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Forma orbitelor cometare

2.5 Forma orbitelor cometelor lui

              În ceea ce privește cometele, ecuația newtonian de forțe este:

                (2.21) în care:

               (2.22) și

hN - energie constanta rămas constantă în timpul mișcării.

              Pentru:

              a) hN <0, E <0, care este   (2.23) cometa descrie o elipsă;

              b) hN = 0, E = 0, care este   (2.24) cometa descrie o parabolă;

              c) hN > 0, E> 0, care este   (2.25) cometa descrie o hiperbolă;

              Din cele aproximativ 830 de orbite ale  cometelor pe care le  stim pana in prezent, conform teoriei lui Newton, 73% au un cvasi-parabolic excentricitate 0,99 <e <1,01 și doar 27% au e <0,99, care este acestea sunt în mișcare pe orbite eliptice în mod clar. Din orbitele aproape parabolice sunt de 14% hiperbolic, 16% elipse foarte alungite, și 43% parabolic. Deducem din această distribuție a orbitelor cometelor lui în teoria newtoniană că aceste comete nu sunt membri permanenți ai sistemului nostru solar.

              Dar sunt multe argumente în favoarea tezei că cometele sunt efectiv membrilor permanenți ai sistemului solar, si mai multi astronomi tind să adere la acest punct de vedere. În 1932, E. Opik enunțat pentru prima dată ipoteza existenței unei "rezervor de comete", situat la capătul sistemului nostru solar, comete care părăsesc  sub acțiunea tulburătoare a stelelor. J. van Woerkom (1948) și J. Oort (1950-1951) au demonstrat, statistic și pe mecanica cereasca bază, că cometele sunt membri permanenți ai sistemului nostru solar.

              Aceste comete poate începe de la Soare pe o orbită eliptică inițial (primar), dar sub influenta planetelor traiectoriile lor pot obține o formă parabolică sau hiperbolică.

              Pana acum doar aproximativ 25 de astfel de orbite primare au fost determinate, fiind dovedit că acestea au fost într-adevăr eliptic. Cu toate acestea, este insuficient pentru a trage o concluzie definitivă. AO Leuschner a publicat un studiu statistic pe orbite comete lui. Rezultatul este: Cu cât este mai lunga observația cometei, mai probabilă este ca orbita sa nu este o parabolă (și cu atât mai puțin este o hiperbolă).

              Această observație este ilustrată de următorul tabel:

Perioada vizibila a unei comete

Orbitele parabolice observate

1-99 days

68%

100-239 days

55%

240-511 days

13%

13%

              <Pentru o cometă vizibilă în timpul 240 zile sau mai mult, este extrem de dubios ca o orbită parabolic fi stabilită definitiv ...>

              Teoria, conform căreia cometele, în general, sunt membri permanenți ai sistemului solar, pare să fie confirmată de datele statistice de mai sus.

              În teoria vortex, ecuația forțelor devine prin introducerea termenul de corecție:

           (2.26)

în cazul în care:  (2,27) și

              Ca   (2,28), viteza cometei (V g) poate fi mai mare decât cea din teoria newtoniană și, în ciuda acestui fapt, propunerea poate fi eliptică.

              Să presupunem că la o cometa, conform teoriei lui Newton, există  si ca orbita este o parabolă, în timp ce prin noua teorie miscarea cometei este o elipsă, pentru că cometa nu ajunge la viteza parabolic necesara. Toate comete parabolice ale teoriei newtoniene devin eliptice prin introducerea termenului de corectare.

              Adăugarea factorului de corecție, este următoarea distribuție a formelor orbitelor cometelor lui:

              - orbitele eliptice clar: 27% + 16% + 43% = 86%

              - Posibile orbite hiperbolice și parabolice: 14%.

              Pe baza acestui tip de distribuție, se poate afirma că cometele sunt membri permanenți ai sistemului, desigur, există,  comete cu orbite parabolice sau hiperbolice, dar ele sunt un rezultat al orbitei eliptice modificate  de planete (Jupiter, Saturn ). Când o cometă se apropie de o mare planetă, câmpul gravitațional al cometei poate fie accelera sau încetini o funcție de mișcarea relativă între planetă și cometa se apropie înainte.

              Dacă viteza cometei este majorata cde câmpul gravitațional al planetei, orbita cometei poate deveni parabolica sau hiperbolica; în cazul în care rămâne eliptic, se modifica parametrii orbitali.

              Dacă viteza cometa este redusă de câmpul gravitațional al planetei, orbita cometei lui devine o elipsă care este mai mică decât înainte "captura".

2.5 Shape of cometary’s orbits

            Concerning the comets, the Newtonian equation of forces is:

             (2.21) where: 

              (2.22) and

hN – energy constant remaining constant during the motion.

            For:

            a)hN<0, E<0 that is  (2.23) the comet describes an ellipse;

            b) hN=0, E=0 that is   (2.24) the comet describes a  parabola;

            c) hN>0, E>0 that is   (2.25) the comet describes an hyperbola;

            From the approximately 830 cometary’s orbits we know till now, according to the Newtonian theory, 73% have a quasi-parabolic eccentricity 0.99<e<1.01 and only 27% have e<0.99, that is they are moving on clearly elliptical orbits. From the nearly parabolic orbits there are 14% hyperbolic, 16% very lengthened ellipses, and 43% parabolic. We infer from this distribution of cometary’s orbits in the Newtonian theory that these comets are not permanent members of our solar system.

            But there are many arguments in favor of the thesis that the comets are effectively permanent members of the solar system, and most of astronomers adhere to this view. In 1932, E. Opik enunciated for the first time the hypothesis of the existence of a "reservoir of comets" situated at the end of our solar system, which the comets leave under the disturbing action of the stars. J. van Woerkom (1948) and J. Oort (1950-1951) demonstrated, statistically and on celestial mechanics basic, that the comets are permanent members of our solar system.

            These comets may start from the Sun on an elliptical initial (primary) orbit, but under the influence of the planets their trajectories may get a parabolic or hyperbolic shape.

            Till now only about 25 such primary orbits were determined, being proved that they were really elliptical. It is nevertheless insufficient to draw any final conclusion. A.O. Leuschner published a statistical study on cometary’s orbits. The result is: The longer is the comet observation, the more probable is that its orbit is not a parabola (and the less is it a hyperbola).

            This observation is illustrated by the following table:

Visibility period of the comet

Registered parabolic orbits

1-99 days

68%

100-239 days

55%

240-511 days

13%

            <For a comet visible during 240 days or more, it is extremely dubious that a parabolic orbit be definitively established...>

            The theory, according to which the comets generally are permanent members of the solar system, seems to be confirmed by the above mentioned statistic data.

            In the theory of vortex, the equation of the forces becomes by introducing the corrective term:

           (2.26)

where:  (2.27) and

            As  (2.28), the speed of the comet (Vg) may be greater than that in the Newtonian theory and, notwithstanding this, its motion may be elliptical.

            Suppose that at a comet, according to the Newtonian theory, there is , the orbit is a parabola, while by the new theory the same comet moves on an ellipse, because the comet does not reach the necessary parabolic speed. All parabolic comets of the Newtonian theory become elliptically orbited comets by introducing the corrective term.

            Adding the corrective factor, there is the following distribution of the shapes of cometary’s orbits:

            - clearly elliptic orbits: 27%+16%+43%=86%

            - possible hyperbolic and parabolic orbits: 14%.

            Based on this kind of distribution, we may assert that the comets are permanent members of the system, Of course, there are also comets with parabolic or hyperbolic orbits, but they are a result of the elliptical orbit disturbing by the planets (Jupiter, Saturn). When a comet gets near to a big planet, the gravitational field of the comet may either accelerate or decelerate it depending on the relative motion between planet and comet before approaching.

            If the comet speed is increased by the gravitational field of the planet, the comet orbit may get either parabolic or hyperbolic; if it still remains elliptical, it modifies its orbital parameters.

            If the comet speed is reduced by the gravitational field of the planet, the cometary’s orbit gets an ellipse which is less than before the "capture".

 

 

2.5 Shape of cometary’s orbits

 

            Concerning the comets, the Newtonian equation of forces is:

 

Cometary orbit 01         (2.21) where:  Cometary orbit 02               (2.22) and Cometary orbit 03

 

hN – energy constant remaining constant during the motion.

 

            For:

 

            a)Cometary orbit 04,  hN<0, E<0 that is  (2.23) the comet describes an ellipse;

 

            b) Cometary orbit 05hN=0, E=0 that is   (2.24) the comet describes a  parabola;

 

            c)Cometary orbit 06 hN>0, E>0 that is   (2.25) the comet describes an hyperbola;

 

            From the approximately 830 cometary’s orbits we know till now, according to the Newtonian theory, 73% have a quasi-parabolic eccentricity 0.99<e<1.01 and only 27% have e<0.99, that is they are moving on clearly elliptical orbits. From the nearly parabolic orbits there are 14% hyperbolic, 16% very lengthened ellipses, and 43% parabolic. We infer from this distribution of cometary’s orbits in the Newtonian theory that these comets are not permanent members of our solar system.

 

            But there are many arguments in favor of the thesis that the comets are effectively permanent members of the solar system, and most of astronomers adhere to this view. In 1932, E. Opik enunciated for the first time the hypothesis of the existence of a "reservoir of comets" situated at the end of our solar system, which the comets leave under the disturbing action of the stars. J. van Woerkom (1948) and J. Oort (1950-1951) demonstrated, statistically and on celestial mechanics basic, that the comets are permanent members of our solar system.

 

            These comets may start from the Sun on an elliptical initial (primary) orbit, but under the influence of the planets their trajectories may get a parabolic or hyperbolic shape.

 

            Till now only about 25 such primary orbits were determined, being proved that they were really elliptical. It is nevertheless insufficient to draw any final conclusion. A.O. Leuschner published a statistical study on cometary’s orbits. The result is: The longer is the comet observation, the more probable is that its orbit is not a parabola (and the less is it a hyperbola).

 

            This observation is illustrated by the following table:

 

Visibility period of the comet

Registered parabolic orbits

1-99 days

68%

100-239 days

55%

240-511 days

13%

 

            <For a comet visible during 240 days or more, it is extremely dubious that a parabolic orbit be definitively established...>

 

            The theory, according to which the comets generally are permanent members of the solar system, seems to be confirmed by the above mentioned statistic data.

 

            In the theory of vortex, the equation of the forces becomes by introducing the corrective term:

 

           Cometary orbit 07(2.26)

 

where:  Cometary orbit 08(2.27) and Cometary orbit 09

 

            As  (2.28), the speed of the comet (Vg) may be greater than that in the Newtonian theory and, notwithstanding this, its motion may be elliptical.

 

            Suppose that at a comet, according to the Newtonian theory, there is , the orbit is a parabola, while by the new theory the same comet moves on an ellipse, because the comet does not reach the necessary parabolic speed. All parabolic comets of the Newtonian theory become elliptically orbited comets by introducing the corrective term.

 

            Adding the corrective factor, there is the following distribution of the shapes of cometary’s orbits:

 

            - clearly elliptic orbits: 27%+16%+43%=86%

 

            - possible hyperbolic and parabolic orbits: 14%.

 

            Based on this kind of distribution, we may assert that the comets are permanent members of the system, Of course, there are also comets with parabolic or hyperbolic orbits, but they are a result of the elliptical orbit disturbing by the planets (Jupiter, Saturn). When a comet gets near to a big planet, the gravitational field of the comet may either accelerate or decelerate it depending on the relative motion between planet and comet before approaching.

 

            If the comet speed is increased by the gravitational field of the planet, the comet orbit may get either parabolic or hyperbolic; if it still remains elliptical, it modifies its orbital parameters.

 

            If the comet speed is reduced by the gravitational field of the planet, the cometary’s orbit gets an ellipse which is less than before the "capture".

 

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