Arduino code for star tracking

StarTracking.ino

// Controls a threaded stepper motor to open levered board at same rate the earth spins
// for astrophotograph.

byte directionPin = 3;
byte stepPin = 2;
byte ledPin = 13;
float adjacent = 0.24;

float earth_rads_per_s = 0.00007272205;

float current_step = 0;
float min_step_size = 0.0001 ;
float stepsize = 0.00001 / 8;

float start_time;

int pulseWidthMicros = 50;  // microseconds
int microsbetweenSteps = 500; // milliseconds

float take_step_distance(float distance)
{
  float step_distance = 0;
  int steps = 0;
  
  while (step_distance < distance)
  {
    digitalWrite(stepPin, HIGH);
    delayMicroseconds(pulseWidthMicros);
    digitalWrite(stepPin, LOW); 
    delayMicroseconds(microsbetweenSteps);
    step_distance += stepsize;
    steps++;
    digitalWrite(ledPin, !digitalRead(ledPin));
  }
  return step_distance;
}

float earth_tracking_adjustment(float adjacent, float elapsed)
{
  float tan_ = sin(earth_rads_per_s * elapsed);
  return adjacent * tan_;
}

void setup() 
{ 
  Serial.begin(9600);
  Serial.println("Starting startracker");
  digitalWrite(ledPin, LOW);
  pinMode(directionPin, OUTPUT);
  pinMode(stepPin, OUTPUT);
  pinMode(ledPin, OUTPUT);
  start_time = millis();
    
  digitalWrite(directionPin, LOW);
  //take_step_distance(0.01);
}

void loop() 
{ 
  float elapsed = millis() - start_time;
  float total_step = earth_tracking_adjustment(adjacent, elapsed/1000);
  float step_required = total_step - current_step;
  if ( step_required >= min_step_size)
  {  
    current_step += take_step_distance(step_required);  
  }
  delay(1000);
}