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The Copernicus Constant K

and Planetary System HR 8799

“ Looking for a simplest theory that is consistent with experimental data “

N. Copernicus . ( year 1543)

Applying the Copernicus Constant K to Planetary System HR 8799 we can

get many interesting results. The Λeff for HR 8799 is about 2/10^30 (/s^2).

Its effect is very very small to planetary system.

(Warsaw University, NCBJ, Le Sy Hoi )

(Email: lephnx@gmail.com)

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The Sun compared to the planets

The Copernicus constant K is dimensionless constant, which related

Hubble constant with G constant , temperature ,entropy and energy

of observable universe with fine structure constant , CMB and large

numbers of Paul Dirac .

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We have got it from the simple Einstein de Sitter model (at

critical mass) .

K = m planck * Ho*G/c^3

Ho = 67, 0022457 km/s(Mpc)

Ho = 2,171416509/10^18 s

(Ho is Hubble constant for expanding universe)

Applying the Copernicus Constant K to Planetary System HR8799 we can

get many interesting results. HR 8799 is a young main sequence star

(~30 million year old) located 129 light years (39 parsecs) away

from Earth in the constellation of Pegasus, with roughly 1.47 times

the Sun's mass and 4.9 times its luminosity. Applying our universal

formulas for planetary system to HR 8799 we would like to check

the validity of our theory.

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n*n = K^7/3 *Rn*G*M*m^2/(hn)^2 (1)

( Proverbs 3.19

The LORD by wisdom founded the earth;

by understanding he established the heavens;)

K = 11,70623761/10^62 dimensionless constant

K^7/3 = 6,703584904/ 10^143

Rn = radius of planetary orbits of planets e,d,c,b

G = Newton gravitational constant = 6,67384/10^11 (m^3/(kg*s^2))

M = mass of star HR8799 = 2,924*10^30 kg

m = mass of planets e,d,c,b

hn = reduced planck constant = 1,054571726/10^34 (js)

n = quantum number of planet n , accounts for their angular momentum

Tab 1 : Quantum numbers for Planetary System HR 8799 with old data

SYSTEM HR 8799

period speed R M n

year km/s AU earth quantum

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Planets

e (mercury) 45 9,596 14,5 2224,81 21223917

d 100 7,147 24 2224,81 27305314

c 190 5,956 38 2224,81 34358433

b 460 4,402 68 1589,15 32829780

Tab 2 : Quantum numbers for System HR 8799 with corrected data

Theory tells us that the data for R should be corrected as following

SYSTEM HR 8799

period speed R M n

year km/s AU earth quantum

Planets

e (mercury) 45 9,53 14,4 1906,98 18129090

d 100 7,267 24,5 2224,81 27588278

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c 190 5,909 37,7 2224,81 34222539

b 460 4,402 68 1589,15 32829780

We can get another formula for System HR 8799

Rn*vn^2 = r*v^2 (2)

2Rn = 2*N mercury/vn^2 (3)

Where planet e takes the role of Mercury in planetary system HR 8799.

( Bible, Psalms 19.1) ( Psalms 19.1

The heavens declare the glory of God,

and the sky above[a] proclaims his handiwork.)

Rn = orbital radius of planet n ( in AU )

( AU = 149 597 870 700 m ~~ 1,5*10^11 m )

Vn = orbital speed of planet n ( km/s)

N of mercury = r*v^2 ( r & v of mercury )

It seems,

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Up to now we have only the Titius Bode law for radius of planetary orbit.

It means radius of planetary orbit is independent of mass .

Now we understand the meaning of Mercury in our stable Solar System.

N quantum / n quantum of mercury = Rn*mn*Vn /(r*m*v)

is a conserved quantity

Vn*nq /mn = constant ( for circular orbits )

mn = mass of planet n

Vn = speed of planet n

nq = quantum number of planet n

The r*m*v belongs to e(Mercury) .

This formula is good for every planet n .The r*m*v belongs to e(Mercury) .

Fr = hs*(G*M)^2 *(m/(hn*nq))^3 (4)

Hs = 0,227763052*K^11/3 (5)

Fr = frequency of planet ( /s )

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G = Newton gravitation constant

M = mass of HR 8799 ( kg ) , m = planet mass ( kg)

Hn = reduced planck constant

Nq = quantum number of planet

K^11/3 = 8,38812455/ 10^224

Applications

Direct imaging of exoplanetary systems is a powerful technique that can

reveal Jupiter like planets in wide orbits /2/ . The observations show that the

HR 8799 system is similar to our Solar system and consistent with models of

planet formation in a disk.

Our formulas are applicable for all planetary system such as Pulsar

PSR1257+12 /1/ and exoplanetary systems HR 8799 …

These formulas can help us to correct some data on R of planetary

system.

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Up to now, our theory can give a lot of applications in micro world and

macro world, because the Copernicus Constant K is the connection between

Quantum Mechanics and General Relativity Theory.

The correction of Λeff in exoplanetary system

Our theory says that Dark Energy and Dark Matter come from the same

source : the curvature of spacetime at global and local levels because of

matter leads to the cosmological term Λ and Λeff /3/. The galaxy rotation

curve is the result of Λeff . We would like to consider the effect of Λeff

in small system like planetary system such as Solar System and HR8799

system.

We can take Λeff(r) = 132300 km^2/ r^2 (/s^2) for a typical galaxy /3/.

The distance r for Sun and HR 8799 is about 27000 light years from

galaxy center. It means Λeff for Solar system and HR 8799 is about

Λeff = 2 / 10^30 ( /s^2) (6)

The Newton potential for planetary system with correction of Λeff will be

v(r)^2 = 2*G*M’/r =2* G*M/r + Λeff*r^2 / 3 (7)

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Please remember the distance r is taken from star to planets.

We can see the second term (correction of Λeff ) is very very small for

planetary system.

ACKNOWLEDGEMENTS

The author Lê sỹ Hội would like to express his gratitude to Prof. (

Warsaw University ), Prof. ( NCBJ Polska ) and Prof. Trần Hữu Phát

for the helps with the work . The work is supported by Warsaw University,

NCBJ and Poland Government . The author also would like to thank the

International Centre for Theoretical Physics (ICTP) many friends and

family for helps . God bless us .

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References

/1/https://www.academia.edu/18601952/The_Copernicus_Constant_K_and_

Solar_System

/2/Christian Marois et al. “ Direct Imaging of Multiple Planets Orbiting the

Star HR 8799”, arXiv : astro-ph/0811.2606v1, Nov 2008.

/3/https://www.academia.edu/26882946/The_Copernicus_constant_K_and_

dark_energy_and_dark_matter.doc.pdf