[dtparr]

Regarding the factually incorrect bit, could you elaborate? I was under the impression that the energy required was proportional to the square of the velocity, so a 10x increase in velocity (from ~Mach 3 to ~Mach 30) would result in a 100x increase in energy required, which seems to be what he's saying.

Is my understanding inaccurate?

[InclinedPlane]

Energy is proportional to the square of the velocity, but the fuel required to reach a given delta-V scales exponentially.

[jsprogrammer]

Well, if you take the sentence:

>The energy needed is the square, i.e. 9 units for space and 900 for orbit.

at face value. It is either claiming that 9^2 = 900 or, it either mistated the units for space or mistated the units for orbit. This is incorrect.

If you take into account the context of the prior sentence:

>Getting to space needs ~Mach 3, but GTO orbit requires ~Mach 30.

you can probably work out 3^2 = 9 and 30^2 = 900. However, as InclinedPlane said, that's only in an idealized number, in reality, you must expend even more energy than that to achieve Mach 30 from the surface of the Earth.

We can check back to the prior contexts:

>Congrats to Jeff Bezos and the BO team for achieving VTOL on their booster

>It is, however, important to clear up the difference between "space" and "orbit", as described well by https://what-if.xkcd.com/58/

To be short: you'd need to find where Jeff Bezos or the BO team claimed anything about "orbit".

Since others have already given up on this conversation, I probably will too.

[mikeash]

You simply misunderstand the "square" statement. It is factually correct.

You seem to understand it later, where you say that 3^2 = 9 and 30^2 = 900, so what's the deal?

[jsprogrammer]

>so what's the deal?

I assume you stopped reading mid-sentence.

Getting to orbit from the surface of the earth requires more energy expenditure than "the square" of getting to space.