Astronomers know that the distance between the Earth and the Sun averages 1.50 x108 km. How can astronomers use the observed stellar parallax and a little knowledge of geometry to measure the distance to nearby stars?

The distance of stars and the earth can be averagely measured by using the knowledge of geometry to estimate the stellar parallax angle (p).

From the equation below, the stars distances can be calculated.

D = 1/p

Distance = 1 / (parallax angle)

Stellar parallax can be used to determine the distance of stars from an observer, on the surface of the earth due to the motion of the observer. It is the relative or apparent angular displacement of the star, due to the displacement of the observer.

Explanation:

Parallax is the observed apparent change in the position of an object resulting from a change in the position of the observer. Specifically, in the case of astronomy it refers to the apparent displacement of a nearby star as seen from an observer on Earth.

The parallax of an object can be used to approximate the distance to an object using the formula:

D = 1/p

Where p is the parallax angle observed using geometry and D is the actual distance measured in parsecs. A parsec is defined as the distance at which an object has a parallax of 1 arcsecond. This distance is approximately 3.26 light years