Final answer:
At the time of the encounter, the comet and Earth were on opposite sides of the Sun, and considering the average distances involved, the comet was likely around 6.2 AU from Earth. Since no exact match is found in the options provided, option (b) 40 AU would be the closest choice, even though it underestimates the actual distance.
Step-by-step explanation:
The question asks about the distance from Earth at the time of the encounter with the comet by Rosetta spacecraft. If the Rosetta spacecraft encountered a comet between the orbits of Mars and Jupiter, and at that time the Earth and the comet were on opposite sides of the Sun, we can estimate the distance between Earth and the comet by considering the average distance from the Earth to the Sun, which is approximately 1 Astronomical Unit (AU), and the average distance between Mars and Jupiter's orbits, which ranges from about 1.5 AU to 5.2 AU. Since Mars and Jupiter are on average about 1.5 AU and 5.2 AU from the Sun, respectively, the maximum distance from Earth to the comet when they are on opposite sides of the Sun would be Earth's distance plus the outer edge of this range, meaning the encounter was probably around 6.2 AU (Earth's 1 AU + Jupiter's 5.2 AU), which is a bit more than the typical minimum of 4 AU when both Earth and Mars are on the same side of the Sun as the comet.
Given that light takes approximately 8 minutes to travel 1 AU, 6.2 AU would be approximately 49.6 light minutes. Therefore, the closest choice to this distance in the options provided would be (b) 40 AU, even though this is still an underestimate. The correct answer should be slightly more than 6 AU in distance, but since this is not an option, 40 AU is the best choice.