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Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
Analytical mechanics calculations for finding reasons of retrograde
opposite and slow rotation of Venus
Author: Akbar Mohammadzade
Iran University of Science and Technology
Email:[email protected]
Abstract
In this work we have prepared a new approach for doing mechanical analysis of sidereal rotation
of planets , satellites and moons .Our goal was finding basic relations between varied factors
effecting on the period and direction of such rotation in gravity field, together with generalization
this obtained relations for whole planetary systems. The other objective of our work was finding
main reason of opposite rotation of the Venus . The case study of our work which has some special
properties, doesn’t obey some rules and we ought to inter some secondary factors which correctly
gives speed ,direction and time durational changing of planet’s rotation model. After finding the
role of secondary parameters which changed its rotation mode ,our work ,for the first time resulted
any basic general scientific approach that with using analytical mechanics factors, we can obtain
the role of Coriolis effect and dense gas break effect on changing direction of original rotation of
planet .
Keywords(Coriolis effect, Solar wind ,Archimedean spiral ,solar CNO cycle)
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
1.Introduction
First we had forecasted that we have any multi factorial problem for solving the security of
bright bountiful and our earth attractive neighbor ,Venus. Venus opposite rotation is remained
mystery for duration of its discovering time till now ,and it has been refereed to some hypothetic
events such as external object impact with planet which supposed it changed its rotational
direction ,or the protoplanetary condition which made global system to retrograde direction of
rotation in solar system .
The position of planet obeys Tithus –bode law, any massive external object could result
considerable displacement causing exiting from such arrangement , in addition any external
massive object normally can create binary system , When any supposed object nears to other one ,
now we don’t see such exchanging. In fact and existing condition we have some observational data
about the Venus as below:
1) The radius of Venus in its pole and equator are near to equal (oblique near zero),this means
two simple results ,first the planet might be have slow rotation for duration of very long time
,may from its accretion ,the second is that the planet has not been tidal locked with sun by its
body.
2) Observations show that the planets tidal locking with sun is occurring in its atmosphere
,creating high speed winds above its clouds ,other helpful information for our study is the
depth and density and temperature of planet’s atmosphere .
3) The planet’s atmosphere contains 95percent carbon dioxide ,for analyzing the combination of
carbon dioxide for atmosphere of planet we can result one of this reasons :
3- 1) The gas has been absorbed from flattened primordial disk
3- 2) The gas has been absorbed from interstellar space
3- 3) The gas has been created from volcanic activities (as there are several high
mountains in planet)
3- 4)Our scenario that the gas has been absorbed from solar wind (the solar wind
carried particles are pulled to atmosphere , the light ones such as hydrogen and
helium cannot remain there for their velocity is shown in Table 1.)
3- 5) Existence of any growth process (for example process which increased oxygen
on earth surface for crust oxidation and its existence in our atmosphere)
4) The way of production of carbon dioxide:
4-1)The planet is lying in hot place of solar system the orbital of about 500Kelvin
Degrees (see figure 1.)
4-2)combination of oxygen and carbon occurs in hot temperature (the atmosphere
has about 750degrees Kelvin)
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
Table1. Vrms of some particles in our atmosphere and Venus on:
equation)
complex
one mole mass
22.4 lit
(molecule name)
1.
2.
3.
4.
5.
Carbon dioxide (CO2 )
Oxygen
(O2 )
Nitrogen
( N2 )
Helium
( He )
hydrogen ( H2 )
(g )
46
32
28
4
2
Vrms on earth
300 0K
(m/s)
407
477
510
1350
1908
Vrms=√3kT/m (Boltzmann
Vrms on Venus
7500K
(m/s)
1750
2054
2200
5805
8204
The escape velocity from planet surface is about 10Km/s then most of light particles cannot
remain there .[3]
But way generally carbon dioxide gas? The main resource is sun ,the star is strongly and
continually ejecting particles ,generally proton and alpha and beta ray and carbon ,nitrogen and
oxygen[2]As it has shown in table1. the Carbon dioxide (CO2 ) is heaviest one and has low velocity.
The next mystery is density of atmosphere ,our atmosphere has 1000km depth ,considerable part of
Venus atmosphere under its clouds has 60 km depth ,and above that is continues under the solar wind effect ,
the farther distance part is not spherical ,specially the planet rotation is slow .The gas surrounding seem dock
,and the planet have to rotate it , the mechanical analysis coming in part 5.
2. Field of study
The time durational increasing of density and condensation of Venus atmosphere may be refer to
its placement and magnetic field. When we are studying solar system members , we see that there is
some common properties in those bodies as the combination of matter as shown in figure 1. Same
as any spectrum of matter. So with referring to theories and simulation and modeling instruments
for solving our problems of finding reason of contractions we do discover the mysteries . However
some questions are remaining unsolved . One of those questions is retrograde rotation of Venus .
Some other unsolved problems in existing theories which I had monitored in my last article are
these :
1)The mechanism which planed for formation and accretion of planets , we got
spongy meteorites and low density dwarf planets ,not rocky one.
2)abnormally sidereal rotation period of Jovian planets not displayed there .
3) the physical reason of retrograde rotation of Venus not displayed .
4)there is not any general formula for calculating planet rotation period.
5)non of theories have not entered secondary currents effect on system.[1]
1000
Neptone
Uranus
CaO AlO Fe Ni
500
Rocky materials
Sillicats
Titan
H
He
100
ed
nim
Ga
30
20
5
CH4
15
H2O
2.8
1
1.5
0.2
0.45
NH3
kuiper belt
Ammonia Ice
Methane
50
10
TEMPERATURE K
saturn
Jupiter
Mars
Venus
Earth
2000
Mercury
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
DISTANCE FROM
Figure 1. planetary system matter distribution diagram
The planets rotate around invisible axis through their centers . Planets rotation period is known
as a stellar day ,most of planets in the solar system rotate in the same direction as they orbit the sun,
which is counter clockwise as seen from above the sun’s north pole ,the exceptions being Venus
and Uranus which rotate clockwise, though Uranus’s extreme axial tilt means there are differing
conventions on which of its poles is north ,and therefore whether it is rotating clockwise or anticlockwise .However ,regardless of which convention is used ,Uranus has a retrograde rotation
relative to its orbit.
The rotation of planet can be induced by several factors during formation .a net angular
momentum can be induced by the individual angular momentum contribution of accreted objects.
The accretion of protoplanetary accretion can randomly alter the spin axis of planet , during the last
stages of planet building .There is great variation in the length of day between the planets ,with
Venus taking 243Earth days to rotate and gas giants only a few hours[1].
Here we want to show either the retrograde and slow rotation of Venus is remaining from
accretion time or secondary factor caused its recent condition .The scenario which we gave in last
article shows that the planets place in gravity field and neighborhood planets properties specially
in rotation period is not natural and obeys from its own characteristics ,and with considering its
special properties we obtained inventive result for the first time[2]. For more and scientific
explaining of such theory we need mechanical analysis of planet motion and rotation.
In many conditions of planet –star or moon -planet systems we have tidally –locked members
(their orbits are in sync with their rotation)and the planet or moon only ever show one face to their
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
stars ,with one side in perpetual day ,the other in perpetual night[1]. These planets and moons rocky
cores may come near day part as we have in our moon.
In solar system without secondary events and factors ,when the rotation period was vary linear
or any routine formula we had seen Venus day length was between Mercury and earth, we solved
this variation for planets according their mass and volume and distance from sun and etcetera ,never
found out any relation between them.
The mars is in farther orbital and has 0.107 Earth mass but equal day as earth ,two gas giants has
major differences in mass and distance from sun but near rotation period ,and Mercury’s day and
year gives very accurate number 1.5007 .We found out two not deniable effect of solar wind in
planetary system solving mystery of retrograde rotation of Venus and gigantic rotation of Jupiter
and Saturn. Together with continual formation process of Jovian planets and comets ,which refers
to solar wind carried particles ,generally proton and electrons and giving some observation project
order for finding our forecasting theoretical facts as these:
1)There might be about 5 percent of solar wind carried particles oxygen and nitrogen
and carbon(solar CNO cycle production particles)[3].
2)The wind is fouling its carried particles in outer part of system ,generally from
Jupiter orbital to Kuiper belt(from calculating wind movement and direction by
Archimedean spiral[2].
3)Mass increasing of Jovian planets and their increasing rotation speed[3].
4) continues strong effect of solar wind and its created condition for Venus for the
reason of its slow and opposite rotating.[2]
5) Forecasting of Venus rotation slowing down[2].The fact which will be further
discussed in this article.
Only we have any unsolved problem ,that the amount of matter ejected from sun corona is less
than which needed to form icy Jovian planets. However we can suppose the strong T-Tauri star
young sun could rejected one Jupiter mass for duration of 108 years :
Solar wind amount per year now : 3.15*1013 ton/year
For T-Tauri star we have:3.15*1019 ton/year
3.The mechanical analysis of opposite rotation of the Venus
The location and velocity vectors for rotating object in gravity field are Perpendicular (tangent to
curve) and acceleration is in opposite direction with location vector toward the center of field . for
the case of tidal locked planet shown in figure2. We are seeing that the planet rotates round its axis
equal its year (synchronies)
Vp =2πr/y
3-1
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
y is the planet's period or its year and Vp is the velocity of the planet in its orbital. For entering
elliptical orbital properties, we have:
V per =2πr (√[(1+e)/(1-e)] )/y
3-2
V ap=2πr (√[(1-e)/(1+e)] )/y
3-3
Where the Vper is the velocity at perihelion and Vap is the velocity at aphelion. The sidereal
rotational velocity of a planet with radius r is:
V s=2 πr/p
3-4
Where the P is the planet's day.
Figure2.tidal locked planet rotation mechanism
Figure2.tidal locked planet rotation mechanism
With solving this equation for moon we have : ω=2π/2.33*106
rad/s
When we are solving the mechanism for any rotating object with distance from star ‘r’ and mass
‘m’:
The equation of elliptic orbital in flattened planetary disk is : y=a√1-x2/b2
So the position vector equation will be:(counterclockwise rotation)
r=rx+ry
r=x+a√1-x2/b2 =r.cos ω.t +a(√1-r2.cos2 ω.t /b2)
ṙ= - r. ω .sin ω.t-[a/(√1-r2.cos2 ω.t /b2)] r. ω .sin ω.t
V= ṙ= - r. ω .sin ω.t[1+ a/(√1-r2.cos2 ω.t /b2)]
a = ȑ=- r. ω2 (sinω.t.cosω.t+ cosω.t)
this is cinematic analysis of motion and rotation .
for mechanical analysis ,first suppose any spherical body .We have three cases :
1)The central force causes all dynamic movements
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
2) There is further forces effecting on movement
3)The object has inertia of some first or secondary effected forces
We see that the rotation period of rotation of planets don’t vary by time or by placement ,for
example the earth has accurate amount of rotation ,and mars is so, then we result that the second
case is not thru .
So we have to find any inertia or whole effect of central force .
With solving the problem by difference between gravity forces effecting on near and farther part
of planet which can produce angular momentum ,we cannot got the result of observational data.
This can be solved with an absolute way ,that we find the period of rotation of planet with mass
“m”, density “ ρ “ ,radius “r”and distance R.
Then we compare thus results with what we are seeing and judge ,whether it is equal or varies ,in
second case we will search behind secondary and abnormal facts .
Tthe gravity force pulls the center of mass of thus body ,for dynamical equilibrium of body we
have :
∑Fi=m∑ai + ∑I.ω/r.t
Figure3. planet rotation mechanism
4.Whole system's galactic rotation
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
A hanging ball tided to roof acts as weightless body , when we want to rotate it ,its inertia resist
against our force ,based on general relativity principal ,the objects free falling in gravity field ,or in
their orbital are weightless , where there be any external force causing planet’s sidereal rotation ,we
simply can find dynamic equation for this force and dynamic of planet .
The main discussion in this field of study is the conservative force and potential , even due the
earth and other planets and moons are rotating continues without variety for considerable period of
time. Too any retrograde rotating body is resisting normal rotating direction creating at least
synchronies mode . Whole system has any galactic rotation that any retrograde rotating object
doesn’t obey that . As it is shown in figure 2. The angular rotating vector for tidal locked object
obeys gravity field force , then we might be able to divide gravity field to some parts same as Roche
limit , synchronies rotating area and normal , and fast rotating area, but the planet mass and radius is
important , that heavy planets have great forces , then the planet’s radius is a factor effecting
directly on momentum of inertia ,the factor which can give good relation between them is density
(mass over volume )
F=G.mM/d2
I=0.4m.r2
ρ = 3m/4.π.r3
Iω= 0.4 π . r2 .ρ .v = 0.5 π ρ√GM.r3
Young Venus might had normal rotation ,this gives the planet day near 15 earth days or
360hours ,and we can suppose first Venus was rotating counter clock wise ,for the reason of our
secondary found resulted effects ,such as changing of spin simply by condensed atmosphere
.although the height of atmosphere is as apple skin ,but the continues blowing of solar wind and
tiding with sun gravity had break effect for planet rotation .
Specially by calculating planets normal day from some ways(comparing with Jupiter moons and
Saturn moons ,other solar system members ) we found that planet might had one period at between
15days to 22.6days .
Figure4.hanging ball
Synchronies rotation velocity vector = v2-v1=v1√2(1-cosϴ)= v1√2(1-cosωt)
V1=√2GM/r
Synchronies rotation velocity vector = v2-v1=2√GM (1-cosωt) /r
Ω=ω p=2πrp/T
For finding any general relation which gives rotation period , direction and amount we have these
observational facts :
1) Nearest objects have slow rotation
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
2)
3)
4)
Massive objects have fast rotation
Rotation comes from dynamic of system ,formation process and secondary events
Rotational spin for continues and stable absolute system might be regular
5.Dense atmosphere against solar wind
As we said the atmosphere of planet is same to dock as shown in figure2. The continues blowing
of high speed solar wind ,and pulling of particles by planet gravity field causes new condition
.Suppose that the gravity field creates only synchronies rotation as we had above , the vector of
force which cause rotation of body is tangent to equator placed on latitudinal borders .We see
reverse case of such effect in Coriolis effect .The Coriolis effect of planet on an object is:
Figure5.solar wind effecting on Venus
In non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis
acceleration of the object is proportional to the velocity of the object and also to the sinus of the
angle between the direction of movement of the object and the axis of rotation.
The vector formula for the magnitude and direction the Coriolis acceleration is
where (here and below) v is the velocity of the particle in the rotating system, and Ω is the angular
velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of
rotation of the rotating reference frame, and the × symbol represents the cross product operator.
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
Figure 6. Forecasting movement and direction of solar wind
Table3.the tangent angle between planet’s position vector and solar wind blowing direction
Planet
distance from sun
AU
angle of solar wind vector
Radian
direction of impact
with planet
---------------------------------------------------------------------------------------------------------------Mercury
0.4
π/10
clock wise
Venues
0.7
π/6
clock wise
Earth
1
π/4
clock wise
Mars
1.56
2 π/ 5
clock wise
Jupiter
5
5π/4
clock wise
Saturn
10
2.5π
surrounding
Uranus
19
5π
surrounding
Neptune
30
7.5π
surrounding
Analytical mechanics calculations for finding reasons of opposite and slow rotation of Venus
6. References
1- Sagan, C.; Mullen, G. (1972). "Earth and Mars: Evolution of Atmospheres and Surface Temperatures".
Science 177 (4043): 52–56.
2.A.Mohammadzade “An introduction to studies of the effect of solar wind and CNO cycle on the
retrograde rotation of Venus” ,the general science journal 4029.
3.A.Mohammadzade “A case study on the effect of the solar wind and solar CNO cycle on the
formation of Jovian planets and comets”, the general science journal 4000.
4)Marc A. Murison “An Introduction to Gravity in the Solar System”
U.S. Naval Observatory, Washington, DC [email protected] 25 October, 200
5)Grant R. Fowles &George L. Cassiday “Analytical Mechanics “Brooks Cole. 7 edition
6) Meyer-Vernet, Nicole (2007). Basics of the Solar Winds. Cambridge University Press.
ISBN 0521814200.
7) Rudolf, Trumann &Wolfgang Baumjohann “basic space plasma physics”world scientific
publishing 1996