The pods in 2001 make no sense
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Inertia. The pod would be automatically moving at the same speed and direction as Discovery, excepting the small relative changes as it maneuvers separately. It's really no different than throwing a baseball up in the air; just because it's left your hands doesn't mean it's suddenly lost the inertial momentum it had from the Earth's rotation.
The Discovery wasn't accelerating either. Its engines were off and it was coasting. The pods and everything inside Discovery is going the same speed. When the pods or a person leaves Discovery, they're still going the same speed.
Do you also think astronauts fall behind the ISS or the shuttle when they step outside?
You can make a case for why the pods were inside the ship (ease of maintenance, and protected from meteors and radiation by Discovery's thicker hull), and even why they each had their own door (space considerations made it impractical to have enough room in the pod bay to move them around internally, so each had to have its own way in or out), but there's really no way to justify that giant retractable docking dome on the moon that opened up to that tiny little elevator for the station-to-moon shuttle.
Hey, it's the 2000s. Everyone wants a dome with a retractable roof. Sports teams, the U.S. Congress... why not the moon base?
That's called gravity they slingshot themselves around planets, but that's not what's happening with the pods. Imagine stepping off a movie etrain even if it's slowing down it's still going to moving faster than you are once you step off.
You are confusing many things.
You compare a train with a space ship, and that's where you are wrong.
A train is surrounded by air. If you step outside the train, you are slowed down by friction.
A space ship is not surrounded by anything. It's a vacuum in space. If you step outside, you will not be slowed down by anything ever. You keep the speed. Virtually forever (unless you are affected by some force. Hit by a meteorite. Affected by the gravity of a planet or moon. Caught by a tractor beam.)
First, AFAIK the last time Voyagers or Pioneers did that maneuver is long, long, long ago. Second, you seriously need to read something about how that maneuver works. You approach a planet, its gravity AND its speed at which it orbits the sun accelerate you. And what you take from that maneuver is the speed from the orbit, and not the speed from the gravity acceleration. Because after you slingshot around the planet and move away from it, you lose exactly that speed again. What's left is the speed at which the planet itself moved through space. And THAT speed you keep forever, until another force affects you, and that's what Silvercrest was referring to.
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This.
Also if one wants to keep the argument ground based, look at Star Trek (2009): young Jim Kirk's stunt with the stolen car.
He drives it down a canyon, but jumps out at the last second. He jumps in the opposite direction but is still moving and sliding towards the canyon and only barely is no not falling to his death.
Same principle. Even though friction, gravity and his own thrust from the jump can't completely negate the motion force provided by the car until that point right away.
Another thought: what happens to a bullet fired from the back of a vehicle that already moves at the same speed as the bullet?
^Did that one on Mythbusters, sort of. They used a ball fired out of an air cannon rather than a gun but the principle is the same.
It'll drop straight down.
It'll drop straight down.
Well... the moviemakers don't. And some people use those as references. Look how many people think the human body would explode when exposed to the vacuum of space.
On the other hand, I'll give DWF some credit if he thought the Discovery was under acceleration at the time.
Don't be too sure.
I teach a unit on the Scientific Revolution in one of my European History courses, and I am frequently appalled by how many of my students do not know basic Newtonian physics.
I would bet $100 that if you asked everyone in America, "What falls faster - a 10 pound weight or a 1000 pound weight?" the majority would get it wrong.
It doesn't fire the engines in 2001. The only thing we ever see it do in that film is coast.
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