The Equation that lets you travel anywhere in an INSTANT

According to Einstein's theory of special relativity as we approach the speed of light time slows down due to time dilation, but also length contracts due to Lorentz contraction.
First we explore how this might potentially be thought as time being meaningless for photons although a disclaimer even though this is found a lot in popular science, we cannot apply this equation and time dilation for a frame of reference which is moving at the speed of light.
Then we look at distances would contract and potentially enable interstellar travel at very high energies. It is pretty amazing that we can use the ideas of limits in calculus in physics and apply them to show how given enough energy we can send things very far away!
The animations are screen grabs from the fantastic free software - Celestia. You should check it out!
This is a pretty interesting question that can be part of undergraduate physics courses, but also can be discussed in courses such as A Level Physics, AP Physics in the States, IB physics, A Level CIE etc. Relativity is also a concept that comes up in most physics olympiads including the international physics olympiad, british physics olympiad, etc.
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