Final answer:
The question involves the concept of time dilation and the twin paradox. The father wants to travel outward from Earth for 1 year and then back to Earth for another year, so that he is then 24 years younger than his daughter. The required constant speed parameter β can be determined using the time dilation formula and solving a quadratic equation.
Step-by-step explanation:
The question involves the concept of time dilation, which is a consequence of special relativity. According to the twin paradox, a space traveler moving at a high velocity relative to the Earth would age less than their Earth-bound twin. In this scenario, the father wants to travel outward from Earth for 1 year and then back to Earth for another year, so that he is then 24 years younger than his daughter. To calculate the required constant speed parameter β (relative to Earth), we can use the time dilation formula:
Δt' = Δt / √(1 - β²)
Where:
- Δt' is the proper time experienced by the moving observer (father)
- Δt is the coordinate time experienced by the stationary observer (daughter)
- β is the constant speed parameter relative to Earth
Using the given information, we can set up the equation:
1 / √(1 - β²) - 1 / √(1 - β²) = 24
Simplifying the equation leads to a quadratic equation, which can be solved to find the value of β. Once we find the value of β, we can determine the constant speed required for the trip.