api di google analytics

salve sto implementando le api di google analytics sul mio pannello di controllo:

codice PHP:

require_once("../include/db.php"); 
$QuerySts=mysql_query("SELECT * FROM statics") or die (mysql_error()); 
$ga_email=mysql_result($QuerySts,0,1); 
$ga_password=mysql_result($QuerySts,0,2); 
$ga_profile_id=mysql_result($QuerySts,0,3); 
mysql_free_result($QuerySts); 

//estrai-dati.php 
define('ga_email','$ga_email'); 
define('ga_password','$ga_password'); 
define('ga_profile_id','$ga_profile_id'); //solo numeri! 
  
require("../gapi.class.php"); 
  
$ga = new gapi(ga_email,ga_password); //accesso 

//una sorta di "query" 
$ga->requestAccountData(); 
  
//per ogni risultato scrivi il profilo attivo sull'account 
foreach($ga->getResults() as $result) 
{ 
  echo $result . ' (' . $result->getProfileId() . ")<br />"; 
} 

ma mi da questo errore:
Fatal error: Uncaught exception 'Exception' with message 'GAPI: Failed to authenticate user. Error: "Request failed, fopen provides no further information"' in D:\SITI WEB\lavori\audit\gapi.class.php:418 Stack trace: #0 D:\SITI WEB\lavori\audit\gapi.class.php(62): gapi->authenticateUser('$ga_email', '$ga_password') #1 D:\SITI WEB\lavori\audit\statics\HelloAnalyticsApi.php(17) : gapi->__construct('$ga_email', '$ga_password') #2 {main} thrown in D:\SITI WEB\lavori\audit\gapi.class.php on line 418