unit of distance used in astronomy is the parsec (pc):

1 pc = 3.26 ly.
The distance to the Earth's next-nearest star, α-Centauri, is 1.3 pc. Find the distance d to α-Centauri in light-years and in meters.

1 pc = 3.26 ly

=> (1 * 1.3) pc = (3.26 * 1.3) ly
=> 1.3 pc = 4.238 ly

So, the distance is 4.238 light years

1 ly = 9.461 * 10^15 m
4.328 ly = 4 * 10^16 m

To find the distance to α-Centauri in light-years and meters, we can use the conversion factor provided: 1 parsec (pc) = 3.26 light-years (ly).

Given that the distance to α-Centauri is 1.3 pc, we can now calculate its distance in light-years:

Distance in light-years = 1.3 pc × 3.26 ly/pc
= 4.238 ly

Therefore, the distance to α-Centauri is approximately 4.238 light-years.

To convert this distance to meters, we need to use another conversion factor. The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s).

We know that 1 light-year is the distance light travels in one year, so:

Distance in meters = 4.238 × (9.461 × 10^15 m/yr)

Thus, the distance to α-Centauri is approximately 4.009 × 10^16 meters.