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Navigation in space

On Star Trek the captain commands 'all stop!'. The navigator relies 'forward motion stopped captain'.

A practical question for space travel. If you think you are stopped in deep space, how do you know?

In the solar system going from Earth to Moon is based on known relative velocities and positions relative to solar system coordinates.

It would be the same question for alleged ET visitors performing precision navigation over light years distance in a constantly changing galaxy.
everything would get farther away.. in deep space that is...
 
On Star Trek the captain commands 'all stop!'. The navigator relies 'forward motion stopped captain'.

A practical question for space travel. If you think you are stopped in deep space, how do you know?

Motion is usually referred to the local environment, with exceptions noted where necessary: What Is the Difference Between Airspeed and Ground Speed?

For a planetary system, that would be motion relative to the nearest dominant mass. Thus, for low Earth orbit, that would be motion relative to the Earth. To quantify that, one would see if one is inside that object's  Hill sphere For the Earth, that is about 1.47 million kilometers or 0.0098 AU, a distance that the Moon is well inside of. For the Moon itself, that is 61,500 km.

For interstellar space, that would be motion relative to nearby stars. For nearly interstellar space, that would be the  Local Standard of Rest

In the solar system going from Earth to Moon is based on known relative velocities and positions relative to solar system coordinates.
One uses Earth-relative coordinates there, since the Earth is gravitationally dominant for most of the trip. Near the Moon, one must use Moon-relative coordinates, however.

It would be the same question for alleged ET visitors performing precision navigation over light years distance in a constantly changing galaxy.
They would likely be traveling much faster than the relative velocities of the stars, and the stars' motions are effectively linear for timescales shorter than their Galactic-orbit timescale. So navigation won't be as difficult as that comment makes it seem.
 
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