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Can physical activity from within a space craft affect it somehow? For example if somebody on the ISS performs repairs involving a lot of hammering, would it perhaps affect the station's orientation a little bit? The vibrations can't be a good thing at any rate.

Also, how about the act of simply moving around inside the craft?

Edit: Are any changes substantial enough to require the ISS or other craft to correct them every now and then?

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This video may help to answer your question. Starting at about 00:24, you can see an astronaut running around the "exercise wheel" of Skylab (an early NASA space station program, which followed the Apollo moon landings). Basically after some time, NASA told the astronauts to stop running around like this because it was causing more propellants to be used to maintain Skylab's correct attitude (orientation) in space (at least this is what I've been told...it would be nice to find a reference to back this claim up).

Anyways, the short answer is yes, an astronaut's physical activity within a spacecraft can absolutely affect its orientation and even its orbit. As to whether it is a large or small effect, this depends on the amount and type of activity and (most importantly) the size of the spacecraft. Even on the ISS, however, astronauts are instructed to avoid or even stop altogether some activities because they can have an adverse affect on the amount of propellants used for attitude control (I have some memory of such instructions during my time working in the ISS Program). Another issue is that an astronaut's activities can affect the microgravity experiments being conducted on the ISS. These are typically conducted over a specified period of time, so an astronaut may be instructed to avoid motion in a certain part of the ISS for a certain period of time, in order not to disturb a particular experiment.

It's not really a simple matter of analyzing starting and ending velocities of an astronaut and assuming that the net change is zero. If you think of it in terms of kinetic energy, an astronaut is all the time transferring small amounts of kinetic energy to his or her spacecraft (the energy being converted from chemical bonds in the food he or she eats into kinetic energy from the work his or her muscles do). Changes in kinetic energy, of course, imply a change in velocity [E = (0.5) m * v^2]. On average, these velocity changes most probably cancel each other out, if they are not applied in a consistent direction. This is why there is no large overall change in a spacecraft's orbit due to these motions. However, the motions can absolutely cause small changes in the orientation of the spacecraft, and these are most often controlled by an active attitude control system (usually small rockets that fire in small bursts to counter unwanted changes in attitude).

I will add, however, that these effects (i.e. astronaut motion) are probably not the largest source of attitude disturbance on a spacecraft. I'm not really an attitude control expert, so I can't tell you the relative magnitude of the different disturbances, but one of the largest (for low Early-orbit spacecraft) is actually aerodynamic drag, caused by the thin layer of atmosphere present at such altitudes.

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    $\begingroup$ During Mir, when a new module was docked, the cosmonauts would stand in the new module, and in the core, and together try to 'shake' the station, to test the strength of the dock. I assume they never expected it to actually fail, rather they wanted to 'settle' it into the docking collar completely. $\endgroup$ – geoffc Jul 24 '13 at 13:32
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    $\begingroup$ The first serious concerns appeared when Mir has grown to 35 meters for the first time (Progress + Kvant + Mir + Soyuz. All in linear configuration.) They have observed elastic oscillations of the whole space complex causing almost critical stress on the docking ports. The recommendations were to avoid certain frequencies on exercise machines. $\endgroup$ – horsh Aug 10 '13 at 21:35
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    $\begingroup$ During assembly of the ISS, I recall certain portions of the crew flight plan corresponding to robotics operations were marked "Physical Exercise prohibited," probably from this exact reason. $\endgroup$ – Tristan Aug 30 '13 at 22:16
  • $\begingroup$ Even the LM in the Apollo missions accounted for the 'spinning' of the recording devices. $\endgroup$ – Magic Octopus Urn Jul 9 '18 at 18:36
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    $\begingroup$ Regarding the Skylab exercise wheel, why would they need to use up RCS propellant to null out the astronaut-induced perturbations, rather than simply having the astronauts run the other way for a while? $\endgroup$ – Sean Jun 26 at 23:17
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Internal activity, other than activation of the drives, will have minimal effects.

Attitude

If everyone goes into one round area, and starts running the walls, the walls will (slowly) start to rotate the opposite direction; this may not be exact, due to the station wanting to rotate upon its own center of mass, but it will attempt to rotate as close as it can to opposite.

Thermal Radiation Acceleration.

If action internal generates significant localized heat, the radiation of that heat from the nearby exterior walls will provide a very tiny thrust. For comparison, the asymmetric thermal loads on the Pioneer probes were sufficient to generate 400km/year off-coast position differences; that's 8e-10 m/s² (0.8 nanometers per second per second).

Note that this force is dwarfed in the inner system by other interactions, but is a real effect that crew could cause.

Kinetic linear Acceleration

Any kinetic acceleration from kicking off one side is canceled by impact with the other side, save for the very very tiny amount converted to heat by friction with internal atmosphere. But, to reset for additive, you're knocking about the same amount off in the other direction, for a long-term net of 0 acceleration (excepting asymmetric thermal loading).

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Physical activity can absolutely affect a space craft from within, and measures are taken to mitigate the effects.

There are a few exercise machines aboard the International Space Station that the occupants use to stay fit and maintain bone strength: the Advanced Resistive Exercise Device (ARED), Cycle Ergometer with Vibration Isolation and Stabilization System (CEVIS), and the Treadmill with Vibration Isolation and Stabilization System (TVIS). Those are all really fancy names for a weight lifting machine, an exercise bike, and a treadmill.

These machines are not bolted to the wall because they do not want to add any unwanted vibration forces to the solar arrays. Sunita Williams provides a great explanation in her departure video:

You'll probably see that the bike bounces around a little bit. As I move it, it's not steady and held to the wall firmly. The reason for that is the space station is pretty big; you saw that there's also solar arrays on the space station. If we start putting any forces into the space station, it's going to make those solar arrays bounce around a little bit. So to prevent that, the machines bounce around a little bit and move around a little bit. That way, we don't put any forces on to the structure of the space craft out to the solar arrays.

She goes on to demonstrate the ARED at 13:26 which also "floats" around.

Advanced Resistive Exercise Device (ARED) Cycle Ergometer with Vibration Isolation and Stabilization System (CEVIS) Treadmill with Vibration Isolation and Stabilization System (TVIS)
All images courtesy of NASA. Click any of them for full resolution

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    $\begingroup$ I seem to remember that when Suni Williams ran her marathon on the ISS, this wasn't particularly appreciated by the structures and ADCO (attitude determination and control officer) guys. $\endgroup$ – robguinness Jul 25 '13 at 7:06
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    $\begingroup$ That departure video is fantastic! Recommended viewing. $\endgroup$ – coleopterist Jul 25 '13 at 17:43

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