The nearest stars are around 4×10 exponent 18. If light travels 300,000km/s, how long does the light from nearest stars take to reach us?
The correct answer and explanation is:
To calculate how long light from the nearest stars takes to reach us, we need to first convert the distance to a more manageable unit of measurement and then calculate the time it takes for light to travel that distance.
Given:
- Distance to the nearest stars = 4 × 10^18 km
- Speed of light = 300,000 km/s
Step 1: Calculate the time it takes for light to travel this distance
The formula to calculate time is: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}
Substitute the given values: Time=4×1018 km300,000 km/s\text{Time} = \frac{4 \times 10^{18} \text{ km}}{300,000 \text{ km/s}}
Step 2: Perform the calculation
Time=4×10183×105=43×1013=1.33×1013 seconds\text{Time} = \frac{4 \times 10^{18}}{3 \times 10^5} = \frac{4}{3} \times 10^{13} = 1.33 \times 10^{13} \text{ seconds}
Step 3: Convert the time into a more understandable unit
To convert seconds into years, we use the following conversions:
- 1 minute = 60 seconds
- 1 hour = 60 minutes = 3600 seconds
- 1 day = 24 hours = 86,400 seconds
- 1 year = 365 days = 31,536,000 seconds
Now, convert 1.33 × 10^13 seconds into years: Time in years=1.33×101331,536,000≈4.22×105 years\text{Time in years} = \frac{1.33 \times 10^{13}}{31,536,000} \approx 4.22 \times 10^5 \text{ years}
Final Answer:
The light from the nearest stars takes approximately 422,000 years to reach us.
Explanation:
This calculation highlights the vast distances between us and even the closest stars. While light travels at a speed of 300,000 km/s, these distances are so large that even at that incredibly fast speed, it takes hundreds of thousands of years for light to travel from one star to another. This also illustrates why we see distant stars as they were in the past and why observing distant objects in space can provide insights into the history of the universe.