RELATIONS IN SOLAR FAMILY
-BY ABHINAV P PRADEEP
Solar family mainly consist of sun and 8 planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune)and its satellites and a lot.
There are lot of theories to explain how the solar system is formed (https://abhinavspaceindia.blogspot.com/2020/03/theories-about-origin-of-solar-system.html) but in a conclusion we can said that-The Sun and the planets formed from the contraction of part of a gas/dust cloud under its own gravitational pull and that the small net rotation of the cloud created a disk around the central condensation. The central condensation eventually formed the Sun, while small condensations in the disk formed the planets and their satellites. The energy from the young Sun blew away the remaining gas and dust, leaving the Solar System as we see it today.
In a conclusion we believe that solar system was formed together not separately as a result there might be exist lot of relations between the members of solar family. Here i am trying to explore the relations of the solar family.
1. Distance from the sun.
We can see that the distances of the planets from the Sun follow a simple arithmetic progression. According to Titius–Bode law the distance from the sun is in an AP which is
Here m is starting from -ve infinity, 0,1,2...........
first put infinity to this equation we get a=0.4 that is 0.4 AU
really it is 0.39 AU, and it is approximately right.
When we giving m=0 we get 0.3+0.4=0.7 AU, the real distance between sun and venus is 0.723 AU and this also right.
Now i am tabulating the results.
• For m=1 a=1 distance between earth and sun is really 1AU and this is correct.
• For m=2 a=1.6 distance between moon and sun is really 1.524 this also approximately right.
• For m=3 a=2.8 for jupiter 2.8 is wrong but for ceres this is right.
• For m=4 a=5.2 and correctly right for jupiter.
• For m=5 a=10.0 and for saturn it is 9.55 AU.
• For m=6 a=19.6 and true for uranus.
• For m=7 a=38.8 not true for neptune.
• For m=7 a=38.8 this is true for pluto.
• While going like this we get for m=8 is true for Eris and n=11 for sedna.
• I am concluding that in m=12,13,14 etc there is a chance too for the existence of planet 9.
This all shows that in the exception of neptune all other family members are arranged like an arithmetic progression.
2.Tilt relations
We know that all planets on the solar system are not straight boys! all have a little tilt from its own orbital plane. On this tilt too we could understand that the solar system is related well.When we divide mars axial tilt 25.2 by earth axial tilt we got 1.0769.
In the case of Satrun 26.7 and mars 25.2 dividing we get 1.0595
In neptune and saturn too we get 1.0599.
from this we could understand that this values are approximately equall.
another relation from this if we arrange the axial tilt of planets mercury earth mars saturn neptune pluto we can saw that this are in ascending order.
0.034, 23.4, 25.2, 26.7, 28.3, 122.5
The exception on this is mars jupiter and uranus but for venus axial tilt is 177.3 but if we dont consider the direction of rotation and subtracting it from 180 we got 2.7 and with a small exception venus also obey the ascending order. Now jupiter and uranus are the only planets which dont obey the order.
Hypotheses;
• Here uranus does not have any relations and it is rolling on its orbit around sun.• Its axial tilt is about 97.77.
• This axial tilt may occur due to collision of uranus with a big massive object.
• Due to this there is some mistakes in the distance from sun calculation by Titius–Bode law of uranus and neptune.
• We can conclude that long ago all solar system obey Titius-Bode law and the similarities in the axial tilt but after the formation of solar system due to some collisions solar system become like this.
3.Orbital velocity
In orbital velocity too there is loot of similarities on planets. We know that orbital velocity is inversely proportional to distance from the sun.• Venus orbital velocity(35.0) /mercury orbital velocity(47.4)
=0.7
• Earth ov(29.8) / venus ov(35.0) =0.8
• Mars ov(24.1) / Earth ov(29.8) =0.8
• Jupiter ov(13.1) / Mars ov(24.1) =0.6
• Saturn ov(9.7) / jupiter ov(13.1) =0.7
• Uranus ov(6.8) / saturn ov(9.7) =0.7
• Neptune ov(5.4) / uranus ov(6.8) =0.8
• Pluto ov(4.7) / neptune ov(5.4) =0.8
Hypotheses;
• for all planets orbital velocity of a planet by orbital velocity just before that planet is constant(0.77). [Small variation range (0.72-0.82) ].• for jupiter by mars is 0.6 this is an exception.
• Now let us consider the dwarf planet ceres in the asteroid belt. Its orbital velocity is about 17.9km/sec
• ceres ov(17.9) / mars ov(24.1) =0.7
• jupiter ov(13.1) / ceres ov(17.9) =0.7
• yes, when we considering the ceres too in the planet list we get the continues constant 0.7 in orbital velocity dividing.
Main Hypotheses
• In this i am considering no of planets = 11• mercury, venus, earth, mars, ceres, jupiter, saturn, uranus, neptune, pluto, eris.
• My criteria for planet is more than 10^20kg.
• Orbital velocity of this planets are respectively (47.4 – 35.0 – 29.8 – 24.1 – 17.9- 13.1 – 9.7 – 6.8 – 5.4 – 4.7 – 3.4)
• I had found that this is not an AP but a GP(geometric progression) with first term 47.4 and ratio 0.77
• in a GP
• In our case nth term will be
47.4 x 0.77^n-1
• Let us check this relation for all planets and deviation of the data from original value in a table.
• From this we could learn that there is only small variations in the orbital velocity so equation that i made is approximately right.
• From this i could predict that PLANET 9 have orbital velocity about 2.67km/sec if exist.
Equation for distance from sun
Now i had found equation for orbital velocity. We know that orbital velocity of anything is square root of product of universal gravitational constant and mass divided to distance that is
Here v^2 = GM/r
Equation i mentioned here is for orbital velocity of artificial satellite that we launch. I am going to modify this to apply for planets rotating around sun.
So G = 6.674 x 10^-11
M = Mass of sun ie= 1.989 × 10^30 kg
GM = 1.327 x 10^20 i will denote GM with #
r is the distance from sun i denote it with D
Vo is orbital velocity
Now v^2 = GM/r
v^2 = #/D
D = #/v^2
Here we have the value of # = 1.327 x 10^20
In above we got that the equation for velocity = 47.4 x 0.77^n-1
Here all other values are in m there fore velocity equation will
be 47400 x 0.77^n-1
Final equation for distance from sun=
D=#/(47400 x 0.77^n-1)²
SOLVING THISNow i have
D=(5.906282825 x 10¹á´¼)/ (0.77^(n-1))²
I will denote this constant 5.906282825 x 10¹á´¼ as ÂDistance from sun= Â/(0.77^(n-1))²
• My equation is working for all planets
• Titius–Bode law fails to explain the case of neptune on that sequence neptune is absent but my equation also include neptune.
• My criteria for planets is massive than 10^20 kg so i considered ceres, pluto and eris other than 8 planets that accepted by astronomical union.
• And the equation is also true for this three dwarfs.
• I am predicting that PLANAT 9 is in between 18550 million km from the sun.
GENERAL HYPOTHESES
• on this research i had tried to prove that solar system is formed together not separately. So i had proved that solar family is fully related.
• First relation is Titius–Bode law that explain the planets of solar family is arranged in a pattern but it failed in explaining neptune.
• Next relationship is relations in tilt relations.
• Axial tilt of planets increase as distance from sun increases.
• But on this uranus is different i think this is due to collision of uranus with a massive object so now it rolls around sun.
• On a few exception we can say that on axial tilt the solar system is related this implies on the time of origin of solar system all axial tilt increases according to distance but later collisions and changes in the solar system cause it become like as we see now.
• Then i explained some relations on orbital velocity. I found that orbital velocity of a planet by orbital velocity of a planet just before it is a constant. That is approximately about 0.775.
• Then I found that orbital velocity of planets are in a geometric progression. And i made an equation for axial tilt of planets is equal to 47.4 x 0.77^n-1. Where n is the planet number.
• My criteria for planet is massive than 10^20 kg but no satellite.
• Using this i had made an equation for distance from sun that is Â/(0.77^(n-1))² where  = 5.906282825 x 10¹á´¼.
• With small variations this equation is true for all planets in the solar system.
• It is perfect than titius bode law because it could explain distance to neptune too and no confusions in the equations.
• Using this law i had predict distance to eris(11002 million km) correctly.
• I predict the PLANET 9 will be in the range of 18550 million km from the sun if exist.
• I am concluding that the solar system is formed together as a centre at sun and planets satellites etc.
• All my relations are true without any exception at the time just after the origin of solar system.
• Now exceptions are due to collision and imbalances.
• So solar system is originated together.
Research and Composed by
Abhinav P Pradeep, wayanad, Kerala, India
Email:Abhinavppindia@gmail.com
Twitter: Abhinav P Pradeep
(@Abhinavppindia)
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