Final answer:
Given the distance to Alpha Centauri and the speed of light, it can be calculated that a radio message received from there today would have traveled for approximately 4.4 years, meaning it would have been sent 4.4 years ago.
Step-by-step explanation:
The nearest star beyond the sun is Alpha Centauri, which is 4.2×10¹⁶ meters away. To show that a radio message received today from Alpha Centauri would have been sent 4.4 years ago, we must calculate the time it takes for light (or a radio message) to travel this distance. The speed of light is approximately 299,792,458 meters per second.
To find out the time in seconds, we divide the distance by the speed of light:
Time (seconds) = Distance (meters) / Speed of light (meters/second)
Time (seconds) = 4.2×10¹⁶ m / 299,792,458 m/s
Time (seconds) = 1.401×10°⁹ s
To convert this time into years, we use the fact that one year is equal to 31,557,600 seconds (365.25 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute).
Time (years) = Time (seconds) / Seconds per year
Time (years) = 1.401×10°⁹ s / 31,557,600 s/year
Time (years) = 4.4 years
Therefore, a radio message received from Alpha Centauri today would have been sent approximately 4.4 years ago.