Traveling at near-light speeds presents significant challenges due to relativistic effects, energy requirements, and technological limitations. However, let's explore the hypothetical scenario of traveling close to the speed of light and the distances that could be covered within certain time frames according to an observer on the spacecraft.
According to Einstein's theory of special relativity, as an object approaches the speed of light, its mass increases, time dilation occurs, and length contraction takes place along its direction of motion. These effects become more pronounced as the object's speed approaches the speed of light.
Let's consider some examples:
One year onboard time: Suppose the travelers want to experience one year of onboard time while traveling. From the perspective of an observer on Earth, more time will have passed due to time dilation. Assuming constant acceleration and deceleration to reach near-light speeds, the distance that can be covered within one year of onboard time would be limited by the effects of time dilation and the available energy. However, it's difficult to provide an exact distance without specific technological capabilities.
To a nearby star: Let's consider the closest star system to our solar system, Alpha Centauri, located about 4.37 light-years away. Suppose we could travel at 90% of the speed of light. From the perspective of the travelers onboard, time dilation would make the journey seem shorter. However, from the perspective of an observer on Earth, the journey would take more than 4.37 years.
Across the Milky Way galaxy: The Milky Way galaxy has a diameter of about 100,000 light-years. Even at near-light speeds, the time required to traverse such distances would be immense. From the perspective of the travelers onboard, time dilation effects would make the journey shorter, but it would still take a considerable amount of time from the perspective of an observer on Earth.
It's important to note that the practical challenges associated with achieving and maintaining speeds close to the speed of light, as well as the energy requirements and technological constraints, make interstellar travel at near-light speeds highly challenging with our current understanding and technology.
Additionally, the distances between galaxies and the expansion of the universe introduce further complexities and limitations when considering travel on cosmological scales.