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Why is it believed that astronauts live longer than earthlings?
So, what I would like to know is that "If the belief is correct". If the belief is correct, how does that happen (what are the principles behind it).
And also from the INTERSTELLAR movie, which shows that the protagonist is still lesser in age than his daughter.
Correlation is not causation.
The time dilation effects are indeed present, but they account for making the astronauts "younger" by a couple milliseconds over their lifetime. Not something detectable in the grand scheme of things.
But astronauts aren't just Joe Averages taken off the street. They are chosen from, amongst other features, the healthiest, most fit, most durable candidates. They get optimal nutrition, they are required to remain in perfect condition, they get absolutely best medical care - and they end up rather rich when retiring, meaning they can afford to continue receiving great health care and living fit, healthy lives.
And obviously, people matching such health and lifestyle profile tend to live longer than the average, regardless of being astronauts or not - but people not matching such health profile don't become astronauts.
Note - as others in comments mentioned: radiation takes its toll, especially increasing mortality in astronauts who crossed the Van Allen belts source. Interestingly, LEO missions don't seem to have this effect despite radiation dose being similar (though more spread over time) and 0g effects on health being far more pronounced. Still, an average astronaut (space-faring or just "reserve") lives considerably longer than their country average.
I couldn't find actual papers on life expectancy of astronauts, so I performed some general calculations to give the number a 'bottom bar'. Using the list of space travelers I averaged lifespan and birth date of all space travelers deceased to date. Average birth year: 1937; average lifespan: 61.4 years. Only two of the 79 entries were women, so the result predominantly favors men; US life expectancy for 1937 was 58.0 years; I couldn't find the number for Soviet Union, only information that it overtook the US expectancy much later. Regardless, my figure is a heavy underestimation of the life expectancy - as it doesn't include any of the astronauts who were born before 1952 (when male expectancy was 65.8, meaning average man born then would die about now) and are still alive, bringing the average life expectancy of the astronauts way up.
So the article mentioned by OP did refer to time dilation. An astronaut in orbit does indeed experience time slowing down compared to humans on the surface on earth. However, this difference is incredible tiny for current astronauts. Quoting the Wikipedia article:
[A]fter 6 months on the International Space Station (ISS) (which orbits Earth at a speed of about 7,700 m/s) an astronaut would have aged about 0.005 seconds less than those on Earth.
You already experience a time dilation if you climb up a mountain or even a ladder. However, we're talking about incredibly small amounts of time here which are hard to measure.
See also: Have we attempted to experimentally confirm gravitational time dilation?
Your question is difficult to answer because it is ambiguous and conflates several ideas. I'll try to take them one by one.
No. There is nothing special about space itself that changes the perception of time. Even the word space is ill-defined, but it usually means "outside of Earth's atmosphere", that is, if you go up far enough, you'll end up there. An altitude of 100km is commonly accepted.
Therefore, if we define an astronaut simply as someone who goes into space, then obviously that won't change anything to their perception of time.
No. From your perspective, the rate at which time passes never changes. If you have a working clock with you, nothing you can do will alter the speed of the second hand.
Yes. It is possible for two people with identical clocks to meet again at a later time and see a difference in what the clocks indicate. This can happen even though neither individual ever saw a change in how fast the second hand moves.
This phenomenon is called time dilation. It happens when there is a difference in either velocity ("speed") or gravity. If I go faster than you, or if I am on a planet that has greater gravity than yours, then when we meet again, my clock will show a time earlier than yours.
This will happen even though both of us felt the time pass at the same rate. It's only when we compare our clocks that we'll notice a difference.
Sure. It will affect anything that moves at a different speed or experiences a different gravitational field. In the the case of an astronaut, they're probably in orbit, and so are going very fast. Therefore, their clock would show a time earlier than yours when they come back down on Earth.
But they're also at a higher altitude, and so will experience less gravity than you who is standing on Earth (about 90% on the ISS). Less gravity means that their clock would show a time later than yours when they come back.
The effects are opposite, but not equal. The net result is that after 6 months on the ISS, the astronaut's clock would be about 0.005 seconds earlier than a clock on earth.
Indeed. If we're both 30 years old and I hop on a very fast ship, I might come back after 50 years have passed on Earth, but only one year has passed for me. I will have aged less than you.
This is the ambiguous part and it is more of a language issue.
No, in the sense that if we were born at the same time and we both died at 80, we will both have lived the exact same time. If we had counted every second since our birth, we would end up with the same number. We both experienced the same amount of time even though we didn't die at the same time.
Yes, in the sense that after we reunited on Earth, I would die 50 years after you did. I would have been able to see things you couldn't. But once I die at 80, my second count will be the same as yours.
