The Problem:
Light travels at a speed of 3.00 × 108 m s. Light from the star Sirius takes 8.65 years to reach the earth. What is the distance of Sirius from the earth in kilometers?
.Problem Statement
Light travels at a speed of 3.00 × 108 m/s. Light from the star Sirius takes 8.65 years to reach the Earth. What is the distance of Sirius from the Earth in kilometers?
Solution
Given:
- Speed of light (c) = 3.00 × 108 m/s
- Time taken (t) = 8.65 years
Step 1: Convert Time from Years to Seconds
1 year = 365.25 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds.
t = 8.65 years × 365.25 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute t = 8.65 × 31,557,600 seconds t = 273,000,000 seconds (approximately)
Step 2: Calculate the Distance
Use the formula: Distance = Speed × Time
Distance = 3.00 × 108 m/s × 273,000,000 seconds Distance = 8.19 × 1016 meters
Step 3: Convert Distance from Meters to Kilometers
1 kilometer = 1000 meters, so:
Distance = 8.19 × 1016 / 1000 km Distance = 8.19 × 1013 km
Final Answer:
The distance of Sirius from the Earth is approximately 8.19 × 1013 km.
