Is the physics behind planetary travel simpler than atmospheric travel? I've been watching a bunch of documentaries lately and had a question that I couldn't really figure out the answer to online. When spacecraft travel through space, are the equations and physics used for them less complex than for, let's say, airplanes on Earth?
I know "complex" is a vague term, but what I mean is, to understand the physics behind an airplane movement, we'd probably have to consider many minor things such as altitude, humidity, air resistance, etc. 
However, for space, I was thinking that there might be less factors to consider, since none of the factors I mentioned above need to be taken into account. 
So, is the physics behind planetary travel (not the rocket takeoff part... just travel through space) not as complicated with as many significant factors (so ignoring minuscule variables), when compared to air travel? If so, do rocket scientists actually use "basic" equations (like Kepler's equation) when dealing with spacecraft? Or am I just very naive, and this question isn't possible to answer? 
 A: Spacetravel is simpler but more demanding.
You're right that there are fewer sources of complexity in space travel.  However, you need to be much more correct in your numbers, which typically makes space travel harder.
Consider an airplane that starts its 100km long journey 1 degree off.  Most airlines wouldn't even think of such a detail. They'd be 1.7km off at most, and somewhere along the line, you'd almost certainly correct it by accident.  Indeed, we actually see this in the Coriolis effect.  Its very rare for aerodynamic systems to need to take into effect the Coriolis effect because it's so small compared to other sources of noise (like wind) that you'll correct for it by accident.
Now consider a trip to Mars.  You start your 54,000,000km trip 1 degree off.  Now you're going to be about a million km off.  Also, you can't just assume corrections are easy. Spacecraft have to haul their fuel and reaction mass with them.  That correction could become exorbitantly expensive if you don't catch it early.
Why so expensive?  Airplanes get to correct their course by pushing on the air.  A 747 has a Lift-over-drag ratio of roughly 15.  That means for every 15kN of force they use to turn themselves by banking costs them just 1kN of thrust. They then get to produce that thrust using very energy-dense fuels, like jet fuel.
On the other hand, spacecraft have to haul their reaction mass with them.  This leads to something known as the "tyranny of the rocket equation." As you want to have more "delta-V", there is an exponential increase in fuel costs because not only do you need to plug up the fuel to provide that delta-V, you need to provide the fuel that hauls the fuel up to where you want to burn it.
As a result of this, while a fighter jet might have 30% of its mass in fuel, spacecraft regularly have 80-90%.  They also use incredibly exotic fuels to get there.  Because of the way the equations work, high "specific impulse" (ISP) fuels are highly prized.  Due to the quirks of units, ISP is typically measured in seconds.   While a typical air-breathing turbofan may get an ISP of 3000s, by stealing oxygen and other reaction masses from the air, rockets have to haul everything with them. The space shuttle SRBs weighed in at 250s and a high-end liquid hydrogen/oxygen system might reach 450s. That's right. The most exotic compounds we have for rocket fuel are 1/6th as efficient as a plain ol' turboprop because they have to haul everything with them, while the turboprop gets to breathe air.
Of course, those LOX/H2 engines are cryogenic. They need their fuels to be kept cold. If you're going on a many-month long journey, your fuels need to be able to be stored. For that, we tend to use rather exotic compounds like Hydrazine and N2O4. These are nasty compounds that call for their own unique handling. Hydrazine, for example, is hypergolic. This means that, if you expose it to the air, it catches fire.  Then it likely melts a hole in whatever was holding the rest of the hydrazine, and a flow of toxic flaming fluid will coarse through wherever you're holding it!
Not that the cryogenics are any easier.  A recent SpaceX failure was finally root caused to solid oxygen (not gas or liquid) forming inside the walls of the container of liquid helium they had.  Not many people in the world have experience with solid oxygen, much less any dangerous effects in might have had.
To get around this, many space missions rely on ion thrusters.  An ion thruster can get 3000s of ISP, but they generate millinewtons of force.  So missions that rely on ion thrusters have to do the equivalent of controlling an aircraft with the forces generated by a common housefly.
So in the end, yes, there are many more complex little nuances in aerodynamics.  It is more complex. But space is much more unforgiving.  There's a reason we had wars fought in the skies before we ever got anything to fly in space.
A: Just to add to what Cort said, most destinations in the solar system require an elaborate and lengthy series of sling-shot maneuvers around the existing planets, each requiring very precise aim. It's the only way they can build up sufficient speed to get where they want to go, and the only way they can slow down when they get there.
Every planet is traveling around the sun at a particular speed. If a spacecraft passes on the back side of the planet, it can pick up momentum from the planet and gain up to twice that speed.
If it passes on the front side, it will transfer momentum to the planet and slow down.
If it needs to go up or down out of the planetary plane, it can pass the downward or upward side of the planet, respectively.
Of course, to do this it has to make tiny course adjustments long before getting to the planet.
