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What advantages could time dilation have for interstellar travel? What could be some disadvantages?

An advantage of time dilation is that the same crew can operate a long term mission. A disadvantage results from communication back to Earth.

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Let me start by being clear that this question is asking for a subjective answer. While various sources may claim something is an advantage or disadvantage, you may safely disagree with those claims and explain why.

Time dilation is a wonderfully fun scientific phenomenon. In a simple explanation, time dilation results when one object, person, clock, etc. travels at a speed different from another object, person, clock, etc. There is a formula for it, but for the purposes of this question, that formula is unnecessary. Basically, the faster one clock/person moves, the slower time passes for that clock/person relative to the slower moving clock/person. The inverse is equally true. Time will pass more quickly for the slower moving object.

For speeds on Earth, time dilation is almost a non-issue. It does pose a threat to GPS satellites, but that threat has long ago been solved. For most space travel, time dilation is also a non-issue. The trips are too short or the speeds are too slow to worry about. When time dilation does become an issue is when you are considering interstellar travels at near relativistic (light speed) speeds. In these situations, time for the crews on board these very fast moving ships passes much slower than time passes for people on Earth.

This could be advantageous. It means that a single crew could cross vast stretches of space within the lifetimes of the crew members. There would be no need to design a space craft that supports and requires a crew to reproduce, raise, and train new crew members. A disadvantage is that the entire support staff on Earth would live and die (possibly several times over) before the space craft reached its destination. Political climates could change, and the crew could be left completely unsupported for their mission.

Fortunately, these problems are far in the future as humans haven't even come close to figuring out how to achieve the speeds necessary for realistically pursuing interstellar travel. For example, it took Voyager 1 nearly 35 years just to leave our own solar system.