It is revealed in ‘Kill the Moon’ that it took 10 years for anyone to investigate the missing Mexican mining survey because there wasn’t a space program. The only shuttle they had to go to the moon was recovered from a museum.
This is a startling change to established Doctor Who history, which has generally seen a continued interest in space. Even if the public is some how not aware of the existence of aliens that doesn’t explain why governments and organisations such as UNIT wouldn’t see a need to expand into space.
The Sarah Jane Adventures episode ‘Death of the Doctor’ establishes that UNIT have a moon base in 2010 (where Liz Shaw is stationed). ‘AHistory’ argues that the colony on Vulcan shown in ‘The Power of the Daleks’ is in place by 2020. ‘Waters of Mars’ establishes that there is a healthy space program establishing Project Pit Stop and sending unmanned probes throughout the solar system.
The events of ‘Kill the Moon’ are put in motion by a Mexican mining survey in 2039. It would seem strange that Mexico were the only country to still have space technology, even if it only came from the private sector.
There are multiple reboots and rewrites of history during the 11th Doctor’s era that could explain this discontinuity. It could be that as a result the space program of various countries was seriously reduced.
This could explain why the British Space Program of the 3rd Doctor era isn’t represented in the 21st century setting. Similarly if the alien invasions encountered by the 9th and 10th Doctor never happened then the world might not see the urgency to reach beyond our world.
It might be that there were surveys of the moon that revealed there were no minerals there and thus not worth investigating. Only those without this information or who were desperate would bother to go through the trouble of launching a mission there.
Alternatively this could be a deliberate attempt to cripple humanities path into space. This could be the result of a malevolent time travellers (such as the Master or the Meddling Monk). It could also be the result of a time traveller from the future who has decided that space travel is a bad idea.
There are many alien races who might see the advantage in preventing humanity from developing space travel. Races like the Ice Warriors would certainly not want humanity to reach Mars, let alone the planets beyond.
Several races could band together to contain the human race within the solar system. It could be that humanity has gained a reputation just through their talent of repulsing alien invasions. Now the other races fear what will happen when the humans come to their worlds.
PCs could encounter aliens or time travellers sabotaging various countries space programs throughout the late 20th and 21st century. This could be a good opportunity to get the PCs to encounter important astronauts.
The change to history could be a result of the Doctors actions. One possible alteration could be the alliance with the Zygons in ‘The Day of the Doctor’. The exchange of technology could have diverted focus of space travel to concentrate on bio-tech and the colonisation of the sea floor.
Given the new attitude of the 12th Doctor this could be a deliberate attempt by the Time Lord to confine humanity to Earth. He might have decided that after thousands of years that humans only cause problems when they go to other planets. In his old age he might just be getting lazy and find it easier to visit his favourite species if they are just on one planet.
The Doctor indicates that after the moon dragon emerges there is a renewed interest in space travel that allows humanity to spread out and last until the end of time. One of the first things to be done is the exploration of the new moon.
This creates an exciting new period for the PCs to get involved in. It could be that all the previous Doctor Who stories set in the future have now been erased. It is completely new territory for the PCs to explore.
Now humanity is aware that their moon contains a living creature there would likely be debate about whether they should let it live, even if the last moon dragon proved harmless. They would still know that when it hatches it will cause a natural disaster but maybe the fact it won’t happen for millions of years would make that a low priority.
Study of the egg and the moon dragon could give humanity a better understanding about space and alien beings. Using biotechnology gained from the Zygons they could create living ships based off the basic design of the moon dragon.
Considering the sorry state of the space program, since they seem to be unable to build a new space shuttle in 10 years, they could turn to captured alien technology. UNIT and other organisations might share knowledge of this science to allow it to be used in new spaceships.
There would have to be a new recruitment drive for astronauts to crew these vessels. PCs could be part of this crew or have their TARDIS land on one of these vessels during their maiden voyage using experimental technology.
This could allow you to combine Doctor Who and Star Trek style adventures. During this era the PCs carry the flame for this renewed era of space travel. If they fail it could set back the space program and not making new discoveries could mean that people loose interest.