how to draw a helix in 3d using fragment shader (shadertoy)

Question

I am relatily new to GLSL. I want to create a solar system model and use it as a wallpaper (using shadertoy) (Something like this and while i have the planets moving correctly i cant figure out how to do the helix paths that follow those planets.

Here is my code so far

uniform vec2 iResolution;
uniform float iTime;

#define pi 3.141592653589

float circ(vec2 uv, vec2 pos, float rad, float blur) {
    return smoothstep(blur, 0., length(-uv + pos)-rad); //draws a circle to the screen
}

float line(vec2 uv, vec3 start, vec3 end, float width) {
    vec2 p = uv - start.xy;
    vec2 d = end.xy - start.xy;
    float l = length(d);
    d = normalize(d); //direction
    float t = clamp(dot(p, d), 0., l);
    return (length(p - d*t)) < width ? 1 : 0.;
}

float helix(vec2 uv, vec3 start, vec3 direction, float width, float length, float angle) {
    float delta = iTime / angle;
    vec2 p = uv - start.xy;
    vec2 d = (normalize(direction) * length).xy;
    float l = length(d);
    d /= l;
    float t = clamp(dot(p, d), 0., l);
    return (length(p - d*t)) < width ? 1 : 0.;
}

vec3 rotate(vec3 point, vec3 angle) {
    mat3 rot = mat3(
    cos(angle.y)*cos(angle.z), cos(angle.z)*sin(angle.x)*sin(angle.y)-cos(angle.x)*sin(angle.z), cos(angle.x)*cos(angle.z)*sin(angle.y)+sin(angle.x)*sin(angle.z),
    cos(angle.y)*sin(angle.z), cos(angle.x)*cos(angle.z)+sin(angle.x)*sin(angle.y)*sin(angle.z), -cos(angle.z)*sin(angle.x)+cos(angle.x)*sin(angle.y)*sin(angle.z),
    -sin(angle.y), cos(angle.y)*sin(angle.x), cos(angle.x)*cos(angle.y));
    return rot * point;
}

void main() {
    vec2 uv = fragCoord / iResolution.xy;
    float ratio = iResolution.x / iResolution.y;
    uv -= .5; //center origin
    uv.x = uv.x * ratio;//make screen square
    uv /= .3;//zoom

    float planetA[5] = float[](0., iTime / 0.241, iTime / 0.6152, iTime, iTime / 1.8809);

    vec3 planets[5] = vec3[](
    vec3(0.), // sun
    vec3(cos(planetA[1]) * .4, sin(planetA[1]) * .4, 0.), // mercury
    vec3(cos(planetA[2]) * .7, sin(planetA[2]) * .7, 0.), // venus
    vec3(cos(planetA[3]), sin(planetA[3]), 0.), // earth
    vec3(cos(planetA[4])*1.5, sin(planetA[4])*1.5, 0.)// mars
    );
    vec3 planetsC[5] = vec3[](
    vec3(0.89, 0.9, 0.45), // sun
    vec3(0.54, 0.57, 0.63), // mercury
    vec3(0.9, 0.5, 0.2), // venus
    vec3(0.2, 0.3, 0.8), // earth
    vec3(0.8, 0.3, 0.2)// mars
    );

    vec3 rotVec = vec3(-pi/4, pi/4, 0.);

    fragColor = vec4(0.);
    
    fragColor = mix(fragColor, vec4(1.), line(uv, vec3(0.), rotate(vec3(0., 0., 2.), rotVec), 0.01)); //sun  trail

    for (int i = 1; i < planets.length(); i++) {
        planets[i] = rotate(planets[i], vec3(-pi/4., pi/4., 0.)); //rotate the planet
        fragColor = mix(fragColor, vec4(planetsC[i], 1.), helix(uv, planets[i], rotate(vec3(0., 0., 2.), rotVec), 0.01, 2., planetA[i])); //planet trail
            }
    for (int i = 0; i < planets.length(); i++) { //draws the planets
        fragColor = mix(fragColor, vec4(planetsC[i], 1.), circ(uv, planets[i].xy, 0.05, 0.01));
    }
}

the helix function is currently only a modified version of the line method but i want it to curve around the suns trail. Any advice and/or help would be appreciated as i am still learing.

I have tried to convert the helix equation: x = r * cos(t) y = r * sin(t) z = t but havent gotten it to work

heres the method currently, although it only displays a straigt line:

float helix(vec2 uv, vec3 start, vec3 direction, float width, float length, float angle) {
    float delta = iTime / angle;
    vec2 p = uv - start.xy;
    vec2 d = (normalize(direction) * length).xy;
    float l = length(d);
    d /= l;
    float t = clamp(dot(p, d), 0., l);
    return (length(p - d*t)) < width ? 1 : 0.;
}

how to draw a helix in 3d using fragment shader (shadertoy)

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