Stars: What is the parallax angle for Proxima Centauri, which is Earth's nearest star at 4.3 ly? Earth's orbit around the sun has a mean radius of 1.5 × 10⁸ km, and 1 ly = 9.461 × 10¹⁵ m. A) 1.2 × 10^-14 degree B) 2.1 × 10^-4 degree C) 1.2 × 10^-7 degree D) 2.1 × 10^-7 degree E) 2.1 × 10^-14 degree

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Quizplus · Accepted Answer

The parallax angle can be calculated using the formula for parallax in astronomy, which is $p = \frac{1 AU}{d}$, where $p$ is the parallax angle in arcseconds and $d$ is the distance to the star in parsecs. Since 1 parsec (pc) is equivalent to approximately 3.262 light-years (ly) and Proxima Centauri is 4.3 ly away, we first convert the distance from light-years to parsecs: $d = \frac{4.3}{3.262} \approx 1.318$ parsecs. The parallax angle in arcseconds is then $p = \frac{1}{1.318}$, which is approximately 0.759 arcseconds. To convert this to degrees, we use the fact that there are 3600 arcseconds in a degree, so $p = 0.759 / 3600 \approx 2.1 \times 10^{-4}$ degrees.

Stars: What Is the Parallax Angle for Proxima Centauri, Which