How it works

To get accelaration i used a = G*[Mass of object B] / R*R Also used Verlet Integration for better accuracy.

note

Object B is the object to which object A gravitate(as comparison Earth is B and moon is A)

    float dx0 = BX - ax_pos;
    float dy0 = BY - ay_pos;
    float R0 = SDL_sqrtf(dx0 * dx0 + dy0 * dy0);

    float a0x = 0, a0y = 0;
    if (R0 > 1.0f)
    {
        float a0 = G * MB / (R0 * R0);
        a0x = a0 * dx0 / R0;
        a0y = a0 * dy0 / R0;
    }

    ax_pos += vx * dt + 0.5f * a0x * dt * dt;
    ay_pos += vy * dt + 0.5f * a0y * dt * dt;


    float dx1 = BX - ax_pos;
    float dy1 = BY - ay_pos;
    float R1 = SDL_sqrtf(dx1 * dx1 + dy1 * dy1);

    float a1x = 0, a1y = 0;
    if (R1 > 1.0f)
    {
        float a1 = G * MB / (R1 * R1);
        a1x = a1 * dx1 / R1;
        a1y = a1 * dy1 / R1;
    }

    vx += 0.5f * (a0x + a1x) * dt;
    vy += 0.5f * (a0y + a1y) * dt;

Visualization was created in SDL3