Got it working with a little help on the math from my professor! The two main changes were making j conditional so that the calculation runs only when j != i, and also i needed a sign change in front of the F calculation because subtracting vectors is weird.
from visual import *
myuniv = display(range=vector(7*10**12,7*10**12,7*10**12))
G = 6.674*10**-11 #Gravitational constant
#Masses of each solar body in order starting with the Sun
mass = [1.989*10**30,3.285*10**23, 4.867*10**24,
5.972*10**24, 6.39*10**23, 1.898*10**27,
5.68*10**26, 8.68*10**25, 1.024*10**26]
#Positions of each solar body starting with the Sun
posit = [vector(0,0,0),vector(5.791*10**10,0,0),vector(1.082*10**11,0,0),
vector(1.496*10**11,0,0),vector(2.279*10**11,0,0),vector(7.785*10**11,0,0),
vector(1.429*10**12,0,0),vector(2.871*10**12,0,0),vector(4.498*10**12,0,0)]
#Velocities of each solar body starting with the Sun
vel = [vector(0,0,0),vector(0,4.87*10**4,0),vector(0,3.502*10**4,0),
vector(0,2.98*10**4,0),vector(0,2.401*10**4,0),vector(0,1.307*10**4,0),
vector(0,9.69*10**3,0),vector(0,6.81*10**3,0),vector(0,5.43*10**3,0)]
#Acceleration of each solar body starting with the Sun
acc = [vector(0,0,0),vector(0,0,0),vector(0,0,0),
vector(0,0,0),vector(0,0,0),vector(0,0,0),
vector(0,0,0),vector(0,0,0),vector(0,0,0)]
Ssun = vector(0,0,0)
Msun = 1.989*10**30
t = 0.0
dt = 150000
sun = sphere(pos=posit[0],radius=9.9*10**10,color=color.yellow,make_trail=True)
mercury = sphere(pos=posit[1],radius=2.44*10**6,color=color.red,make_trail=True)
venus = sphere(pos=posit[2],radius=6.052*10**6,make_trail=True)
earth = sphere(pos=posit[3],radius=6.371*10**6,color=color.green,make_trail=True)
mars = sphere(pos=posit[4],radius=3.39*10**6,color=color.red,make_trail=True)
jupiter = sphere(pos=posit[5],radius=6.99*10**7,color=color.blue,make_trail=True)
saturn = sphere(pos=posit[6],radius=5.823*10**7,color=color.yellow,make_trail=True)
uranus = sphere(pos=posit[7],radius=2.536*10**7,color=color.cyan,make_trail=True)
neptune = sphere(pos=posit[8],radius=2.462*10**7,make_trail=True)
while True:
for i in range(0,9,1):
Fnet = vector(0,0,0)
for j in range(0,9,1):
if j != i:
rate(1000000)
t=t+dt
r = posit[i]-posit[j]
F = -((G*mass[j]*mass[i])/(mag(r)**2))* norm(r) #Calculating the force of gravity from object j over object i
Fnet = Fnet + F
acc[i]=Fnet/mass[i]
vel[i]+= acc[i]*dt
posit[i]+= vel[i]*dt
sun.pos=posit[0]
mercury.pos=posit[1]
venus.pos=posit[2]
earth.pos=posit[3]
mars.pos=posit[4]
jupiter.pos=posit[5]
saturn.pos=posit[6]
uranus.pos=posit[7]
neptune.pos=posit[8]
Thanks again for the help!