Find the distance in parsecs to Bernard's Star, which has an annual parallax of 0.549 arcsec.

1. Break Down the Problem

To find the distance to Bernard's Star in parsecs, we utilize the formula that relates distance and parallax: $d = \frac{1}{p}$ where $d$ is the distance in parsecs and $p$ is the parallax in arcseconds.

2. Relevant Concepts

The annual parallax (in arcseconds) is a measure of the apparent shift in position of a nearby star against a distant background due to the Earth’s orbit around the Sun. The formula mentioned above derives from trigonometric principles.

3. Analysis and Detail

Given:

• $p = 0.549 \, \text{arcsec}$

Substituting the value of parallax into the distance formula: $d = \frac{1}{0.549}$

4. Verify and Summarize

Calculating the distance: $d \approx \frac{1}{0.549} \approx 1.819 \, \text{parsecs}$

Final Answer

The distance to Bernard's Star is approximately $1.82$ parsecs.