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 due to Newton's law of universal gravitation. 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 that light travels in a light year.

The following relationships are encoded in the Bully Mnemonic Extension:

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

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

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

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

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

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:

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

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

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:

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

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

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

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

Speed of Light

Step 3

Multiply integers av2) and b) from Step 2.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\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 2s and 3s, and swap 1s with 9s 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. <math display="block"> {\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 == Great Years == === 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: <math display="block">{\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