So I was in the shower today...

[Agamemnus]

In other news, I made an approximation of the gravity using my formulas and the result shows gravity first increasing and then sharply decreasing as the point of measurement reaches a depth at the center of the earth.

Code:

defint A-Z
screen 9
DIM C as double, F1 as double, F2 as double, intF1 as double, intF2 as double, F as double
DIM bigR as double, r as double, x as double
dim g as double, pi as double


G = 6.67300 * 10^-11 'm^3 kg^-1 s^-2
pi = 3.14159265
r = 63.78 'hundreds of kilometers
m1 = 5.98 * 10^24 'kg
C = G*pi*r*m1
'C = 10: r = 1000

for n = 0 to r

F1 = 0: for x = 0 to n
bigR = (r^2 - x^2)^.5
if bigR <> 0 then
intF1 = 0
for b = 0 to bigR
if n^2+b^2 <> 0 then
intF1 = intF1 + b/(n^2+b^2)
end if
F1 = F1 + intF1
next b
end if
next x

F2 = 0: for x = 0 to 2*r-n
bigR = (r^2 - x^2)^.5
if bigR <> 0 then
intF2 = 0
for b = 0 to bigR
if (2*r-n)^2+b^2 <> 0 then
intF2 = intF2 + b/((2*r-n)^2+b^2)
end if
F2 = F2 + intF2
next b
end if
next x
F = F1 - F2

if n > 1 then
'print F2;F;F1
'line ((n-1)*2+50, 300-log(abs(lastF))*10)-(n*2+50, 300-log(abs(F))*10), 15
line ((n-1)*2+50, 300-abs(lastF)/5)-(n*2+50, 300-abs(F)/5), 1
line ((n-1)*2+50, 300-abs(lastF1)/5)-(n*2+50, 300-abs(F1)/5), 2
line ((n-1)*2+50, 300-abs(lastF2)/5)-(n*2+50, 300-abs(F2)/5), 4
line ((n-1)*2+50, 300)-(n*2+50, 300), 15
end if
lastF2 = F2
lastF1 = F1
lastF = F
next n
'print abs(F)

sleep
system