Gravitational potential using spherical harmonics (WGS84)

[ryan88]

Hi,

I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following:

V = \frac{GM}{r}\left [ 1 + \sum_{n=2}^{n_{max}} \sum_{m=0}^{n} \left( \frac{a}{r} \right )^n \bar{P}_{nm} \left( \sin{\phi} \right ) \left( \bar{C}_{nm} \cos{m\lambda} + \bar{S}_{nm} \sin{m\lambda} \right ) \right ]

where:

V is the gravitational potential function
GM is the Earth's gravitational constant
r is the distance from the Earth's centre of mass
a is the semi-major axis of the WGS84 ellipsoid
n,m are the degree and order respectively
\phi is the geocentric latitude
\lambda is the longitude
\bar{C}_{nm},\bar{S}_{nm} are normalised gravitational coefficients

\bar{P}_{nm}\left( \sin \phi \right) = \left[ \frac{(n-m)!(2n+1)k}{(n+m)!} \right] P_{nm}(\sin\phi)

P_{nm}(\sin\phi) = (\cos\phi)^m \frac{d^m}{d(\sin\phi)^m}[P_n(\sin\phi)]

P_n(\sin\phi) = \frac{1}{2^n n!} \frac{d^n}{d(\sin\phi)^n}\left( \sin^2\phi -1 \right )^n

m=0,k=1
m\ne0,k=2

However, I can't find what the definition of d is. Can anyone offer any help?

Thanks,

Ryan

 

[nasu]

It means derivative. As in d/dt, d^2/dt^2, etc

 

[ryan88]

Ah right, now I feel stupid, lol.

Thanks for that,

Ryan