# Physical constants and physical units

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**Table of contents**

Reference: Wikipedia in English

## List of items

### 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 *r*_{0}
uses **cgs units**

*m*_{0}c^{2} is the rest mass of an
electron

**Relation to SI-Units:**

*e*^{2} = e_{el}^{2}/(4_{0}),

with *e*_{el} : electric charge of an
electron

*e*^{2}/r_{0} 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 = e_{el}

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

M_{E} 6 * 10^{27} g

Mass of the Sun

M_{S} 2 * 10^{33} 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} (Nm^{2})/(kg^{2})

(2G)/c^{2} = 0.148 * 10^{-26} (Ns^{2})/kg^{2}

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**, * = 2*f,*

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

**Energy, Impulse**

(1) ,

**Relation of uncertainty**

(2) x * p /2

(3)E * t /2

h_{quer} = (m_{p} * l_{p}^{2}) / t_{p}

h = 2 * pi * h_{quer}

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

M_{SR} = M * 2G/c^{2} ,

M : Mass

**...Relation to the Planck Unit**s

### Velocity of light in the empty space

c = 2.99792458 * 10^{8} m/s

about 300,000 km/s

c^{2} = 1/(_{0
0})

=3.14159265...

_{0} = 4
* 10^{-7}(Vs)/(Am)

_{0} = 8.854187817 * 10^{-12}

(As)/(Vm)

#### Light related units of distances

1**light 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 * 10^{15} m

1 pc = 3.0857 * 10^{16} m (**Kuchling**)

=> 1 pc = 3.262 Lj