WordPress Query custom ordering by temporary variable

Update: The User has clarified the request in the comment to my answer, so i add some info above my original answer. The original answer is still valid 😉

To use external data for your “main” query, you can use the pre_get_posts hook.

Use it like this:

add_action('pre_get_posts','get_radius_instructors_for_my_posts');

function get_radius_instructors_for_my_posts($query){
    if($query->is_main_query() && !is_admin()){
        if($query->is_search()){
             //use your function to get the post ids that are in radius
             $post_ids = do_whatever_to_get_the_post_ids();
             $query->set('post__in',$post_ids);
             $query->set('orderby','post__in');
        }
    }
}

Do you mean that you use the Google Maps Geocoding Service to Geocode the instructors addresses on every pageload? That is not a wise thing to do because of two reasons:
1) Performance. If you have to geocode every address every search, that would very slow.
2) Cost. Googles APIs are only free below a specific use each month.

The better way would be to geocode the instructors addresses on Post Type Save, save the latitude and longitude in the database, and on searching for zip use the Geocoding Feature for the zip to make a custom query based on the latitude and longitude of the searcher.

As i don’t know how exactly you save the addresses, i can’t help you there. But i can give you a function to get the posts that are in a specific radius from your users location: (this presumes that your post type key is “instructor” and the latitude and longitude of their addresses are stored in post meta keys “lat” and “lng”)

function get_posts_in_radius($center_lat,$center_lng,$radius_in_km=50){
    $multiplier=3959; //miles
    $multiplier=($multiplier*1.609344); //use km instead
    $sql = $wpdb->prepare("SELECT $wpdb->posts.ID, pm1.post_id, pm1.meta_value AS lat, 
                                pm2.meta_value AS lng,
                                (%f * ACOS( COS( RADIANS(%f) ) * COS( RADIANS( pm1.meta_value  ) ) * COS( RADIANS(  pm2.meta_value ) - RADIANS(%f) ) + SIN( RADIANS(%f) ) * SIN( RADIANS( pm1.meta_value ) ) ) ) AS distance
                        FROM $wpdb->posts 
                            INNER JOIN $wpdb->postmeta pm1
                                ON $wpdb->posts.ID = pm1.post_id
                                INNER JOIN $wpdb->postmeta pm2 
                                    ON pm1.post_id = pm2.post_id 
                                        AND pm1.meta_key = 'lat' 
                                        AND pm2.meta_key = 'lng' 
                        WHERE $wpdb->posts.post_status="publish" AND $wpdb->posts.post_type="instructor" HAVING distance < %d ORDER BY distance ASC",$multiplier,$center_lat,$center_lng,$center_lat,$radius_in_km);
    $response = array();
    if($rows = $wpdb->get_results($sql,ARRAY_A)){
        foreach($rows as $row){
            $response[] = array(
                                'id' => $row['post_id'],
                                'title' => get_the_title($row['post_id']),
                                'lat' => $row['lat'],
                                'lng' => $row['lng'],
                                'distance' => $row['distance']
                          );
        }
    }
    return $response;
}

Happy Coding!