What challenges will bitcoin face in space? What would the challenges of transacting in outerspace be for bitcoin? What improvements need to be implemented to address these challenges? I'm particularly curious about low-earth orbit.
Biggest problem facing spaceborne bitcoin is communications latency.  Consider possible Mars colony.  

Light speed imposes delay, 4 to 24 minutes.  Bad enough this is.  If miners on both Earth and Mars, each comes up with new block, possibly extends blockchain twice more, before signal from other crosses distance.  Means very long transaction confirmation time, for colonists (assuming on Earth most mining power).  Transactions fine going into local blockchains, but those blockchains not continuing.  Only when individual transaction records reach Earth (meaning lightspeed delay at minimum) does it get into chain that will more likely  continue.  Then must wait while more blocks close at ten minutes approx. each.  

Now further problem appears.  High latency causing deeper depth of chains which abort.  Colonists wanting to be sure of transaction commitment. To be as sure  as six blocks deep in earth-only chain, must being nine or more blocks deep in interplanetary chain.  So now delay is lightspeed delay, plus maybe 90 minutes.  Then lightspeed delay again before news reaches Mars.  

When Mars 24 light minutes from Earth, expect delay confirming Martian transactions minimum around 140 minutes.  Plus whatever network propagation delay on planet, not usually very significant.  Effect much less pronounced when 4 Minutes mars is from Earth;  Need only 7 blocks to be as sure, lightspeed delay much less.  Expect delay around 80 minutes confirming Martian transactions.

Earth mostly unaffected as long as Mars have not significant mining power.  But when real possibility is scenario of Martian blockchain accepted and extended, Earth-only transactions also take ten to thirty minutes extra for confirm.  Problem here is not knowing when Martian miner extends chain, so needs more chain depth before sure of confirmation.  Still, extra delay only about ten minutes. 

Propagation delay problem goes deeper when additional colonies on Ceres, Juno, Pallas, Vesta, Jupiter Moons, &amp;c.  Extra time taken for confirm transactions proportional to approximate diameter of sphere containing vast majority of mining power.  Adding twice lightspeed delay at least from center of mining power to location for confirmation times at location. 

Extra bandwidth too.  Extra bandwidth required because of aborted blockchains.  Not significant too much in reasonable scenarios, but in extreme case scales badly, with square of distance.  

Next, bitcoin client need accurate network time. Establish accurate network time require many iterations of light speed delay.  Bitcoin client not worry about.   Will be provided by operating system.  Must be provided, because MOST network clients want accurate network time.  

However, if too picky about accurate, is not really possible (or at least very interesting) due to Relativity.  Time passing at slightly different rates closer and further from sun, different orbital speeds, different relative vectors, etc.  Einstein is a Meanie. 

Now we have meta-problem.  Mining not really possible unless mining power on site comparable to mining power at largest other single site.  No point mining bitcoin on Martian colony, for example;  Due to lightspeed delay your work will arrive 4 to 24 minutes after you do it, and you'll be working with blockchain 4 to 24 minutes older than miners on earth.  You must work so hard that you get 8 to 50 minutes ahead of Earth's miners.  Very very hard to do.

Interesting though, that if this ever happens, then when Martian extend blockchain, suddenly it is Earth miners who are 8 to 50 minutes behind.  All considerations of delay previously working against Mars colony now work against Earth; roles reversed as long as nobody Earth get 8 to 50 minutes ahead of Martian miner.  Suddenly Earth transactions face 80 to 140 minute delays, Martian transactions clear in only 70.  

Finally, effects of different mining speed various locations on hash rate.  Consider where Martian miners have 1/4 power of Earth Miners.  Due to high variability of block closures, chance of mining "center" switching to Mars and unfairly favoring Martians as above very real is.  So is chance of switching back to Earth and unfairly favoring Earthlings later. When a 2016 block mined, possible that hash difficulty could change suddenly.  Possible for hash difficulty swing back and forth unpredictably, one week to next.  Miners have maybe very prosperous week, then very dry month when no coins at all, and all go broke.  Meanwhile Miners in other location reap huge reward in bitcoin.  Depending on value of bitcoin, sudden swings in direction of money movement affect local economies, destabilize things.  

But in general, value movement caused by mining would be unfair directed away from smaller locations toward major centers of mining, probably bad for development of frontiers. 

Edward.