On an inequality of long period in the motions of the Earth and Venus

1837 ◽  
Vol 3 ◽  
pp. 77-78
Keyword(s):  
Principal Term ◽  
The Sun ◽  
Method Of Calculation ◽  
The Third ◽  
Long Period ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
The Difference

The author had pointed out, in a paper published in the Philosophical Transactions for 1828, on the corrections of the elements of Delambre’s Solar Tables, that the comparison of the corrections of the epochs of the sun and the sun’s perigee, given by the late observations, with the corrections given by the observations of the last century, appears to indicate the existence of some inequality not included in the arguments of those tables. As it was necessary, therefore, to seek for some inequality of long period, he commenced an examination of the mean motions of the planets, with the view of discovering one whose ratio to the mean motion of the earth could be expressed very nearly by a proportion of which the terms are small. The appearances of Venus are found to recur in very nearly the same order every eight years; some multiple, therefore, of the periodic time of Venus is nearly equal to eight years. It is easily seen that this multiple must be thirteen; and consequently eight times the mean motion of Venus is nearly equal to thirteen times the mean motion of the earth. The difference is about one 240th of the mean annual motion of the earth; and it implies the existence of an inequality of which the period is about 240 years. No term has yet been calculated whose period is so long with respect to the periodic time of the planets disturbed. The value of the principal term, calculated from the theory, was given by the author in a postscript to the paper above referred to. In the present memoir he gives an account of the method of calculation, and includes also other terms which are necessarily connected with the principal inequality. The first part treats of the perturbation of the earth’s longitude and radius victor; the second of the perturbation of the earth in latitude; and the third of the perturbations of Venus depending upon the same arguments.

scholarly journals IV. On an inequality of long period in the motions of the Earth and Venus

1832 ◽  
Vol 122 ◽  
pp. 67-124
Keyword(s):  
The Sun ◽  
Long Period ◽  
Mean Motion ◽  
The Earth ◽  
The Mean

In a paper “On the corrections of the elements of Delambre’s Solar Tables,” published in the Philosophical Transactions for 1828, I stated that the comparison of the corrections in the epochs of the sun and the sun’s perigee given by late observations, with the corrections given by the observations of the last century, appeared to indicate the existence of some inequality not included in the arguments of those Tables. As soon as I had convinced myself of the necessity of seeking for some inequality of long period, I commenced an examination of the mean motions of the planets, with the view of finding one whose ratio to the mean motion of the earth could be expressed very nearly by a proportion whose terms were small: and I did not long seek in vain. It is well known that the appearances of Venus recur in very nearly the same order every eight years: and therefore some multiple of the periodic time of Venus is nearly equal to eight years. It is easily seen that this multiple is thirteen: and consequently eight times the mean motion of Venus is nearly equal to thirteen times the mean motion of the Earth. According to Laplace,(Méc. Cél. liv. vi. chap. 6.) the mean annual motion of Venus is 650 g. 198; that of the Earth 399 g. 993.

scholarly journals On an inequality of long period in the motions of the Earth and Venus

1837 ◽  
Vol 3 ◽  
pp. 108-113 ◽  
Keyword(s):  
Long Period ◽  
Mean Motion ◽  
The Earth ◽  
Actual Motion ◽  
Mutual Inclination ◽  
The Mean ◽  
The Difference ◽  
Academy Of Sciences ◽  
Great Complexity

The object of this memoir is similar to that of Laplace’s celebrated investigation of the great inequality of Jupiter and Saturn, announced in the Memoirs of the Academy of Sciences for 1784, and given in the volume for the succeeding year. The occasion of that investigation was an acceleration of the mean motion of Jupiter and a retardation of that of Saturn,—which inequalities in the motions of the two planets Halley had discovered by a comparison of ancient and modern observations: and Laplace showed, in the Memoirs just referred to, that inequalities like those thus noticed would arise from the action of gravitation; that they would reach a considerable amount in consequence of twice the mean motion of Jupiter being very nearly equal to five times the mean motion of Saturn; and that their period would be nearly 900 years. The occasion of the investigation of Professor Airy was an inequality in the sun’s actual motion, as compared with Delambre’s Solar Tables, which appeared to result from a comparison of late observations with those of the last century,—as Professor Airy has explained in a memoir published in the Philosophical Transactions for 1828. This comparison having convinced him of the necessity of seeking for some inequality of long period in the earth’s motion, it was soon perceived that such an inequality would arise from the circumstance that 8 times the mean motion of Venus is very nearly equal to 13 times the mean motion of the earth. The difference is 1,675 centesimal degrees in a year,—from which it follows, that if any such inequality exist, its period will be about 240 years. To determine whether such an inequality arising from the action of gravitation, amounts to an appreciable magnitude, is a problem of great complexity and great labour. The coefficient of the term will be of the order 13 minus 8, or 5, when expressed in terms of the excentricities of the orbits of the Earth and Venus, and their mutual inclination; all which quantities are small; and the result would therefore, on this account, be very minute. But in the integrations by which the inequality is found, the small fraction expressing the difference of the mean motions of the planets enters twice as a divisor; and by the augmentation arising from this and other parts of the process, the term receives a multiplier of about 2,200,000. In the corresponding step of the investigation of the great inequality of Jupiter and Saturn, it was only necessary to take terms of the 3rd order of smallness, and the multiplier by which the terms are augmented has 30 2 instead of 240 2 for its factor.

Data Fusion of Total Solar Irradiance Composite Time Series Using 40 years of Satellite Measurements: First Results 

2021 ◽  
Author(s):  
Jean-Philippe Montillet ◽  
Wolfgang Finsterle ◽  
Werner Schmutz ◽  
Margit Haberreiter ◽  
Rok Sikonja
Keyword(s):  
Time Series ◽  
Data Fusion ◽  
Solar Irradiance ◽  
Total Solar Irradiance ◽  
Maunder Minimum ◽  
The Sun ◽  
Climate Reconstructions ◽  
The Earth ◽  
First Results ◽  
The Difference

<p><span>Since the late 70’s, successive satellite missions have been monitoring the sun’s activity, recording total solar irradiance observations. These measurements are important to estimate the Earth’s energy imbalance, </span><span>i.e. the difference of energy absorbed and emitted by our planet. Climate modelers need the solar forcing time series in their models in order to study the influence of the Sun on the Earth’s climate. With this amount of TSI data, solar irradiance reconstruction models  can be better validated which can also improve studies looking at past climate reconstructions (e.g., Maunder minimum). V</span><span>arious algorithms have been proposed in the last decade to merge the various TSI measurements over the 40 years of recording period. We have developed a new statistical algorithm based on data fusion.  The stochastic noise processes of the measurements are modeled via a dual kernel including white and coloured noise.  We show our first results and compare it with previous releases (PMOD,ACRIM, ... ). </span></p>

scholarly journals XXXIV. Observations on the transit of Ve­nus, June the 6th, 1761, made in Spital-Square; the longitude of which is 4' 11" west of the Royal Observatory at Green­wich, and the latitude 51° 31' 15" north

1761 ◽  
Vol 52 ◽  
pp. 182-183
Keyword(s):  
The Sun ◽  
Royal Observatory ◽  
The Mean ◽  
The Difference ◽  
Made In

Having measured the diameter of Venus, on the sun, three times, with the object-glass micrometer, the mean was found to be 58 seconds; and but 6/10 of a second, the difference of the extremes.

scholarly journals A Symplectic Mapping Model as a Tool to Understand The Dynamics of 2/1 Resonant Asteroid Motion

1999 ◽  
Vol 172 ◽  
pp. 65-76
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Chaotic Motion ◽  
The Sun ◽  
Symplectic Mapping ◽  
Mapping Model ◽  
The Third ◽  
Secondary Resonances ◽  
Mean Motion ◽  
Slow Diffusion ◽  
Third Dimension ◽  
Asteroid Orbit

AbstractWe present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear. The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.

scholarly journals The yielding of the earth to disturbing forces

1909 ◽  
Vol 82 (551) ◽  
pp. 73-88 ◽  
Keyword(s):  
Spherical Surface ◽  
The State ◽  
Equilibrium Theory ◽  
Uniform Density ◽  
The Sun ◽  
Additional Hypothesis ◽  
Long Period ◽  
The Earth ◽  
Additional Qualification

1. Any estimate of the rigidity of the Earth must be based partly on some observations from which a deformation of the Earth’s surface can be inferred, and partly on some hypothesis as to the internal constitution of the Earth. The observations may be concerned with tides of long period, variations of the vertical, variations of latitude, and so on. The hypothesis must relate to the arrangement of the matter as regards density in different parts, and to the state of the parts in respect of solidity, compressibility, and so on. In the simplest hypothesis, the one on which Lord Kelvin’s well-known, estimate was based, the Earth is treated as absolutely incompressible and of uniform density and rigidity. This hypothesis was adopted to simplify the problem, not because it is a true one. No matter is absolutely incompressible, and, the Earth is not a body of uniform density. It cannot be held to be probable that it is a body of uniform rigidity. But when any part of the hypothesis, e. g ., the assumption of uniform density, is discarded, the estimate of rigidity is affected. Different estimates are obtained when different laws of density are assumed. Again, whatever hypothesis we adopt as regards the arrangement of the matter, so long as we consider the Earth to be absolutely incompressible and of uniform rigidity, different estimates of this rigidity are obtained by using observations of different phenomena. Variations of the vertical may give one value, variations of latitude a notably different value. It follows that “the rigidity of the Earth” is not a definite physical constant. But there are two determinate constant numbers related to the methods that have been used for obtaining estimates of the rigidity of the Earth. One of these numbers specifies the amount by which the surface of the Earth yields to forces of the type of the tide-generating attractions of the Sun and Moon. The other number specifies the amount by which the potential of the Earth is altered through the rearrangement of the matter within it when this matter is displaced by the deforming influence of the Sun and Moon. If we adopt the ordinarily-accepted theory of the Figure of the Earth, the so-called theory of “fluid equilibrium,” and if we make the very probable assumption that the physical constants of the matter within the Earth, such as the density or the incompressibility, are nearly uniform over any spherical surface having its centre at the Earth’s centre, we can determine both these numbers without introducing any additional hypothesis as to the law of density or the state of the matter. We shall find, in fact, that observations of variations of latitude lead to a determination of the number related to the inequality of potential, and that, when this number is known, observations of variations of the vertical lead to a determination of the number related to the inequality of figure. [ Note added , December 15, 1908.—This statement needs, perhaps, some additional qualification. It is assumed that, in calculating the two numbers from the two kinds of observations, we may adopt an equilibrium theory of the deformations produced in the Earth by the corresponding forces. If the constitution of the Earth is really such that an equilibrium theory of the effects produced in it by these forces is inadequate, we should expect a marked discordance of phase between the inequality of figure produced and the force producing it. Now Hecker’s observations, cited in § 6 below, show that, in the case of the semidiurnal term in the variation of the vertical due to the lunar deflexion of gravity, the agreement of phase is close. If, however, an equilibrium theory is adequate, as it appears to be, for the semidiurnal corporeal tide, a similar theory must be adequate for the corporeal tides of long period and for the variations of latitude.]

scholarly journals On the Causes of Palaeoclimatic Variations and of the Ice Ages in Particular

1953 ◽  
Vol 2 (13) ◽  
pp. 213-218
Author(s):  
E. J. Öpik
Keyword(s):  
Nuclear Reactions ◽  
Gas Diffusion ◽  
Seasonal Temperature ◽  
The Sun ◽  
Orbital Elements ◽  
Ice Ages ◽  
Solar Mass ◽  
The Earth ◽  
Change In The Mean ◽  
The Mean

AbstractA method of quantitative climatological analysis is developed by applying the principle of geometric similarity to the convective heat transport, which is assumed to vary with the 1.5 power of temperature difference. The method makes possible the calculation of the change in the mean annual, or seasonal temperature, produced by a variation in insolation, cloudiness, snow cover, etc.It is shown that the variations in the orbital elements of the earth cannot account for the phenomena of the ice ages; the chronology of the Quaternary, based on these variations, has no real foundation.Palaeoclimatic variations are most probably due to variations of solar luminosity. These can be traced to periodical re-adjustments in the interior of the sun, produced by an interplay between nuclear reactions and gas diffusion, repeating themselves after some 250 million years. Complications from the outer envelope of the sun lead to additional fluctuations of a shorter period, of the order of 100,000 years to be identified with the periodical advance and retreat of the glaciers during the Quaternary.Calculations of the variations of luminosity in a star of solar mass substantiate this hypothesis.

Reply to Discussion by J. R. Hearst and R. C. Carlson

Geophysics ◽  
1979 ◽  
Vol 44 (8) ◽  
pp. 1464-1464
Author(s):  
J. R. Hearst ◽  
R. C. Carlson
Keyword(s):  
Outer Radius ◽  
The Other ◽  
Gradient Term ◽  
The Earth ◽  
Other Hand ◽  
Free Air ◽  
Inner Radius ◽  
The Mean ◽  
The Difference

Our equations (3) and (4) are correct. They represent the difference between the attraction of the shell viewed from [Formula: see text], the outer radius of the shell, and [Formula: see text], its inner radius. (The attraction of the shell viewed from [Formula: see text] is zero.) On the other hand, equations (5) and (6) of Fahlquist and Carlson represent the difference in attraction of the entire earth from the same viewpoints and thus, as they say, include a free‐air gradient term. However, their equation (5) would be correct only if the mean density of the earth were equal to that of the shell, and the free‐air gradient obtained by their equation (10) is correct only under these circumstances.

scholarly journals I. An account of the Sun's distance from the Earth, deduced from Mr. Short's observations relating to the horizontal parallax of the Sun: In a letter from Peter Daval, Esq; V. P. of R. S. to James Barrow, Esq; V. P. of R. S

1763 ◽  
Vol 53 ◽  
pp. 1-2
Keyword(s):  
The Sun ◽  
The Earth ◽  
The Mean

According to Mr. Short, the mean horizontal parallax of the Sun is 8", 65. Now this parallax is the angle, which the semidiameter of the earth subtends, being seen from the Sun.

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