Convert the speed of light, 2.99 x 10m/s, to km/day also mph. If the Sun is 93 million miles away, how long will it take light to cover that distance?
The Correct Answer and Explanation is :
Correct Answers:
- Speed of Light in Kilometers per Day:
( 2.58 \times 10^{10} ) km/day (25,833,600,000 km/day) - Speed of Light in Miles per Hour (mph):
668,845,614 mph - Time for Light to Travel from the Sun to Earth:
500.56 seconds (approximately 8 minutes and 20.56 seconds)
Explanation:
The speed of light in a vacuum is approximately ( 2.99 \times 10^8 ) meters per second. To convert this into different units:
- Converting to Kilometers per Day:
- Since 1 kilometer = 1000 meters, we divide by 1000 to get km/s.
- There are 86,400 seconds in a day (( 24 \times 60 \times 60 )).
- Multiplying, we get:
[
\left( \frac{2.99 \times 10^8}{1000} \right) \times 86,400 = 2.58 \times 10^{10} \text{ km/day}
]
- Converting to Miles per Hour (mph):
- Since 1 mile = 1609.34 meters, we divide by 1609.34 to get miles per second.
- There are 3600 seconds in an hour (( 60 \times 60 )).
- Multiplying, we get:
[
\left( \frac{2.99 \times 10^8}{1609.34} \right) \times 3600 = 668,845,614 \text{ mph}
]
- Time for Light to Travel from the Sun to Earth:
- The average distance from the Sun to Earth is 93 million miles.
- Using the formula Time = Distance / Speed, we divide:
[
\frac{93,000,000}{668,845,614} \times 3600 \approx 500.56 \text{ seconds}
] - Converting to minutes, we divide by 60, giving 8 minutes and 20.56 seconds.
This confirms why we often say it takes about 8 minutes for sunlight to reach Earth.