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.

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