This is like Snakes on a Plane but on steroids. Instead of a plane, you’re on a spacecraft. Instead of Snakes, there’s a dead captain. And your mission, should you choose to accept it, would be to dock the craft right onto the ISS. With six degrees of freedom for translatory motion and six more for rotational alongside the ordeal of matching the speed of a giant artificial satellite that’s revolving around the Earth at 7.66km/s, all while trying not to fall back upon thy mother Earth and get roasted by the atmosphere in the process, you might have to pop a sweat or two to achieve your goal.
So, you start 1km away from the ISS travelling at 8.1km/s. You see the ISS approaching you at 0.5km/s. This speed seems to be lesser but it actually is 1800km/hr or 300 times faster than your ordinary speed limit. So, it’s fast!
Life in the orbit, however, is not very simple. The faster you go around the Earth, the higher you go above the Earth. The ISS hovers at about 408km above Earth. Your craft has achieved this height thanks to the effort by your captain who is chilling beside you. You look over. “Wait! He’s dead”, you say. He is indeed dead. There’s important cargo in your ship (we’ll cal it a ship from now on). And, it’s your duty to get it safely onboard the ISS.
On Earth where we usually move on two dimensions, with gravity keeping us grounded, going from A to B is quite easy. In space, a dimension gets added. In orbit, thanks to gravity your height becomes a function of resultant velocity in the two perpendicular directions. In vacuum, every force you exert is not cancelled out by air resistance. Combine all this and you’re in for a treat.
You calm yourself and try to visualize the 6 dimensions. If you move fast, you go up. You can’t. Your height is ok. So, for every reduction in speed, you must move up a little. Thankfully there are thrusters just for that. So, you try to slow down and move up simultaneously.
Right at this point, you see six more controls. You hit one and boom, ISS starts to rotate clockwise! No wait, it’s your craft that’s rotating counterclockwise. How do you cancel it? You try to rotate it in the opposite direction and suddenly the ship starts to tumble. Your pitch is now constantly changing and your nose is moving up. ISS seems to move down.
You might want to cancel these two but just for fun, you hit the third button. This alters your yaw. Now your ship’s trajectory is a mess! The question therefore becomes, can you really dock it?
Well, I can’t really answer for you, can I? Here, try out the simulation and let me know if you succeed…