DISCUSSION OF LARSON’S
GRAVITATIONAL 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.²    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).