dt = .000001
t = 0
epsilon = .000001

low = 81000000.0
high = 84000000.0

while abs(t - 3.036) > epsilon:
  c = (low + high)/2
  a = 0
  x = 6.371*(10**6)
  v = 0
  t = 0

  while x < 3.831606*(10**8):
    v += a*dt
    x += v*dt
    a = c + (6.67*(10**(-11))*(7.34767309*(10**22)/(3.84898*(10**8)-x)**2 - 5.972*(10**24)/(x**2)))
    t += dt

  if t > 3.036:
    low = c
  elif t < 3.036:
    high = c
  
print c

#c = 81757141.1133