To calculate the distance to Proxima Centauri in kilometers, we need to know the distance light travels in one year, which is defined as one light-year.

Step 1: Distance Light Travels in One Year

The speed of light, $c$, is approximately: $c = 299,792 \, \text{km/s}$

There are:

• $60$ seconds in a minute
• $60$ minutes in an hour
• $24$ hours in a day
• $365$ days in a year

So, the total number of seconds in a year is: $\text{Seconds per year} = 60 \times 60 \times 24 \times 365 = 31,536,000 \, \text{seconds}$

Step 2: Calculate One Light-Year in Kilometers

Using the speed of light, the distance that light travels in one year is: $\text{Distance of one light-year} = 299,792 \, \text{km/s} \times 31,536,000 \, \text{s} = 9.454 \times 10^{12} \, \text{km}$

Step 3: Distance to Proxima Centauri

Since Proxima Centauri is 4.3 light-years away, we multiply the distance of one light-year by 4.3: $\text{Distance to Proxima Centauri} = 9.454 \times 10^{12} \, \text{km} \times 4.3 = 4.06522 \times 10^{13} \, \text{km}$

Answer:

The distance to Proxima Centauri from the Sun is approximately: $4.06522 \times 10^{13} \, \text{km}$

Would you like more details or have any further questions?

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1. How is the speed of light measured?
2. What is the significance of Proxima Centauri in space exploration?
3. How does light travel through space, and what influences its speed?
4. Are there other stars closer than Proxima Centauri?
5. How long would it take a spacecraft to reach Proxima Centauri with current technology?

Tip: Remember, light years are used for vast distances in space because kilometers or miles would result in impractically large numbers!