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I've seen in some videos of astronauts that they used to use a jetpack type system to maneuver in the vacuum of space around the ISS and other satellites using pressurized gas.

From Wikipedia

Gaseous nitrogen was used as the propellant for the MMU. Two aluminium tanks with Kevlar wrappings contained 5.9 kilograms of nitrogen each, enough propellant for a six-hour EVA depending on the amount of maneuvering done. Typical MMU delta-v (velocity change) capability was about 80 feet per second (25 m/s).

This is perhaps a convoluted question because of the circumstances that surround my asking of this question. I was explaining to a friend that we don't really "pilot" shuttles to the moon or other objects, rather it is like a calculated throw, a one time launch that will get us to the object because of our velocity, direction, and the gravitational pull of objects in space. To that, she raised the question, "Well why do jetpacks work in space if there is nothing to push against?".

To my knowledge, there isn't anything for the gas to push against. The best answer I could muster was that expelling gas from a pressurized container still results in a force, and according to Newton's Third Law, there is an opposite force pushing the astronaut away. This can also theoretically be accomplished by throwing an object to propel yourself away from the direction of the thrown object.

I would like to know more specifically how a pressurized container creates force if there is nothing to push against, if indeed there is nothing to push against. Another question may arise from this answer, but I will save it for it's own thread.

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As you said, action = reaction, Newton's third law. In a rocket engine, a fuel is burned, creating gas that expands. Now this gas wants to expand equally in all directions. In the 'front' and 'side' directions, the gas encounters the rocket nozzle and pushes against it. In the 'rear' direction, the gas goes out the end of the nozzle and into the vacuum of space.
The gas pushing against the sides of the nozzle produces no net force: the various directions cancel each other out. But the gas pushing against the front of the nozzle has no counterpart, so there is a net force on the nozzle pointing forward.
Here's a diagram of the forces exerted by the expanding gas inside the engine:
diagram

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To my knowledge, there isn't anything for the gas to push against.

That is not how a reaction engine - a family of which rockets and thrusters are a part - works.

In short: you got it backwards. The gas that is expelled is not pushing against a medium (such as the atmosphere)... the gas is pushing against the thruster. Or - to be accurate - they are pushing at each other.

The long explanation, in layperson terms: when the thruster "throws out" the gas, the work is already done. Anything that happens after the gas molecules leave the nozzle of the thruster is irrelevant. It is the process of getting the gas molecules up to speed that causes thrust.

And why is that?

Because in order to get the gas molecules up to speed, the thruster must push at them. And when that happens, the gas molecules push back at the thruster. They are both pushing the other away from them.

The long explanation, in slightly more scientific terms: when inside the fuel tank, the gas molecules are in constant motion... they are bouncing hard against the walls of the gas tank, creating pressure as they recoil back into the tank every time they impact the walls. But since the tank is closed, the net forces on the tank balance each other out.

What happens when you use the thruster is essentially that you open a hole in the side of the tank. Now there is no wall there for the gas molecules to bounce off of; instead they just escape. That means that on the other side of the tank, where gas molecules are still bouncing against the wall, there is a force that doesn't have a balancing counterpart. That means that suddenly you have a net force on the tank, and so it starts accelerating.

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By conservation of the center of momentum. The center of mass of a jetpack plus it's propellant stays on a constant course (along an inertial frame of reference, e.g. the ISS orbit). This remains true whether the propellant is inside or outside the jetpack. By moving a mass of propellant one way, the jet-pack-wearing astronaut moves the other way, according to this relation, the essence of rocket science:

$$ m dv = -v_e dm $$

  • $m$ - mass of astronaut + jetpack + remaining propellant
  • $dv$ - change in astronaut's velocity
  • $v_e$ - velocity of the ejected propellent, relative to jetpack
  • $dm$ - mass of ejected propellent, also the change in stored propellent

By Noether's Theorem this conservation law is the same as translational symmetry, that moving through space doesn't change your laws of physics.

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