There seems to be at the very least two vehicles that would qualify as “space planes” that NASA has in current operation. These machines are capable of astonishing speeds and astronomical heights and possibly low Earth orbit flight, though much of their specific capabilities are classified.
Boeing, under the direction of NASA, built the X-37 which was originally planned to be an “orbital experimental vehicle” capable of returning to Earth on its own accord. The Boeing X-37 is 27.5 feet long with a wingspan of 15 feet capable of orbit propulsion via the AR-2/3 engine.
The X-37 was seen landing at Kennedy Space Center on Sunday, May 7, 2017 after a long awaiting appearance. It did not disappoint as it’s landing seemed to be picture perfect.
Next there is the X43A AKA Hyper-X. Per NASA, “Four decades of supersonic-combustion ramjet propulsion research culminated in a successful flight of the X-43A.” This piece of research completed a test flight off the coast of southern California in which it reached a height of around 95,000 feet just before it detached from the Pegasus booster rocket and powered its self to an airspeed of Mach 6.8. That is 6.8 times the speed of sound or 5,000 miles per hour. After that test run, NASA initiated another flight for the X43A in which it reached the astonishing air speed of Mach 9.6 or 6,800 miles per hour.
Of course, both flights set new world air speed records and is understandably touted as proof per NASA, “scramjet propulsion is a viable technology for powering future space-access vehicles and hypersonic aircraft.”