DISCUSSION OF LARSON’S
G
RAVITATIONAL EQUATION

As brought out at the recent convention, some confusion has arisen over Larson’s gravitational equation, eq. (2) of the original edition of the Structure of the Physical Universe:

F = mm‘/s²
(1)

The correct expanded version of this equation is

 
(m × 3.7115 x 10-32) × (m’ × 3.7115 x 10-32)
 
F =
—————————————————
(2)
 
1521 × 10-15 × (s/1)²
 

where 3.7115 x 10-32 sec³/cm³ is the value of the natural unit of mass and m and m’ are simply numbers. The number .1521 x 10-15 sec is the natural unit of time. From equation (2), the natural value of the gravitational constant can be determined:

Gn.u.= (3.7115 × 10-32)²/.1521 × 10-15 = 9.0567 x 10-48
(3)

Thus equation (1) might better be written as

Fn.u = 9.0567 × 10-48 mm’/s²
(4)

where all values are in natural units. The expression for G in equation (3) can be converted to conventional units. First, the cgs system:

  Fn.u.sn.u    dynes
Gcgs = 9.0567 ×10-48 ———— × 109.7 ——–
     mn.u²    Fn.u

  (.456 x 10-5 cm         mn.u²
× —————— × ——————
          sn.u² (.5565 x10-24 g

= 6.67 x 10-8 dynes cm²/g²
(5)

The MKS system

  Fn.usn.u²      N
GMKS = 9.0567 ×10-48 ———– 109.7 10-5 ——
    mn.u²    Fn.u

  (.456 × 10-7 m)²          mn.u²
× —————— × ———————
         sn.u² (.5565 × 10-27 kg)²

= 6.67 × 10-11 N-m²/kg²
(6)

Both check. The importance of this cannot be overestimated. These equations completely confirm Larson’s identification of all the fundamental units.

Note that if in equation (2), the value 3.7115 × 10-26 sec³/m³  

is used then the correct time value must be .1521 × 10-3 sec for the denominator (or 1012 units of time).