In that case you should upgrade to 5.3.
But you can find out yourself as well. Just start by checking what day of week the 1st of January is. Then add the appropriate number of days to get to the first tuesday.
$wd = date('w', mktime(0, 0, 0, 1, 1, 2013));
# days to add to get to tuesday (2nd day of the week)
$day_of_week = 2; # tuesday
$days = 2 - $wd;
if ($days < 0)
$days += 7;
$date = date('Y-m-d', mktime(0, 0, 0, 1, 1 + $days, 2013));
echo $date;