2.3 Acceleration of particles in tails of type I

 

            S.V. Orlov observed in case of comets with tails of type I, that the value 1+μ cannot be precisely determined by Bredihin's method, these tails being nearly rectilinear.

            He proposed in this case another method based on the examination of the motion of ,,nodosities” along the tails. It is frequently observed that from the comet nucleus get out swarms of particles, all of them "repulsed" by the Sun with the same force. These swarms move along the tail as a whole, slightly dilating and loosing brightness towards the tail tip.

            Such bright swarms or "nodosities" may be followed (especially on photographs) with a very high precision and, consequently, it is possible to determine exactly both their trajectories in relation to the nucleus and the value (1+μ) of the "repulsive" acceleration. By examining 1+μ values of type I tails, the following law is ascertained:

            The acceleration values of type I tails have the form:

                         1+μ=22,3n     (2.11)

                                      where    n = 1, 2, 3, 4, 5, 6, 7, 8, 9.

            In the following table there are some values (1+μ) experimentally determined in the motion of ,,nodosities” observed in commentary tails of type I, and the extent of checking on the above mentioned law:

 

Comet

No. of

Obs.

1+

Multiplicity

1892 I

5

45,5

( 1+ ) :2=22,8

1899I

5

22,5

( 1+ ) :1=22,5

1903IV

6

86,8

( 1+ ) :4 =21,7

1908III

16

66,4

( 1+ ) :3=22,1

1908III

16

87,8

( 1+) :4=21,9

1908III

16

155,4

( 1+ ) :7=22,2

1908III

9

160,4

( 1+ ) :7=22,9

1908III

9

200

( 1+ ) :9=22,2

1910I (Halley)

20

66,5

( 1+ ) :3=22,2

Mean     ( 1+   )=22,3n

 

            Let us try to explain the accelerations of the gas nodosities.

            We therefore suppose that from the fragmented cometary’s nucleus is detached a particle of "frozen" gas with mass m and volume v, which under the influence of the solar heath vaporizes instantaneously. We are interesting to know how was modified the acceleration of the particle of frozen gas by vaporization.

            For the particle of "frozen" gas:

                  

mode    (2.12) where

            For the gas nodosity resulted by evaporation of the ,,frozen” gas particle:

             

  mode     (2.13)

where  and vgas=volume of nodosities resulted by evaporation and also m-evaporated nodosity mass ≈ m-initial particle mass.

            The difference of acceleration is (2.14):

 

where vgas – v ≈ vgas (the volume of the solid particle is negligible in relation to the volume of the same particle in gaseous form).

As    (2.15)

where M = molecular mass of gas and Vm = 22,4 l – molar volume

                        Then:

   (2.16)

            Particle of ,,frozen” gases by evaporation are accelerated in proportion to the molar volume.

            The origin of factor 22,4 was established in the expression of gas nodosities accelerations. Now we intend to demonstrate that the different accelerations of gas nodosities (for example, the comet 1908 III) are a consequence of different molecular masses of the evaporated gases.

            Let us consider that there are two nodosities at the same distance from the Sun (r), which are composed of gases with different molecular masses (M1 and M2).

            In the hypothesis M1<M2 we are interested to know which of the two nodosities will be more intensely accelerated.

            Related to the Sun, the accelerations of the nodosities will be:

 (2.17)

 (2.18)

 (2.19)

For:  M1 < M2                a2<a1               r1>r2  (2.20)

 

            The gas with less molecular mass moves farther away from the nucleus than the gas with higher molecular mass and implicitly the latter gets a stronger acceleration.