GravitationalAcceleration

from pylab import *
from numpy import *

Me = 5.98E+24 # KG
G = 6.67E-11  # KG^2/(MS^2)
Re = 6378137  # M
Rp = 6356752 # M

DEG = pi/180
lat = arange(-90, 91, 1) * DEG
alt = arange(0, 100 * 1000, 100) # meters

r = sqrt(((Re ** 2 * cos(lat)) ** 2 + ((Rp ** 2 * sin(lat)) ** 2))/
         ((Re * cos(lat)) ** 2 + ((Rp * sin(lat)) ** 2)))

d = r[newaxis,:] + alt[:,newaxis]
g = (G * Me)/d**2


pcolormesh(lat / DEG, alt/1000., g)
colorbar()
title(r'Gravitational Acceleration [$\frac{m}{s^2}$]')
xlabel('Latidude [deg]')
ylabel('Altitude [km]')
show()