occurrence of leap years are also discussed. Using the seismic-induced gravitational weakening model, probable trigger mechanisms of the faint young sun paradox and the Allais effect are also presented. An estimate of the age of the earth based on the observed values of the Hubble parameter and the USGS earthquake data for the past century is also presented. A new model of the seismic-driven expanding universe and a new equation to determine the expansion rate of galaxies and the universe is also proposed. The sudden earth’s retreat due to gravitational weakening and its implication on anomalous astronomical refraction and flight risk at night especially near the equatorial region, and its effect on the abrupt satellite orbital decay, spin and drift are also discussed. This study may also shed light on the occurrence of sinkholes and massive landslides. Finally, this study proposes a new equation that can explain the observed changes in the fine structure constant.

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