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Replying to Scott Manley's tweeted table of payload mass for a given geocentric C3, Musk tweeted:

We could stretch the Falcon Heavy upper stage & increase this a lot, but FH already covers all known payloads.

Starship, especially with orbital refilling & dedicated deep space variants (no heatshield, flaps or header tanks) will take this up orders of magnitude.

"Orders" is plural, so assuming (without justification) that we always round to the nearest integer order, conservatively speaking the least this can be is 101.5 or a factor of 31.6, though it sounds like a fancy way to say "hundreds".

Question: I can see that making a "Stretch Starship" with lots of landing-associated hardware removed just shuttling between LEO and C3 > 0 is helpful, but how can this actually make an "orders of magnitude" improvement in payload performance?

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[...] with orbital refilling [...]

This seems to be the part were orders of magnitude can be snuck in .

Refilling the 1,200t propellant tanks of the 120t starship makes it possible to start with a 1,320t stage in LEO, rather than the 20-50t than can be brought up there today.

Since the rocket equation only concerns mass ratios, you can scale this $\approx10^{1.5}$ factor up to any C3 you like.

Of course, hauling up to 1,200t of extra propellant into orbit is a minor detail one doesn't have to spend time on when tweeting.

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