Chapter 33, Problem 5P

To determine

To Find: The parallax angle.

Answer to Problem 5P

  $p=0.0593\text{ second of arc}$

Explanation of Solution

Given:

Parallax distance of star, $d=55\text{ ly}$

Formula used:

Formula of parallax:

  $d=\frac{1}{p}$

Where,

  $p=$ Parallax angle.

  $d=$ Parallax distance.

Calculation:

  $\begin{array}{l}\because \\ 1\text{ pc = 3}\text{.26 ly}\end{array}$

Therefore, parallax distance of the star:

  $d=55\times \frac{1}{3.26}\text{ pc = 16}\text{.87 pc}$

Plugging in the given values in the formula:

  $\begin{array}{c}\text{16}\text{.87 pc = }\frac{1}{p}\\ \therefore \\ p=\frac{1}{16.87\text{ pc}}\\ =0.0593\text{ second of arc}\end{array}$

Conclusion:

Hence, the parallax angle: $0.0593\text{ second of arc}$ and $55\text{ ly = 16}\text{.87 pc}$ .