Question

The star (other than the Sun) that is closest to Earth is Proxima Centauri. Its distance from Earth can be measured using parallax. Parallax is half the apparent angular shift of the star when observed from Earth at points on opposite sides of the Sun. The parallax of Proxima Centauri is 769 milliarcseconds. How far away is Proxima Centauri? (Give your answer in light- years with the correct number of significant digits.)

Short answer

Answer: The approximate distance between Earth and Proxima Centauri is 4.242 light-years.

Step-by-step solution

Convert milliarcseconds to arcseconds

First, we need to convert the parallax from milliarcseconds to arcseconds. We know that 1 arcsecond = 1000 milliarcseconds. So, let's convert the given parallax value (769 milliarcseconds) into arcseconds: 769 milliarcseconds = 769/1000 arcseconds = 0.769 arcseconds Now, we have the parallax in arcseconds, which is required for the parallax formula.

Calculate distance in parsecs using the parallax formula

Next, we need to calculate the distance between Earth and Proxima Centauri using the parallax formula. The parallax formula is: distance (in parsecs) = 1 / p (in arcseconds) Now, let's plug in our value of 0.769 arcseconds for 'p': distance = 1 / 0.769 ≈ 1.300 parsecs Now we have found the distance to Proxima Centauri in parsecs as 1.300 parsecs.

Convert distance from parsecs to light-years

Now that we have the distance in parsecs, we must convert it into light-years. To do this, we use the conversion factor 1 parsec ≈ 3.262 light-years. Therefore, distance (in light-years) = distance (in parsecs) * conversion factor ≈ 1.300 parsecs * 3.262 light-years per parsec ≈ 4.242 light-years Thus, the distance between Earth and Proxima Centauri is approximately 4.242 light-years.

Key concepts

Proxima Centauri Distance

Understanding the distances between stars and our planet offers valuable insight into the scale of the universe. Among the closest neighbors to Earth is Proxima Centauri, known to be the nearest star to our solar system, excluding the Sun.

Through the use of parallax—an apparent angular shift in position of an object viewed from two different points—astronomers can calculate how far away Proxima Centauri is from Earth. In the specific example provided, Proxima Centauri's parallax is given as 769 milliarcseconds. This tiny angle is a critical piece of information for astronomers, allowing them to unlock the secrets of stellar distances.

Arcsecond Conversion

Astronomical measurements rely on precise units, and one such smaller unit used is the milliarcsecond. It represents one-thousandth of an arcsecond.

To grasp the scale, imagine the sky as a vast dome overhead, divided into 360 degrees. Each degree is further split into 60 arcminutes, and each arcminute is then divided into 60 arcseconds. To convert milliarcseconds to arcseconds, as essential in our example, you divide the number of milliarcseconds by 1,000, thereby expressing the angle in a format more commonly used in astronomical formulas.

Parsecs to Light-Years

When the distance is evaluated in parsecs using the parallax angle in arcseconds, a new challenge arises: expressing this distance in a more familiar term—light-years. A light-year is the distance that light, traveling at an unimaginable speed of roughly 299,792 kilometers per second, covers in one year.

What is astonishing is the conversion rate: 1 parsec equals approximately 3.262 light-years. This ratio is used to convert the computed 1.300 parsec distance of Proxima Centauri into a more relatable measure—light-years—giving us the magical figure of approximately 4.242 light-years, a distance which light covers in over four years, highlighting the vast and wondrous expanse of space.

Why Light-Years Are Used

Light-years are much easier for us to comprehend since it relates to the speed of light, a constant we are familiar with, making interstellar distances a bit less abstract.