Losing mass in space So I came across a question while studying laws of motion. Roughly, this is how it goes:
There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage to lose 80 kg, what will be the percentage increase in speed of the shuttle. The question is pretty straight forward, if thought about directly. However, my instant reaction was that by conservation of mass, the mass that the astronauts lose will still be contained within the space ship in the form of water, CO2, etc. So technically there won't be any change in mass, thus no change in speed. 
I would like to know if this assumption is correct and in what forms is the mass we lose released.
 A: I'll attempt an answer, though someone knowing the precise ground realities will most likely improve on my answer. 
You make a very good point about the speed staying constant IF the space ship can be treated as a closed system. That's the sole point that we need to worry about. 
Naturally, the atmosphere within a space ship has to be maintained (at the values that can support human beings). If it was just a case of filling up the shuttle once with $21 \%$ oxygen and being done with it, astronauts would keep consuming it so that its levels would fall, and percentage of ${\rm CO}_2$ would keep increasing. That's undesirable and in a simplified description, one can get around this by removing ${\rm CO}_2$ via a chemical reaction with Lithium Hydroxide ${\rm LiOH}$. (By the way, this is a fairly common use of ${\rm LiOH}$, as a Carbon Dioxide Scrubber in breathing purification systems, as can be seen here.) Upon the reaction, these ''canisters'' can be stored and disposed off later. All the excess water (i.e. discounting the potable variety) is  directed to tanks, which can again be disposed later. Excess heat is handled by converting to ammonia vapor and subsequent STORAGE. (Though somewhat simplified, a description of this process can be found in the first link of this article.)
So, while space shuttles would ''maintain'' a requisite atmosphere, (apparently) nothing gets dumped on there an then basis. Now, your question pertained to what would happen if this release happens (or doesn't happen) while the shuttle continues moving ahead at a uniform velocity $v$ - if it got dumped, then $v$ would change. DOESN'T SEEM TO BE THE CASE.
See, everywhere in physics, we make all sorts of approximations, the question is how valid they are in real situations. Irrespective of which materials you may choose to build the spacecraft with, it won't make a perfect thermal insulator. While they may try to reduce this radiation loss to as low a value as possible, there will be some amount of heat radiated by the craft. So, while not absolutely ideal, it may be be a good approximation to an insulated body, or in the context, let's say a closed system. In textbook situations, one always considers simplified descriptions. 
Thus, armed with these links, I think you can safely go and pester your instructor, telling him that his original logic had a flaw!! 
A: What we have to consider here is conservation of momentum. Assuming that the mass/energy that is leaving the astronauts' bodies is still contained within the spaceship, there will be no change in the total mass/energy of the latter. Since momentum is given by mass times velocity, in the absence of external forces, constant mass implies constant velocity. In this sense, your assumption is correct and the spaceship will move on at the same speed. 
A: I think there is another look into this,
When you lose weight you are converting Mass to energy. 
so the question is how does momentum truly work?
The mass is down but the inherent energy is up. 
The deeper question is does energy have mass? 
I remember in the distant past reading about a battery that gained weight when charged. 
So the mass does go down but where has the energy gone to?
A: As others have already pointed out, nothing happes as the result of astronauts losing mass if the system is closed.  In that case the mass is merely moved around within the shuttle and the system as a whole still has the same mass.
However, even if the system isn't closed, its not the loss of mass that matters but the momentum imparted onto the shuttle by ejecting that mass.  The speed of the shuttle has to do with its orbit, not with its mass.  Any other object, regardless of mass and size, will have the same trajectory given the same initial velocity.  Even if the shuttle were to magically lose 80 kg somehow, it's speed wouldn't change as a result.  This is a result of the same physics that says a feather and a lead ball will fall at the same speed in vacuum.
The way for the shuttle to change its velocity is to eject mass in a particular direction.  This is exactly the purpose of the rocket engines.  If the 80 kg were somehow packaged up and ejected out the back, the shuttle would go a little faster forward.  If it was broken into two 40 kg chunks with one ejected out the back and the other out the front at the same time with equal speed, there would be no net effect on the shuttle's speed.
Again, the point is that the shuttle's continuing velocity isn't a function of its mass in the first place.
