Bully Mnemonic Extension

The Bully Mnemonic Extension is a technique for remembering the exact number of meters that light travels in one second, and the approximate range of gravitational accelerations that occur on the surface of the Earth. Using the Bully Mnemonic and Bully Mnemonic Extension in conjunction allows one to calculate a significant number of physical quantities, including the exact number of meters in a light year.

The following relationships are encoded in the Bully Mnemonic Extension:

$$Speed\,of\,light\,in\,vacuum={299,792,458\,meters\,per\,second}$$

$${High\,end\,of\,g_{Earth}}={9.8624\,meters\,per\,second^{2}}$$

$${Low\,end\,of\,g_{Earth}}={9.7644\,meters\,per\,second^{2}}$$

The following relationship can be derived using the Bully Mnemonic Extension in conjunction with Bully Mnemonic:

$$1\,light\,year={9,460,528,412,464,108\,meters}$$

Bully Mnemonic Extension Steps

Initial Definitions

Step 1

Complete steps 1 and 2 of the The Bully Mnemonic to form integers a) and b) as shown below:

$${\begin{matrix}{\color {Red}1}&\scriptstyle {\text{2}}&{\color {Red}3}&\scriptstyle {\text{4}}&{\color {Red}5}\end{matrix}}$$

$$a)\,{\color {Red}1}0{\color {Red}33}0$$

$$b)\,{\color {Red}3}0{\color {Red}55}$$

Step 2

The Bully Mnemonic Extension will use two variants of integer a). The first variant will have 33 removed and replaced with 00. The second variant will have 330 removed and replaced with 22:

$$av1)\,{\color {Red}1}0000$$

$$av2)\,{\color {Red}1}0{\color {Red}22}$$

$$b)\,{\color {Red}3}0{\color {Red}55}$$

Speed of Light

Step 3

Multiply integers av2) and b) from Step 2.

$${\color {Red}1}0{\color {Red}22}\times {\color {Red}3}0{\color {Red}55}=3122210$$

Using Long Multiplication:

     3055
×    1022
————————————
     6110
    6110
   0000
  3055
————————————
  3122210

Step 4

Drop the zero from the integer obtained in step 3, swap each 2 with 3, and swap each 1 with 9, to obtain integer f) shown below:

   312221
f) 293339

Step 5

Multiply integer av2) from Step 2, and integer f) from step 4, to get the total number of meters that light travels in one second.

$${\color {Red}1}0{\color {Red}22}\times 293339=299792458$$

Using Long Multiplication:

         1022
×      293339
——————————————
        9198
       3066
      3066
     3066
    9198
   2044
——————————————
   299792458

Gravity on Earth

Step 6

The Great Year is, by definition, a least common multiple of the sidereal year and the tropical year. From steps 4 and 5 above, we have that the ratio of tropical years to sidereal years is:

$${\frac {1\,Tropical\,Year}{1\,Sidereal\,Year}}\approx {\frac {(10330-0.40)\times 3055\,sec}{10330\times 3055\,sec}}$$

Divide top and bottom by amount d) and use the Distributive Property of Multiplication to obtain:

$${\frac {1\,Tropical\,Year}{1\,Sidereal\,Year}}\approx {\frac {({\frac {10330}{0.40}}-{\frac {0.40}{0.40}})\times 3055\,sec}{({\frac {10330}{0.40}})\times 3055\,sec}}$$

From whence:

$${\frac {1\,Tropical\,Year}{1\,Sidereal\,Year}}\approx {\frac {(25825-1)\times 3055\,sec}{(25825)\times 3055\,sec}}$$

Consequently:

$${\frac {25825\,Tropical\,Year}{25824\,Sidereal\,Year}}\approx {\frac {25825\times (25824)\times 3055\,sec}{25824\times (25825)\times 3055\,sec}}=1$$

Finally:

$$1\,Great\,Year\approx 25825\,Tropical\,Years\approx 25824\,Sidereal\,Years$$

In terms of Long Multiplication; 0.40, 25825, and 10330 are related as follows:

       0.40
×  25825
————————————
       2.00
      08.0
     320
    200
   080
————————————
   10330.00

Galactic Years

Step 7

Multiply integer c) by the square of integer a) to get a rough approximate galactic year (the number of tropical years required for the Solar System to orbit once around the galactic center).

$${\color {Red}2}\times {{\color {Red}1}0{\color {Red}33}0}^{2}=213417800\approx {\frac {1\,Galactic\,Year}{1\,Tropical\,Year}}$$

Using Long Multiplication:

       10330
×      10330
——————————————
       00000
      30990
     30990
    00000
   10330
——————————————
   106708900

And finally:

106708900 × 2 = 213417800