Well, hopefully this is going to be my last help-thread for a while, i'd like to start repaying the members. You may have noticed i've posted a few threads asking for help tonight, and I thank the members who have read my threads very much. I've narrowed down points of my course that I remain unsure about (after hours, believe me) of reading my textbooks and any others I can find and I *think* this is the last of it. I have attached two documents (yeah I know, attached) of scanned in questions that require prooving. Unfortunately, I haven't been able to prove these myself, yet, and I have spent alot of time trying to do so. I also apologize for the lack of latex, I spent ages trying to 'tex these questions up, but kept getting error messages to be honest I need to take a break, so I'd appreciate it alot if some of you guys would look at my problems. Note: these are not homework problems, I'm just trying to understand my course - any help with any of these proofs is greatly appreciated - be it completed proofs or guidelines. I promise that when I'm back on after a nap, I'll give latex another bash and respond to any queries you may have about these questions. They require pre-honours level astronomy knowledge (or good thermal/bit o' quantum physics) - The first ones are on spectral broadening, and theres a quick relativity related proof (I think these ones are the easiest). Thank you, and yes I'm aware that several members don't like handwritten documents so i'll try and get it sorted. thanks, [tex] \delta [/tex] ftj.