I could attempt to contact my chosen idol a range of different ways. He has a twitter account which he uses daily, so I could message him via that, however there is a good chance he doesn't answer his private mails because of the amount of messages he will get.
I could write a letter or email to the Hayden Planetarium where Neil deGrasse Tyson works, hopefully to get a reply from him, but I may also get a reply from an assistant or co-worker who could help me contact him.
Hand writing a letter will feel more personal and I think would have a better chance of getting a reply because it shows effort has been put into contacting him which would be appreciated, where as emails can feel cold and uncaring.
