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I recently bought A Brief History of time by Stephen Hawking and has since been very intrigued by the whole idea of time dilation. I've been searching on the internet and reading a lot about it and it is beginning to make sense :)

However I have a problem that I just don't seem to get. I've been trying to find an answer online for the last couple of days, hopefully someone here can help me out.

The example is as follows:

If I'm sitting in a spacecraft, traveling at half the speed of light towards the sun, which again is shining light in my direction at the speed of light (duh!), Newtonian logic says that the light should pass by me at the speed of 3/2 c, right?

Since we know that this isn't possible, time dilation must be occurring, since the speed of light is always the same no matter my velocity.

My problem is the following. In order to experience the light as approaching me at the speed of c, time must be slowed down by 33% for me, right?

But according to the good old 1/sqrd(1-(v^2/c^2)) formula, the Relativistic Change Factor is only 1.1547005383792517 ?!

Now, I'm sure that I'm missing something, it's just what?

Can someone please explain this for me.

Thanks :)