If my spaceship was going 70% the speed of light and was 80,000 miles ahead of you and you are going 72%?

Question

You are going 72% speed of light. How long before your spaceship hits my spaceship?

Answer 1

you've got a space ship... really....?

Answer 2

Hmmm, not long ? I dunno.

Answer 3

That's a tricky question because of the way distances and time intervals are affected by relativity.  The answer to "how long" will be different in different reference frames.

If we assume your numbers are measured from the point of view of some third party watching the two spaceships, then that observer would say that the ships' speed relative to each other is 2% of  "c", and therefore the 80,000 mile distance would be closed in:

t = (80,000 miles) / (0.02c) = 21.47 seconds.

However, it won't seem like 21.47 seconds to the ships' inhabitants (it will seem like a shorter time, due to the effect of time dilation).  And their initial separation won't seem like  80,000 miles, either (it will seem like less, due to relativistic length contraction).

Answer 4

well to expand off of another answerer's answer, ill use 21.47 seconds till the collision. if we factor in time dilation from your point of view. we get:

t=21.47/sqrt (1-(c * .02)^2/c^2)

which comes out to 21.4742953. so from your point of view, a clock inside the other ship would tick for 21.4742953 seconds before the collision. but that really wouldnt matter, because i doubt you would pay attention to their clock, youd pay attention to yours. which would still read 21.47 seconds till impact.

EDIT: eh, let me start over. with length contraction you would get 79 983.9984 miles between the 2 ships. so it would take 21.46848 seconds. the equation for length contraction is L = L0 * sqrt(1-v^2/c^2)

so to figure out how much time the slower ship would see the bigger ship experience, we would have to use that equation again. we get 21.472775 seconds, so the small ship would see the big ship experience that much time.

Answer 5

Whose clock are you measuring with?

To an outside observer it will be 21.47 seconds, but the people on the ships will measure different times.