# Distant and luminous stars using parallax angles?

Star A has a measured parallax angle of 0.1 arcseconds, while Star B has a parallax angle of 1.0 arcseconds. From the Earth, both stars are measured to have the same apparent brightness.

How do I find which star is more distant?

And how do I find which star is more luminous?

TIA!

Relevance

By definition a star which has a parallax angle of 1 arc second is at a distance of 1 parsec. A parsec is the commonly used distance measure in Astronomy. It is approximately equal to 19 trillion mines. Think of a triangle formed by the earth, the sun and the star. Its a very thin triangle. The angle at the star tip is the parallax angle - 1 arc second. The base of the triangle is the distance between the earth and the sun.

Star A at a parallax of 0.1 seconds is at a distance of 1/0.1 = 10 parsecs.

Star B is at 1 parsec.

Since Star A is more distant but appears just as bright, it must be more luminous.

Incidentally, there are no stars known within 1 parsec of earth. The closest star is the triple star system Alpha Centaurus at a distance of 1.26 parsecs.