Final answer:
According to Einstein's theory of relativity, the space traveler ages less than their Earth-bound twin due to time dilation. Triplet A, who stays on Earth, will be older than Triplets B and C after their journey.
Step-by-step explanation:
According to Einstein's theory of relativity, time dilation occurs when an object is moving at a high velocity relative to another object. In the case of the twin paradox, the space traveler (Triplet B in this case) ages less than their Earth-bound twin (Triplet A). That means Triplet B would be younger than Triplet A after their journey.
To calculate the amount each triplet ages, we need to consider time dilation. Time dilation is given by the equation:
Δt' = Δt / √(1 - (v^2 / c^2))
Where Δt' is the proper time experienced by the traveling triplet, Δt is the time experienced by the Earth-bound triplet, v is the velocity of the traveling triplet, and c is the speed of light.
In this case, Triplet B travels to a planet and back, while Triplet C only travels to the planet and then returns at the necessary speed to arrive back at the same time as Triplet B. Both Triplets B and C will experience time dilation, but since the time experienced by Triplet C is the same as Triplet B, they will age the same amount. Triplet A, who stays on Earth, will age more than both Triplet B and C. Therefore, Triplet A will be older than Triplets B and C.