Chapter 33, Problem 6P

To determine

To compare:

The parallax angle of the farther star with nearer star.

Answer to Problem 6P

  $p_2=\frac{p_1}{2}$

Explanation of Solution

Given:

Parallax distance of nearer star, $d_1=d$

Parallax distance of further star, $d_2=2d$

Formula used:

Formula of parallax:

  $d=\frac{1}{p}$

Where,

  $p=$ Parallax angle.

  $d=$ Parallax distance.

Calculation:

Let the parallax angle of the nearer star be $p_1$ and farther star be $p_2$

According to the formula, parallax angle is inversely proportional to the to the parallax distance, therefore:

  $\begin{array}{c}\frac{p_2}{p_1}=\frac{d_1}{d_2}\\ =\frac{2}{1}\\ p_2=\frac{p_1}{2}\end{array}$

The parallax angle of the farther star would be less than that of the nearest star.

Conclusion:

Hence, the parallax angle of farther star would be half that of the nearer star.