When an astronaut goes on a space walk outside the space station will she float away unless she has a tether hold her to the station or she constantly fires thrusters on her space suit?

Answer 1

It depends upon the situation you place the astronaut in question. A tether is generally used only to act as a life line in case an astronaut starts to come adrift from their spacecraft or station, instead Velcro toe straps and handholds are used to keep astronauts where they need to work. However, this does not answer your question directly so allow me to create three scenarios.

Scenario 1:

An astronaut leaves their spacecraft and manages to completely stop themselves (although this would both be impossible, or close to it, and would result in the astronaut reentering the Earth's atmosphere) perfectly somehow in the middle of space. From there they will drift away from the space station; simply because they have stopped and the spacecraft hasn't.

Scenario 2:

An astronaut leaves their spacecraft and, while still orbiting the Earth at the same velocity as the spacecraft, stops moving in any other direction (again this would be near to impossible to achieve). In this case they would not float away from their spacecraft as there is very little force acting upon them and as f=ma (force = mass x acceleration) there would be no acceleration; thus no drifting.

Scenario 3:

An astronaut leave their spacecraft, and goes to do some work on a part of it from the outside; doing this they touch the spacecraft. Now there is a force being applied and so there would be an acceleration away from the spacecraft. This acceleration could and would be quite small, however with little resistance the velocity of the astronaut would pick up quickly and they would soon find themselves a long way away from their spacecraft.

So to reiterate my earlier point, the answer to your question would lie in the senario.