Speed of Light: Length Contraction & 20AU Paths

[EbolaHost]

traveling at the ~speed of light leads to length contraction.
based on that wouldn't a 20AU path be shorter if traveled at speeds near the speed of light ?

 

[Nugatory]

traveling at the ~speed of light leads to length contraction.
based on that wouldn't a 20AU path be shorter if traveled at speeds near the speed of light ?

Yes. However that doesn't change the speed of light. Because of time dilation both the traveler (who sees the distance contracted) and an observer at rest relative to the endpoints of the traveler's journey will find that a flash of light travels between the two points at the speed of light - divide the contracted length by the dilated time and you'll get $c$.