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)
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The correct expanded version of this equation is
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(m × 3.7115 x 10-32) × (m’ × 3.7115 x 10-32)
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| F = |
—————————————————
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(2)
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1521 × 10-15 × (s/1)²
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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)
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Thus equation (1) might better be written as
| Fn.u = 9.0567 × 10-48 mm’/s² |
(4)
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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)
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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)
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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).