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Does launching a space shuttle or rocket change the earth's orbit?

After all, to get momentum in space you need to throw something out.

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    $\begingroup$ This question reminded me that: xkcd.com/162 $\endgroup$ – Crowley Apr 17 '18 at 7:41
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    $\begingroup$ @Crowley See also xkcd.com/146. $\endgroup$ – Dan Pichelman Apr 17 '18 at 14:29
  • $\begingroup$ ..change earth's orbit around what? The common center of mass with the rocket? The sun? $\endgroup$ – atmelino Apr 18 '18 at 2:17
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    $\begingroup$ See also: en.wikipedia.org/wiki/The_Purchase_of_the_North_Pole They fire a cannon on Kilimanjaro in order to change the earth orbit. But (Spoiler!) due to a calculation error, the force was 12 orders of magnitude too small. $\endgroup$ – Robin Apr 18 '18 at 7:01
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Technically yes, but not in any way that matters.

Planets are enormous; Earth's mass is about 6,000,000,000,000,000,000,000 tons. All the spacecraft to ever leave Earth's gravitational sphere have probably totaled less than 1000 tons; we couldn't even measure the change in Earth's orbit produced by those launches.

In the case of the US space shuttle, and any low-Earth-orbit space mission, almost all the mass exhausted in launching the spacecraft returns to Earth in short order, so the orbital changes are canceled out in any case.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – called2voyage Apr 18 '18 at 13:19
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As long as "what happens in GEO stays in GEO" and there's no mass lost to deep space, the Shuttle and the Earth will mostly orbit around their common center of mass.

When the Shuttle is moving (relative to Earth) in the prograde direction (Earth's motion around the Sun), the Earth will be moving slightly slower than it normally would, but a half-orbit later when the Shuttle is moving retrograde, the Earth will be moving slightly faster than it normally would.

When the Shuttle returns, to 1st order (and maybe 2nd order as well) the Earth will be in the same place it would be if the Shuttle had never taken off.

It's quite a bit like the Earth and Moon orbiting around their common barycenter, and it being pretty much the EM barycenter that moves in a nice elliptical orbit around the Sun, except that as @RussellBorogove points out very effectively, it's a quite a bit smaller effect than that.

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    $\begingroup$ You might get some very small changes in Earth's orbit from the fact that tidal forces from the Sun & Moon act differently on the Earth-Shuttle system when the Shuttle is in orbit, due to its different mass distribution. But to an excellent approximation, the CM of the Earth-Shuttle system keeps trucking along at a constant speed. $\endgroup$ – Michael Seifert Apr 17 '18 at 17:37
  • $\begingroup$ @MichaelSeifert that right! It's why I was not sure if this is correct only to 1st order, or to 2nd order. I may something like that as a new question if I can't figure it out in the next day or so. $\endgroup$ – uhoh Apr 17 '18 at 17:49
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    $\begingroup$ In case anyone is interested, last years magnitude 8.8 earthquake in Chile is estimated (by NASA) to have shortened the length of day by over a microsecond. $\endgroup$ – JohnS Apr 18 '18 at 1:21
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    $\begingroup$ The Earth sucks up about 40K tons of dust and other things yearly which also impacts the orbit around the sun and angular momentum. It is also losing mass from H and He leaving Earth's gravity. The changes are tiny, nothing to worry about for a very long time. $\endgroup$ – JohnP May 18 '18 at 15:30

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