With all the recent announcements from several companies looking to finance and develop the asteroid mining industries, Planetes may well be the first science fiction series to hit their specified time line. The series sees the crew going about their business in 2075, although in reality it will be more likely all the future space mining jobs will be left to the robots. NASA themselves noted that the scenario presented the manga is highly unlikely due to the high cost, and low value of salvageable materials. Japanese space agency JAXA must have a permanent division just for dealing with anime and manga consultations after they were asked to help in the development of this series, and even more recently with the Space Brothers franchise.
A 26 episode anime series was produced by Sunrise in 2003. They are also responsible for several series of Gundam, Freedom and Patlabor, so they definitely know how to handle their SF. Although my personal preference is to leave out the giant robots, so I strongly recommend Planetes.