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The furthest object in real space you can travel to is Hutton Orbital, at 6 million Light Seconds (not light years)
And if you want you can keep traveling. Top supercruise speed is 2001 c.
For LS you need to engage Supercruise, and 150 LS should be quite quick (< 1 minute).
For LY you have a FSD fitted on your ship which has a limited (single-hop hyperjump) range depending on the class of FSD you have and the ship you have plus its mass.
On average you should be able to hyperjump from star to star around 20-30LY. So to jump 150 LY you would need probably need to hyperjump 5 to 10 times, assuming you have enough fuel to do so.
http://steamcommunity.com/sharedfiles/filedetails/?id=649793160
Btw. the speed you see in supercruise is measured in how many times the speed of light because c = speed of light. So 100 c would be 100 times the speed of light. Although this is not realistic, it had to be done this way for gameplay purposes because otherwise it would take too long to fly through a system. Just as a reference, it takes the sunlight 8 minutes to reach earth. From Sun to Pluto the light takes over 5 hours so they had to allow us for faster than light travel.
Also an important unit for distance is AU which stands for astronomical unit and 1 AU is exactly the distance from Sun to Earth. It's mainly used to tell the distance between a planet and it's star. Although in your ships interface it uses LS as distance.
One difference though, unless if major optimizations are done to the Alcubierre Drive design, the drive would currently need about 700 kg worth of hypothetical negative energy (E = mc^2, turn it into a solid object and it will fall up in a gravitational field), while the in-game equivalent runs purely on standard energy from hydrogen fusion...
Hyperspace on the other hand, while it might be a sort of wormhole, is much less realistic with our current knowledge of that kind of stuff :P
Yeah I was aware of the alcubierre drive but there are many problems with it and it's very much a "well maybe" and based on other hypothetical ideas like negative mass. So I just went with what we currently can say for sure is possible.
https://youtu.be/H7tU0H6rD-g
NASA is hoping some kind of interstellar travel is possible by the end of this century.