The irony is: you can actually see Earth on the Galaxy Map (scroll with right MB, zoom/unzoom with wheel). But if you think you can reach it as you say by just plotting a course then sorry, you are plain wrong...
About the game:
TLJH is a mix of space adventure, strategy and tactics which you constantly need to apply in deciding what to do next. What you can do mainly depends on your ship status, your crew health, your status with aliens and other things. There is a trading system in place, you need to earn credits to buy important ressouces for your ship, and unlike many space games, your credits will not always increase and be on the high side, just another challenge for you to do things right.
Do not expect to succeed once you launch the game for the first time, the game is damn difficult (even in Story Mode suited for beginners) and more often than not you will get stranded in space, lose all of your crew or get sunk during a combat. Do not get frustrated, but start a new game that will be different when you use a new 'Seed', the seed totally changes the galaxy. You will have learned from your past experience and you can improve and - slowly but surely - get closer to Earth next time. The highlight in this game IMO is the nice intereaction with the aliens. Do not interact at random because every dialogue will have impact on your mission.
I find this game way too difficult, but that's exactly what makes it captivating, if you are not frustrated by the many failures it should get you come back soon. Very high re-playability.