The time it would take for a ship traveling at nearly the speed of light to reach another star system depends on the distance between the star systems and the speed at which the ship is traveling. Let's consider some examples to get a sense of the timescales involved.
The nearest star system to our solar system is the Alpha Centauri system, located approximately 4.37 light-years away. For the purpose of this calculation, let's assume the ship is traveling at 99% of the speed of light (0.99c).
At this speed, time dilation effects predicted by Einstein's theory of relativity come into play. From the perspective of an observer on Earth, time onboard the ship will appear to pass more slowly. However, for the travelers on the ship, their experience of time will be unaffected.
Using the time dilation formula, the time experienced by the travelers onboard the ship would be given by:
Δt_ship = Δt_earth / √(1 - v^2/c^2)
Assuming Δt_earth is the time it takes from the perspective of an observer on Earth, we can calculate the time experienced by the travelers.
For the Alpha Centauri system, if we consider Δt_earth to be 4.37 years (the distance in light-years), and plug in the values:
Δt_ship = 4.37 years / √(1 - 0.99^2)
Calculating this, we find that the time experienced onboard the ship would be approximately 0.14 years, or about 51 days.
So, from the perspective of the travelers on the ship, the journey to the Alpha Centauri system would take around 51 days, while from the perspective of an observer on Earth, it would take 4.37 years.
It's important to note that reaching speeds close to the speed of light is currently beyond our technological capabilities, and the calculations above are purely hypothetical. Additionally, factors such as acceleration, deceleration, and the need for energy sources capable of sustaining such high velocities pose significant challenges for interstellar travel.