Question

A star is located 12.5 parsecs away from us. What is its parallax angle? D = 1/p

Answer 1

Answer:

The parallax angle is 0.08 seconds of arc.

Explanation:

In the image attached you can observe where is the parallax angle placed.

Now, this parallax angle is inversely proportional to the distance measured in parsecs. That means, the greater the distance, the smaller the parallax angle.

Mathematically, it's defined as

$D=\frac{1}{p}$

Where $D=12.5 pc$, replacing this value, we have

$D=\frac{1}{p}\\p=\frac{1}{D}=\frac{1}{12.5 pc} =0.08''$

Therefore, the parallax angle is 0.08 seconds of arc.

Answer 2

You are given a star that is located 12.5 parsecs away from us (let us assume that the reference point is on earth). You are tasked to find the parallax angle. The equation to get the parallax angle is D = 2 (AU)/ tanФ wherein D is the distance of the star from the earth, AU is the distance of earth from the sun and Ф is the parallax angle. Note that 1 parsec = 1,000,000,000,000 million meters and that the distance of earth to the sun is about 149,600,000,000 meters.

D = 2 (AU)/ tanФ
tan Ф = 2 (AU)/D
Ф = tan⁻¹ [ 2(AU) / D]
Ф = tan⁻¹ [ 2(149,600,000,000) / 12,500,000,000,000]
Ф = 1.37°