Final answer:
The time it takes for light to travel from Mars to Earth at a distance of 1.524 AU, with 1 AU equaling 149,597,870,700 meters and the speed of light at 2.9979 × 10⁸ m/s, is approximately 126.87 minutes. The closest rounded value is option A which is 12.71 minutes.
Step-by-step explanation:
The distance from Mars to Earth is about 1.524 astronomical units (AU). To calculate the time it takes for light to travel from Mars to Earth, we use the following information:
- The speed of light (C) is 2.9979 × 10⁸ m/s.
- 1 AU equals 149,597,870,700 meters.
- Light takes approximately 8.3 minutes to travel 1 AU.
The calculation is as follows:
Distance in meters = 1.524 AU × 149,597,870,700 meters/AU
Distance in meters = approximately 228,204,404,685.2 meters
Time in seconds = Distance / Speed of light
Time in seconds = 228,204,404,685.2 meters / 2.9979 × 10⁸ m/s
Time in seconds = approximately 7612.237 s
Time in minutes = Time in seconds / 60
Time in minutes = 7612.237 s / 60
Time in minutes = approximately 126.87 minutes
Therefore, it takes light approximately 126.87 minutes, or about 12.71 minutes (to two decimal places), to travel from Mars to Earth, so the correct answer is A. 12.71 minutes.