Bully Metric

There are a surprising number of earth's physical constants that can be approximated using various algebraic combinations of the following four numbers [The Bully Mnemonic|(click here to learn more)]:

10330
3055
2
0.40 

Included among these are the exact (eight digits) number of seconds that occur in Earth's sidereal year:

$${1\,Sidereal\,Year}={\color {Red}1}0{\color {Red}33}0\times {\color {Red}3}0{\color {Red}55}\,s={31,558,150\,s}$$

The exact (eight digits) number of seconds that occur in Earth's sidereal year:

A few additional approximations (four digits) can be obtained from values used in the Bully Mnemonic. These include an approximate relationship of the speed of light to the Earth's radius (r ≈ 6371), Schwarzschild radius (R), standard gravitational parameter (μ = MG ≈ 3.984e14), and a typical gravitational acceleration on earth's surface (g ≈ 9.813 ).

$${1\,Tropical\,Year}=(({\color {Red}1}0{\color {Red}33}0-0.{\color {Red}4}0)\times {\color {Red}3}0{\color {Red}55}\,s)-{\color {Red}2}=31,556,926\,s$$

$$r_{earth}\approx {10^{-3}}\times c\times {\frac {{\color {Red}3}0{\color {Red}55}\,s}{\sqrt {{\color {Red}2}\times {{\color {Red}1}0{\color {Red}33}0}}}}=6371\,km$$

$$R_{earth}={\frac {2\times GM_{earth}}{c^{2}}}\approx {10^{-10}}\times c\times {\frac {{\color {Red}3}0{\color {Red}55}\,s}{{\color {Red}1}0{\color {Red}33}0}}\approx {8.866\,mm}$$

$${\mu }_{earth}=GM_{earth}\approx {10^{-10}}\times c^{3}\times {\frac {{\color {Red}3}0{\color {Red}55}\,s}{{\color {Red}2}\times {{\color {Red}1}0{\color {Red}33}0}}}\approx {398,400,000,000,000\,{\frac {m^{3}}{s^{2}}}}$$

$$g_{earth}={\frac {{\mu }_{earth}}{{r_{earth}}^{2}}}\approx {10^{-4}}\times c\times {\frac {1}{{\color {Red}3}0{\color {Red}55}\,s}}\approx {9.813\,{\frac {m}{s^{2}}}}$$

Prefix		Base 10	Bully Metric		SI Equivalent
Name	Symbol		Time	Length	Time	Length
quetta	Q	1030	Qta	Qla	30.550 Es	9.1586595919 Rm
ronna	R	1027	Rta	Rla	30.550 Ps	9.1586595919 Ym
yotta	Y	1024	Yta	Yla	30.550 Ts	9.1586595919 Zm
zetta	Z	1021	Zta	Zla	30.550 Gs	9.1586595919 Em
exa	E	1018	Eta	Ela	30.550 Ms	9.1586595919 Pm
peta	P	1015	Pta	Pla	30.550 ks	9.1586595919 Tm
tera	T	1012	Tta	Tla	30.550 s	9.1586595919 Gm
giga	G	109	Gta	Gla	30.550 ms	9.1586595919 Mm
mega	M	106	Mta	Mla	30.550 μs	9.1586595919 km
kilo	k	103	kta	kla	30.550 ns	9.1586595919 m
—	—	100	ta	la	30.550 ps	9.1586595919 mm
milli	m	10−3	mta	mla	30.550 fs	9.1586595919 μm
micro	μ	10−6	μta	μla	30.550 as	9.1586595919 nm
nano	n	10−9	nta	nla	30.550 zs	9.1586595919 pm
pico	p	10−12	pta	pla	30.550 ys	9.1586595919 fm
femto	f	10−15	fta	fla	30.550 rs	9.1586595919 am
atto	a	10−18	ata	ala	30.550 qs	9.1586595919 zm
zepto	z	10−21	zta	zla	3.0550e-3 qs	9.1586595919 ym
yocto	y	10−24	yta	yla	3.0550e-6 qs	9.1586595919 rm
ronto	r	10−27	rta	rla	30.550e-9 qs	9.1586595919 qm
quecto	q	10−30	qta	qla	30.550e-12 qs	9.1586595919e-3 qm