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Keep your letter short and to the point. Introduce yourself to the celebrity. Mention your favorite book, movie, or show of theirs. Ask them for an autograph politely if you're mailing a letter. Thank them and wish them well.
Show respect for the celebrity by keeping your letter to about a page in length. Since they're busy people, and likely have a lot of fan mail, a page is the perfect length for them to read quickly. Remember, if you do write a longer letter, it's unlikely that the celebrity will read more than the first page. If you're sending the letter through social media, be aware of length constraints. For example, if you plan to tweet at a celebrity on Twitter, keep your message under the 280 character limit! Start by writing 2 or 3 sentences about yourself, including your name, where you're from, and how old you are. Talk about how you first heard about them, and what kind of impact they've had on your life. Don't be afraid to tell a short story about how you first encountered their work. It's okay to make it a little personal! If you're writing to Britney Spears, you might say something like "My name is Kate, and I'm 19 years old. I've been a huge fan of yours ever since I heard your song 'Oops, I Did It Again' on the radio when I was a kid!" Be as specific as possible when writing your fan letter. Tell them why that specific book, show, or movie is your favorite, and mention your favorite line or scene. Talk about how it has shaped you as a person. This helps to make a connection with the celebrity and might make them more likely to respond to your letter. For example, if you were writing to J.K. Rowling, you might say, "I loved The Goblet of Fire because it really showed me what it means to be brave in the face of impossible challenges." If you're writing to get an autograph, don't be afraid to ask for one! Simply be gracious about it, by saying something like, "It would mean the world to me if you could send me an autograph." Keep in mind that there's no guarantee that you'll get anything back from the celebrity, but there's also no harm in asking. It's important to be kind to the celebrity in your letter, and express your happiness to get a chance to communicate with them. Say something like, "Thanks so much for taking the time to read my letter," or "I wish you well in your next project!" You can even ask a thought-provoking question to encourage them to respond! This will show the celebrity that you're not just looking to get an autograph from them, but that you really care about them.