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Few will ever forget the flight of Starship 24/Booster 7.

Perhaps the first moon rocket to perform aerobatics and hold itself together before finally self destructing. But would it be aerodynamicly unstable once most of the Booster fuel and Lox were gone?

Center of Gravity plays a key role in longitudinal stability. As Booster propellant is consumed, center of gravity moves forward and the Booster becomes ... a tail!

Just like the ones Congreve rockets had. For stability.

It makes one wonder if uneven thrust played more of a role, perhaps coupled with loss of gimballing. One may even speculate that the second stage control fins may have been tried.

But, with most of the Booster fuel gone, is the full stack inherently unstable?

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  • $\begingroup$ Related, but not a dupe (it’s referring to just the second stage, while this question is about the full stack) $\endgroup$
    – fyrepenguin
    Commented Apr 25, 2023 at 2:52
  • $\begingroup$ Elon plans to use this ''inherent instability" to get a second stage separation almost for free, without shaped charges and special mechanics. Starship will tip over from the first stage, naturally, only using gravity. That way, there is no damage to a reusable first stage. $\endgroup$
    – TheMatrix Equation-balance
    Commented Apr 25, 2023 at 2:59
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    $\begingroup$ @TheMatrixEquation-balance, Starship/Super Heavy starts out unstable, because of the grid fins and flaps well ahead of the center of gravity, and is only able to move in a straight line because of active steering. As the fuel in Super Heavy is burned, the center of gravity moves forward, making the rocket less unstable. The question here is whether it moves far enough forward to enter the realm of passive stability. $\endgroup$
    – Mark
    Commented Apr 25, 2023 at 3:47
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    $\begingroup$ I'm not sure anyone has the answer to this other than SpaceX themselves, and they haven't shared that information. $\endgroup$
    – Darth Pseudonym
    Commented Apr 27, 2023 at 12:33
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    $\begingroup$ @DarthPseudonym knowing the dry weights of the 2 stages, the location of LNG and LOX, and their (liquid) densities, a "ballpark" CG could be derived. Other stability considerations would be location of shockwaves in the supersonic regime. $\endgroup$
    – Robert DiGiovanni
    Commented Apr 27, 2023 at 19:15

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As the booster depletes its propellant the stack Cg moves forward which improved that static margin. The lowest static margin would be at or near liftoff with the Cg aft and the air dense. Its easy to get mixed up on static margin. I always think of a dart with ballast forward and feathers aft.

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