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They've made some amazing progress! However, a landable booster can't put itself into orbit -- its engine cutoff is always well under 3000 m/s (today's was about 9800 kph according to the YouTube broadcast, or about 2700 m/s, and that was with no fuel margin left for landing), but about 7800 m/s is required for orbit.

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Elon's tweet today (https://twitter.com/elonmusk/status/669132749500887040) was that a booster with no payload could put itself into orbit. And that certainly supports your statement. It clearly would not be possible to launch a second stage and have the booster stage make it all the way into orbit. But it isn't as far out of whack as it might be.

Tsiolkovsky is very clear about the propellant mass fraction needed for single stage to orbit, and it is unachievable with current materials, i.e. you can't build a useful SSTO using Al-Li tanks.

https://en.wikipedia.org/wiki/Single-stage-to-orbit#Design_c...

SSTO with a significant payload then, presumably.

Yup. Even carbon composites don't really work out (minimal payload) until the rocket is very large (see: ITS)

The first stage has a fuel mass fraction of 95.5%. Propellant densification and high thrust to weight ratio engines buy you lot. That should be enough to make orbit.

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