The Bully Mnemonic & Calendar Variations

Julian Years & Gregorian Years

Initial Calculations

The Bully Mnemonic reminds us that there are approximately 31556928 seconds in a tropical year:

$$1\,Tropical\,Year\approx ({\color {Red}1}0{\color {Red}33}0-0.{\color {Red}4}0)\times {\color {Red}3}0{\color {Red}55}\,sec=31556928\,sec$$

There are 86400 seconds in a day:

$${1\,Day}={24\,hours\times {\frac {60\,minutes}{1\,hour}}\times {\frac {60\,seconds}{1\,minute}}}=86400\,seconds$$

The number of seconds in 365 days is:

$${365\,Day}={365\times 86400\,seconds}=31536000\,seconds$$

which is 24.222% of a day less than a full tropical year:

$${\frac {31536000-31556928}{86400}}={365\times 86400\,seconds}=31536000\,seconds$$

The number of seconds in 366 days is:

$${366\,Day}={366\times 86400\,seconds}=31622400\,seconds$$