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How many rocket launches are needed to change the axial tilt of the Earth so much that it is noticeable with instruments available today?

We can assume that we are talking about the heaviest rocket ever launched and that all launches are done from the same place, in the same season and at the same hour, all chosen for the biggest effect on the axial tilt.

(I know that the axial tilt is already changing due to natural reasons, my question regards an additional change attributable only to space launches)

Later edit: I'm looking for an answer that involves the kinetic energy derived from the mass and speed of the rocket at launch (and possibly later in the atmosphere). An explosion or an earthquake is usually not directed and much of the energy would be lost.

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The earthquake of Tohoku in 2011 shifted the Earth axis by 10 cm. It had a magnitudo of 9.0, meaning it released an energy of about 2 EJ, or 477 MTon.

The Saturn V could release a total energy of about 5 kTon.

We see that to have a comparable release of energy we would need about 500 thousand Saturn V, assuming that the effect of each single launch can simply sum up without losses of any kind.

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    $\begingroup$ I think that only works if the launches are done in a very short time span. Earthquakes, and I think hurricanes and tidal bores as well, keep changing the tilt too - the effect of rockets would be lost among the effects of nature itself. $\endgroup$ – Renan Jan 6 at 13:08
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    $\begingroup$ @Renan No, that's not how physics works. The total effect of 365 Saturns V launched simultaneously would be the same as one Saturn V each day for a year. $\endgroup$ – Mr Lister Jan 6 at 13:18
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    $\begingroup$ @MrLister if I lit one match per day under a frypan for an year it will receive the same amount of energy as if I had let it rest on a lit stove for a few minutes. One way gets the meal ready, the other one does not. I believe that's how physics work. $\endgroup$ – Renan Jan 6 at 14:17
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    $\begingroup$ This is this is kind of besides the topic here, but I wonder why the Earth's axial tilt isn't completely askew given that the Earth has likely seen many such events throughout its history. Perhaps the randomness involved neutralizes those effects. $\endgroup$ – B.fox Jan 6 at 15:36
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    $\begingroup$ @B.fox: Because the Earth's spin absorbs most of the wobble, just like a bullet fired from a rifle $\endgroup$ – nzaman Jan 6 at 17:09

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