Chapter 10, Problem 1RD

To determine

The way in which the stellar parallax used to measure the distances.

Answer to Problem 1RD

The astronomers view a nearby star from opposite side of the Earth’s orbit, but relative to the background starts, the position of this star changes. The amount of this motion is inversely proportional to the distance. The inverse of this motion measured in arc seconds equal to the distance

Explanation of Solution

The distance to the nearest stars can be measured using parallax. Parallax is the apparent motion of nearby objects due to the change in viewing position of the observer. The parallax is determined by comparing photographs made from the two ends of the baseline.

Astronomers are convenient to measure the parallax in arc second rather than in degree, because that stars are so far away, and the stellar parallax are always very small. The parallax decreases as distance increases. The relation between the distance and parallax can be expressed as,

    $\text{distance}\left(\text{in parsecs}\right)=\frac{1}{\text{parallax}\left(\text{in arc seconds}\right)}$

Conclusion:

Therefore, the astronomers view a nearby star from opposite side of the Earth’s orbit, but relative to the background starts, the position of this star changes. The amount of this motion is inversely proportional to the distance. The inverse of this motion measured in arc seconds equal to the distance.