Final answer:
In 2003, the distance between Earth and Mars when they were closest could be calculated using the time it takes for light to travel from the Sun to each planet. The distance came out to approximately 56 million kilometers, which corresponds to option (a).
Step-by-step explanation:
In 2003, Earth and Mars were the closest they had been in 50,000 years, with Earth positioned between Mars and the sun. Light took 500 seconds to reach Earth from the sun and 687 seconds to reach Mars. The question asks what the distance was from Mars to Earth.
Given that it takes light 499.004854 seconds to travel one astronomical unit (AU), which is the average distance from Earth to the Sun (approximately 149,597,870.7 kilometers), we can calculate the distance in AUs. Since Earth was between Mars and the sun, we subtract the light travel time from Earth to the Sun (500 s) from that of Mars to the Sun (687 s) to find the light travel time from Mars to Earth, which is 187 seconds (687 s - 500 s).
Now, to convert the light travel time into distance, we divide the 187 seconds by 499.004854 (the number of seconds it takes light to travel one AU) to find the distance in AUs, and then multiply by the distance in kilometers for one AU:
Distance (AU) = 187 seconds / 499.004854 seconds/AU
Distance (km) = Distance (AU) × 149,597,870.7 km/AU
Performing the calculations will result in a distance of approximately 56 million kilometers, which corresponds to option (a) 5.6×107 kilometers.
The correct option in the final answer is (a).