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I 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 kind of ignore the 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)

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)

I 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 kind of ignore the 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 of you want an idea of what happen)

I 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 kind of ignore the 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)

I currently writing a code to generate solar system and N number of plantets/moons.

I use real data to test (earth/sun/moon datas).

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 kind of ignore the earth:

at start x,y:
-sun : 0,0
-earth : 1.4959826e8
-moon : 1.4959826e8-384400;

using F = (G * a.mass * b.mass) / (dist * dist)

at start F :
-sun & earth : 3.5855635298968626E22
-earth & moon : 1.9817101152925866E20
-moon & sun: 4.379973928784021E20

since i placed them on y=0 , moon have an fy of 0 and fx of -2.39826381349143456E17 (because she'es placed between sun and earth

at start the moon have a velocity of 0.001022 km/sec

after  velocity update ( v = v + dt * F / mass)
v = 0.28200845732138924 
vx = -0.28200660544886147 
vy = 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 of you want an idea of what happen :video)

I 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 kind of ignore the 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 of you want an idea of what happen)