Apologies for asking a dumb question, but I'm going to ask it anyway... I was watching a music video where the singer duct-tapes her ex to the side of a rocket to exile him into space, and it made me wonder -- if someone actually attached a person to the outside of the rocket (or, if you prefer less cruelty in your hypotheticals, a roughly person-shaped and person-sized mass), would the rocket's control systems be able to compensate and still reach (roughly) its intended orbit? Or would that be enough imbalance to cause the rocket to lose control of its trajectory? For my hypothetical, assume a Falcon-9 or comparable rocket, and that the duct tape is sufficiently strong to hold :)
For the Falcon 9, the worst-case point should be near the end of the second-stage burn, when the mass of Alison Goldfrapp's ex is largest relative to the remaining mass of the rocket, and only a single engine is available to steer, with a relatively short moment arm between the gimbal and the center of gravity.
I assume that we are not launching any non-ex-boyfriend payload. The dry mass of the stage is not precisely known, but is close to 4000kg; the payload fairing is about 1700 kg. Stage is 12.6m long; let's assume for simplicity that the ex-boyfriend is mounted at the same height as the normal center of gravity and masses 100kg, contributing 0.0172 of the total mass stage. This moves the CG proportionately; assuming the CG is normally centered, the CG will offset by about 31 millimeters toward our special guest.
I don't know precisely how high up from the engine gimbal the normal CG is, however. The engine contributes somewhere around 10-15% of the mass (the Merlin 1D masses ~470kg, but the vacuum version on the second stage adds a big (but thin-walled) nozzle extension that I don't know the mass of) and the rest of the mass should be fairly symmetrically distributed in the portion above the engine, so the same proportional distribution logic suggests the CG would be something like 4 meters above the gimbal plane.
The gimbal angle needed to reach a 31mm-off-center CG at a distance of 4 meters is about 0.43º. As long as the engine can gimbal this far, it can keep the thrust line pointing through the offset center of gravity, and as long as it can gimbal a few more degrees than that, it can steer its way efficiently onto any sensible trajectory.
I haven't ever seen a source for the gimbal range of the Merlin engines, but it's certainly multiple degrees, probably more than 5º in any direction. This worst-case point, when the second stage is burning the last of its propellant, also happens to be when the least steering authority is needed -- the stage is light, and atmospheric pressure is near zero. Throughout the rest of the flight, the CG will be closer to the centerline, requiring less gimbal deflection, so we should have scads of control authority throughout the flight.
Alison's former paramour will interfere with the aerodynamics a bit, producing some additional drag and creating some supersonic shockwave effects that might cause structural failure, but I think this can be mitigated by using additional duct tape to create a smooth fairing.
Thus, I believe the dead weight that Ms. Goldfrapp is trying to jettison will go to space today.