Physical constants and physical units

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Astronomical Unit

1 AE = 149,598,000 km
(Kuchling)

149,597,870,691 m
(Wikipedia in German)

Average distance of the Earth from the Sun.

this are about 8 light minutes


Classical radius of an electron

The formula of r0 uses cgs units
m0c2 is the rest mass of an electron
Relation to SI-Units:
e2 = eel2/(40)
with eel : electric charge of an electron
e2/r0 is an energy 


Coulomb-Potential in SI Units

Q is the electrostatic charge
is the electrostatic potential in the distance r of the charge, for an electron Q = eel

Q is assumed to be a charge localized at one point in space


Potential energy of the charge q at distance r from Q

for q = Q = e


Einsteins field equations

G ist the Newtonian constant of Gravitiy (see below).


Elemental charge

e = 1.60217733 * 10-19 C
(Kuchling) - 1991 -

positive: charge of a Proton 

negative: charge of an Electron

1.602 176 53(14) · 10-19 C
(Wikipedia in German) - 2006 -


Masses

Mass of the Earth

ME 6 * 1027 g


Mass of the Sun

MS 2 * 1033 g


Rest mass of the Electron

9.109 382 6(16) · 10-31 kg (Wikipedia in German)


Newtonian constant of gravity

G = 6.673 * 10-11 (Nm2)/(kg2)

(2G)/c2 = 0.148 * 10-26 (Ns2)/kg2

Usage: Newtonian law of gravity
Einstein field equations
Planck units
Schwarzschild radius


Newtonian law of gravity


M, m : masses with a spherical distribution, 
r: distance between the centers of the masses


Pi

approximate: 3.141592654


Planck length

G: Newtonian constant of Gravity 
c: velocity of light in the empty space


Planck time

The Planck length divided by the Planck time results in the velocity of light constant c


Planck Mass


Planck Constant

h = 6.6260755 * 10-34 Js

h = * 2 = 2f,
E = h * f  , f : frequency

Energy, Impulse
(1  , 
Relation of uncertainty
(2) x * /2
(3)E * /2

hquer = (mp * lp2) / tp
h = 2 * pi * hquer

The dimension of << h>>  is the dimension of  << energy * time >>,
an << effect >>, or the << quantum of action >>

Consider the angular momentum
$\vec{L}=\vec{r} \times \vec{p}$

It has the same dimension like h.


Schwarzschildradius

MSR = M * 2G/c2
M : Mass

...Relation to the Planck Units


Velocity of light in the empty space

c = 2.99792458 * 108 m/s
about 300,000 km/s

c2 = 1/(0 0)
=3.14159265...

0 = 4 * 10-7(Vs)/(Am)
0 = 8.854187817 * 10-12
    (As)/(Vm)


Light related units of distances

1light second is a distance of 299,792,458 km

1 ligh minute is about 18,000,000 km

8 light minutes are about 144,000,000 km

1 light year (Lj) = 0.3066 pc(Parsec) (Wikipedia in German)

1 light year = 9.4605 * 1015 m

1 pc = 3.0857 * 1016 m  (Kuchling)
=> 1 pc = 3.262 Lj