Well, let’s not put the cart before the horse. Right now we don’t know for sure that any life exists anywhere other than Earth. We suppose it does by mathematical calculations, but we haven’t even found a fossil of a microbe from space.
Secondly, suppose there is some super advanced civilization (your use of “exponentially” doesn’t seem to make any sense), the reason they probably haven’t completely colonized the entire Milky Way Galaxy is that for them, as for us, the laws of physics make it pretty much impossible to achieve interstellar travel because of the vast distances involved. And even if they could colonize some surrounding systems by now, it would take light and radio waves 100,000 years to reach us from the other side of the galaxy.
Proxima Centauri, is our nearest star, about 4 light years away.
A light year is the distance light travels in one year, or 9,460,730,472,581 kilometers. That’s 9.46 trillion kilometers, or about 5.88 trillion miles.
The fastest space ship we ever built was the Juno spacecraft, which in 2016 broke all speed records in space with a gravity assisted acceleration up to 164,700 mph.
The problem with going much faster than that is General Relativity and propulsion. Even with all the fuel in the solar system, it would still take an infinite amount of fuel to approach the speed of light. There’s no warp speed or aliens that have somehow “broken” the laws of physics. You can’t approach the speed of light.
If, however, you could go, say 40 times faster than Juno (there’s no existing technology that would come anywhere near this speed), you’d be going about 6.58 million miles an hour. That’s a hypothetical but impossible speed by either humans or space faring aliens, but none the less, for the sake of argument, let’s say you could go that fast.
Light travels at 670,616,629 miles per hour (as a layman and lazy American I think in miles more easily). So your space craft is amazingly, impossibly, traveling slightly less than 1% the speed of light. We’ll round it up for arguments sake. You’re going now 6.7 million miles an hour. Don’t crash into an asteroid at that speed!
How long would it take to make the trip to Proxima Centauri 4 light years away? Well, if you were going 1% the speed of light (6.7 million miles an hour) it would take you 400 years to reach the nearest star.
Unfortunately, you can’t just get up and go 6.7 million miles an hour. You’ve got to build up speed, which conceivably would take years burning some kind of fuel source that would weigh as much as the Moon because you’d need so much of it (which would slow your acceleration). The problem is the faster and longer you want to burn fuel, the more fuel you need, which increases your weight and decreases your acceleration. Remember, also, as you approach any percentage of the speed of light at all, the amount of fuel required to accelerate your spacecraft any faster begins to increase exponentially because of the law of General Relativity.
At the other end of the trip you’d need the same time and fuel to slow down so you don’t overshoot your target.
People have thought about using light propulsion. From somewhere in Earth orbit, shooting a powerful laser at a reflector at the back of the outgoing spaceship. It would be slow, but eventually it would increase in speed. They’d still need fuel at the other end to slow down.
It’s difficult to know how to figure in that acceleration and deceleration process, so I usually, for the sake of argument, just double the time, which probably isn’t far off.
That would mean it would take you about 880 years to start out, accelerate to 6.8 million miles per hour, and then slow down at the other end. That’s how long it would take to reach our nearest star.
As far as we know, there’s not even any interesting planets over there. If you want to go somewhere more interesting you’d probably have to go farther out in a different direction to the Trappist-1 system, which is 40 light years away.
That would only take you 8,000 years each way. We’re talking eight thousand years. You’d need a generational spacecraft, where hundreds of people lived and died for thousands of years before they reach where they’re going. Would these descendants of the original pioneers have any idea what to do when they got there? Would they resent being in space because their ancestors decided they should be? Would the spacecraft hold up and not fall apart after 8,000 years of usage? How would they have enough food and water?
Depressingly, these are only the closest stars, right around our neighborhood. There are many more stars in our local group, and billions more in the galaxy, and millions of galaxies.
All we can do is watch them, study them, wonder about them and so on. We will, however, never be able to visit them, and those aliens out there unable to visit us.
Faster than light speed will never be possible, ever. The best you’ll be able to do is maybe 1/10th the speed of light given an enormous amount of propellant, and then you’ll have to slow down at the end of the trip using just as much fuel as it took you to go that fast in the first place. There will be no warp drive or something that folds space. These are all convenience devices for story telling on science fiction movies.
Maybe in 200 or 300 years generational space environments will be the way to travel to other planetary systems. A generational space environment is a huge ship that rotates for a sense of gravity inside, where whole generations are born and die over hundreds of years – often resenting that their ancestors trapped them on that ship – to reach far away places.
Your given time frame of 100 years from now is not very far away in the bigger picture, but having a huge telescope on the far side of the moon is possible and would help with astronomical observations.
Great question, and you see, that’s what we mean when we say everything is relative. Your “speed” is always relative to something else. If you don’t compare it to something else, you might as well be standing still.
Relative to you, the other spaceship is standing still. You are both just floating there while Earth quickly moves away from you.
If you were going 90% the speed of light relative to your launching site on Earth, then if you looked back at Earth through a telescope you’d see them all aging very quickly, but to you and your neighboring spaceship, you’d both not experience any personal change. You’d be able to see the other ship and vice versa quite normally.
In fact, if you took a flashlight and pointed it straight ahead in the direction of your travel, even though you were going 90% the speed of light relative to Earth, the beam of light would leave your flashlight at the speed of light relative to you. That’s only possible because time has slowed down for you, making light always look like it’s going light speed. You will not notice any change personally.
On Earth, people looking at you in a telescope would see you were moving and aging very slowly, and although the light of your flashlight would not appear to be going much faster than your spaceship, because your time has slowed down, you see it going out at the speed of light and people on Earth are moving slowly.
Consider this. Here you stand or sit. But the earth is spinning at about 1000 mph at the equator. We are also going around the sun at about 67,000 mph and orbiting the galactic center of the Milky Way galaxy at about 514,000 mph, and our galaxy is approaching the Andromeda Galaxy at about 250,000 mph. So you are not standing or sitting still at all! You are moving very fast right now, but when you shine a flashlight in all directions the beam leaves your flashlight at the speed of light relative to you and your sense of time.
The same happens to you and your friend in the nearby spaceship. You can look out the porthole, see him, and wave and he can see you and wave back as if both your ships were stationary in space and just floating next to each other. It’s all relative.