The Bully Mnemonic is a technique for remembering the exact number of seconds that occur in Earth's sidereal year and tropical year, a good approximation of the Earth's Great Year, and a rough approximation of the Solar System's galactic year.
The following relationships are encoded in the Bully Mnemonic:
The second step is to select odd digits and intersperse them with zeros to form integers a) and b) as shown below:
(important to remember that the first integer ends with 33 followed by a 0, whereas the second integer ends with 55 with no trailing 0)
The tropical year has a slightly shorter duration than the sidereal year. The approximate number of seconds in a tropical year is obtained by reducing integer a) by amount d), and then multiplying by b).
The exact number of seconds in a tropical year is obtained by reducing integer a) by amount d), multiplying by b), and then reducing by c).
Using the Distributive Property of Multiplication:
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:
Divide top and bottom by amount d) and use the Distributive Property of Multiplication to obtain:
From whence:
Consequently:
Finally:
In terms of Long Multiplication; 0.40, 25825, and 10330 are related as follows:
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).