The distances to nearby stars can be
measured using
parallax. However, it is not sufficient to measure a
nearby star's position from two different places on
Earth, even the
nearest star to the Sun is too far away for there to be
a measurable change in its apparent position. Even measuring from the
Moon wouldn't get you very far, we need a much larger baseline.
Since
Copernicus, we have known the Earth is not stationary, it orbits the Sun.
So, all we need to do is measure the stars' positions once, then wait six
months for Spaceship Earth to carry us 300 Million km (2 AU)
to the other side
of the Sun, and remeasure the positions. Some of the stars will appear
to oscillate very slightly due to parallax. The oscillating star
forms a very skinny isosceles triangle with the Earth, and the
six-months-ago Earth. The skinny angle is just the angular size of the
parallactic oscillation, and its opposite side is the
2-AU distance between the two instances of the Earth.
Thank Euclid, we can thus find the distance to the nearby star.
Using
ground-based telescopes, we can use this method to measure stars as far away
as several light-years. The limit is imposed by our
atmosphere, which blurs images of the stars, and hides oscillations
smaller than about 0.1 arcsecond. Recently, the Hipparcos satellite
was launched to measure parallax oscillations as small as a milli-arcsecond,
extending the reach of this method out to a few hundred light-years.
This is pretty far, but it's still only a tiny fraction of our
Galaxy.