I'm currently writing a code to generate solar system and $N$ number of planets / moons.
I use real data to test (earth / sun / moon data).
I succeeded in placing the earth and make it orbit around the sun using the correct mass and velocity. But when I place the moon around the earth and launch the simulation, the moon is a kind of ignoring Earth.
At start $(x,y)$:
Sun : 0,0
Earth : 1.4959826e8
Moon : 1.4959826e8-384400
using $F = (G \times a.mass \times b.mass) / (dist \times dist)$
At start $F$:
Sun & Earth: 3.5855635298968626E22
Earth & moon : 1.9817101152925866E20
Moon & Sun: 4.379973928784021E20
Since I placed them on $y=0$, moon has an $f_y$ of $0$ and $f_x$ of -2.39826381349143456E17 (because she's placed between sun and earth
At start, the moon has a velocity of 0.001022 km/sec
After velocity update ($v = v + dt \times F / mass$)
$v =$ 0.28200845732138924
$v_x =$ -0.28200660544886147
$v_y =$ 0.001022
So regarding the result, it make sense that the moon is attracted more by the sun than the earth (since vx is negative), but why? Where in my formulas I make a mistake ? I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth
(I surely forgot to put some info, don't hesitate to tell me to add things , I'm not really used to ask physics questions)
(Here's a video if you want an idea of what happen)