First off, I try not to make specific predictions — -sometimes I do, but they are best avoided because they will almost always be wrong somewhere.
I try to plant ideas — examine the ‘what ifs‘ ’that we a faced with, examine to possibilities and come up with debatable ideas. I like to think in a complex abstact form. If that makes sense.
Yes, the earth receives xx Tw from the sun, always has, always will. But that energy cannot be used without complex machinery — -which, if you think about it, is exactly the same situation as digging up fossilised sunslight.
Coal and oil are useless without complex machinery.
And how do you build complex machinery?
By utilising the same energy forces that drive it.
But complex machinery requires sophisticated society — -which itself is energy dependent.
We are faced with imminent collapse of these systems through shortages and climate change over maybe the next 20 years or so.
So if we do not solve our problems in that time period, the necessary complexity of systems will cease to exist in a manner in which they can be utilised for our benefit. Fusion is as yet not invented, it is questionable if sufficient infrastructure can be put in place to battery-power our culture.
Your comment about space exploration led me to believe that you meant settling humankind elsewhere.
My 1bn number is the population before oil and coal started to be used in quantity. Without oil, the conclusions are obvious I would have thought. Oil is cheap right now because so many of us use it. If it because restricted, its cost would be prohibitive for any use at all.