Failing to calculate earth's standard gravitational parameter

Question

I am using this equations from Wikipedia:

$$\frac{4\pi^2 a^3}{T^2}=\mu$$

Where:

$\mu$ = standard gravitational parameter ($\mbox{km}^3 \mbox{s}^{−2}$)

$a$ = the orbiting body's semimajor axis (AU)

$T$ = the orbital period (s)

For earth:

$a = 1$

$T = 31\; 556\; 926$

No matter what I do, I always get $3.964e-14$ as an answer while the answer should be $398600.4418$ according to Wikipedia. That is many decimal points off and not completely accurate.

Now my knwoledge of math is not incredible, but I know how to do simple equations like this. I must have made a mistake, but I cannot find what.

Answer 1

By using Earth's orbital parameters, you are calculating the sun's standard gravitational parameter. You need to use the orbital parameters for a satellite of Earth to get the value for Earth. You also need to keep the units consistent, so the radius should be in km. For the sun, it comes out close at $1.31E11$ For the Earth, I know GEO is $42164$km and $T=0.997\cdot 86400$ seconds, one sidereal day, giving $3.98811E5$ as it should