FullMetalMachinist

I think this changed with 1.1 when they redid all the orbit line code. Careful, that shows the AN/DN nodes for the future orbit, after leaving and returning to Kerbin's SoI. It does not put the nodes back on your current orbit path.

Ah, you're talking about gravity losses. Strictly speaking, the tsiolkovsky rocket equation doesn't take that into account. A ship will have the same dV no matter what it's local gravity is. As a practical matter, if a ship has 1000 m/s dV but only 1.1 thrust-to-weight ratio, then no it's not going to get up to 1000 m/s. As for figuring that out purely by mathematical means, it's pretty non-trivial. But like you said, it only comes into play when you're climbing a celestial body's gravity well. This is why dV maps are extremely useful. You calculate your dV based on vacuum numbers, and the map tells you how much it takes to get to low orbit.

Not sure what you mean here. The dV equation is the same no matter what your current situation is. The only thing that might effect it is the presence of an atmosphere, which reduces the Isp of the engine. To get dV when you have multiple engines of the same kind is the same as when there's just one. If you have multiple different types of engines then it gets a little more complicated. You need to use the weighted average for thrust and Isp, then use those numbers for the dV equation. I'll admit I don't know the math well enough to quote it to you, but I know @Red Iron Crown does.

To expand on @Benjamin Kerman's answer, it also has to do with the rockets having lower efficiency in atmosphere. When you look at the engine stats in the VAB, there will be two numbers for Isp, one at sea level the other in vacuum. The oft-quoted 3400 m/s number is if you were to calculate the dV as if the whole flight took place in vacuum. This is just to make the math easier. In reality, when the first stage fires at sea level they are less effective, and it basically takes more than 1 m/s vac dV to actually give the craft 1 m/s atmo dV. That difference depends on the engine, but they are all worse in atmo. Combine that with gravity losses (if your rocket can accelerate at 20 m/s/s, gravity gobbles up 9.8 of that) and drag losses, and you get the roughly 1000 m/s difference that you see between the orbital speed and how much dV it took to get there. Also note that the magic 3400 number is an approximation that has been experimentally arrived at. There is no easy way to mathematically determine that number. Some rockets can get to orbit using less than that, some take more.

Awesome, congratulations! I've found that few games give me the sense of accomplishment that KSP does, mostly because you really have to earn those big moments. A bit of general advice for you going forward: less is more. In space flight, mass is everything. Best practice is generally to specifically design what you want each craft/mission to do. Then design a final stage that accomplishes that goal with as little mass as possible. Then stick that on a stage that pushes it where it needs to go with as little mass as possible. Rinse and repeat until you're sitting on the launch pad with the smallest rocket that can get the job done.

On those second two examples you are using the nuclear engine. I would seriously suggest against that for two reasons. First, you're using fuel tanks that have both liquid fuel and oxidizer (LFO), but that engine only uses liquid fuel. That means you're carrying around a bunch of oxidizer that you don't need. And even if you drain the oxidizer out before you launch, it is still not very efficient because now you start with a half-empty tank. Better to use the LF only airplane fuel tanks. The second reason is the mass of the the nuke engine. It's really heavy, which means that it's better efficiency only counters that heavy mass when your ship is really heavy. For a craft that small the heavier engine is hurting you more than the better fuel efficiency it gives you. You'd be better off with the small Terrier engine.

Don't forget that you also have to bring the RCS thrusters. So it's like bringing moonshine and a 300lb guy named Bubba who drinks the moonshine and pushes the car.

You've almost got it. You just don't need the second 860 and 3400. The reason is that you can use Kerbin's atmosphere to do that part of the work for you (called aerocapture or aerobraking). And yes, adding some extra is usually a good idea. I usually add 20-40% more.

Since the SRBs and the LF-O engine have different exhaust velocities, do you not have to use the weighted average for figuring out the dV of the portion when they're firing together?

It is most certainly possible to get a low flyby and also have a re-entry trajectory into Kerbin. It just takes loads of fiddling with the maneuver node. Here's a good and quick tutorial.

Just FYI, you don't need the HG-5 direct antenna. The relay antenna will take care of both talking to Kerbin and to other ships.

Ever since 1.2.2 (or 1.2.1, can't remember now) the default key was changed to back quote (~ key to the left of the 1 key). They did that to avoid a conflict with the default abort action group, which is also backspace.

I don't have any specific numbers for you, but it depends. Whether you are using the small or big converter, whether you have an Engineer kerbal aboard, and what level that Engineer is all have an effect on the conversion rate.

Yes, but they changed the default key to back quote (the ~ button to the left of the 1 key). They did that to avoid a conflict with the default key for the 'abort' action group, which is also backspace.

Not sure without seeing a screenshot. But there most certainly should be one attachment node. The game won't let you save a sub-assembly if there isn't. It might not be exactly where you want it, but there should be one. Probably what you need to do is open the file where you first built the sub-assembly and change the root part to be the docking port on top. Then save that as your sub-assembly.

Maybe try right clicking on the probe core on the rover and select 'control from here'?

Shift+click on any part on the craft does the same thing as clicking on the root part.

When dragging the handles, if you 'push' instead of 'pull' it's a slightly finer adjustment. So if you want to add just a bit of prograde, push the retrograde handle towards the middle instead of pulling the prograde one out. Also for the scroll wheel, it scales with how quickly you spin it. If you go very slowly, like one click a second, the dV added per 'click' is very small. If you spin it quickly, each 'click' is worth more, and you get a very big change.

You don't have to be directly docked to the fuel tank itself to transfer fuel. Any docking port in any location will let you transfer any resource (fuel, oxidizer, ore, electric charge).

Yes, you need either a command pod with a kerbal inside, or a probe core.

Since you obviously completed the contract, I would just force it to complete. Hit mod-F12 ('mod' being whichever key is the modification key for your system, Alt on Windows) to open the debug menu, go to the contracts tab, and hit the "Com" button on the correct contract to complete it.

This bit makes it sound like you might be pressing space bar to try and get the engine to fire again. Correct? If so, don't do that, it stages away your engine and won't be part of your ship anymore. Instead press left shift to throttle up, or press z to go full throttle. If that's not the problem you're having, a screenshot will be helpful.

Because Pythagoras was a magnificent person. Treat the vertical and horizontal percentages as the two short legs of a square triangle and run it through the Pythagorean theorem. It'll give you something very close to 100%.

Dunno. Did you perhaps start that game before 1.2.1 came out? That would cause the game now, even if it's been updated, to have your previous keybindings.

Yeah, I've found that even in small "bugfix" updates, there are at least one or two changes like this that are useful to know. I make a habit of reading the whole changelog when a new version comes out.