America and China will lead the world only if the financiers who are holding their debt permit it.
The US has $17 trillion in debt with commitments for $100 trillion in the future from civil service pensions of those still working, Medicare etc. China has built huge cities with zero population, meaning the grand idea of central planning doesn't seem to be working. Their fortunes are falling as demand drops for their products. I see recession hitting all countries with the exception, maybe, of Germany, but the European Union and the Euro will continue to be dragged down by underperforming member countries. I seriously doubt Trump will make any difference - the American system of checks and balances has devolved into a system of thromboses and embolisms. Much of the time, the government does not work and has to pass temporary bills to ensure funding for essential services while they remain deadlocked. The American standard of living peaked in 1967 and I doubt we will ever see the American dream again. Trump will make America a nation of prison guards. The wars in the Middle East will do exactly what the terrorists want - they will cause America to spend and spend until they don't own their country anymore.
The current level of American debt does not permit much of a space program at all and China is not going to do much better.