When it is mentioned at all, the force of gravity is often portrayed as a sort of cosmic quicksand, an intractable mire that can yank spacecraft out of the sky without any consideration of orbital momentum. Frequently accompanied by exclamations like, "We're caught in the planet's gravitational field!" or "We're being sucked in!"
Obviously not Truth in Television. Gravity is what allows stable orbits to exist — without gravity, Earth would just fly away from the Sun (disregarding for a minute that without gravity, both would fail to form in the first place). Even increasing gravity, until a certain point, would not cause an orbiting body to fall onto the planet, but would simply shift it to a different orbit.
Black Holes are particular offenders of this nature, because everyone knows that their gravitational pull is so powerful even light cannot escape and the subatomic particles that constitute you will be ripped apart. Scientists even called this effect "spaghettification", although this only applies to the event horizon inside the black hole, not the orbiting accretion disk around it. See also Analysis for cases on when this trope does not apply and when it does.
A subtrope of Space Does Not Work That Way and the cousin of Space Friction. See also Gravity Master, when a character has the power to control it.
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In Dragon Ball, the gravity from King Kai's miniature planet, which manages to be pull at 10 times the force as on Earth despite its size, doesn't affect anything unless it gets within a few hundred feet, then you immediately get pulled toward it. To be fair, that is in the afterlife, so there's no reason the physical laws would be the same, or even exist.
When Mike crashes into, then attempts to save, the Hubble telescope in MST3K: The Movie, it immediately drops away and falls to Earth. An incredulous Mike points out that it couldn't possibly do that.
Star Trek III. When the Enterprise's Self-Destruct Mechanism activates, the explosions in the saucer section are sufficient to knock it out of orbit and plummet dramatically as it burns up in the atmosphere.
In the 2009 Star Trek film, Kirk, Sulu and Ensign Ricky drop straight down toward Vulcan's surface as soon as they jump out of the shuttlecraft.
The Super-Star-Destroyer-into-Death-Star was explained in the novel as them being at full speed maneuvering through the battle, and that A-Wing crashing into the bridge disabled the controls and the entire command hierarchy. If they hadn't been aimed directly at the Death Star, then they could have reestablished control from engineering and brought her back around. As Imperial designers were more concerned about a mutiny than the 1-in-a-million chance that you would be aimed at an object large enough to do damage when the bridge is destroyed, it wasn't designed to be easy to do.
The Astronaut Farmer has loads of horrible physics, but one shining example is the eponymous character's reentry. After a de-orbit burn lasting less than a few seconds, the craft appears to stop, and just drops straight down.
Supernova has one scene where the medical ship Nightingale drops like a rock toward a moon as soon as it completes its FTL jump. Most of the movie's physics are accurate, but the ship would have retained the velocity and momentum it had before the jump. Even if the ship's velocity relative to the moon was below the moon's escape velocity, it would not have plummeted straight down.
Actually averted in the Star Wars Expanded Universe novel Vector Prime, where the weird gravity device used by the Yuuzhan Vong to Colony Drop Sernpidal's moon onto the planet does not cause a "sucking" effect, but instead the moon's orbit decays more or less realistically every time it passes over the device. Not that there's anything realistic about a superweapon that produces a gravitational force greater than a planet's.
Live Action TV
In the Doctor Who episode "Voyage of the Damned", the starship Titanic begins to predictably crash into the Earth as soon as its engines fail. This might be justified, though, as the ship's owner was planning to crash it, so it was already on a collision course to begin with.
Let's not forget "The Impossible Planet", where the Doctor repeatedly says that it's "impossible" for a planet to be in orbit of a black hole - and when the artificial gravity machine fails, the planet gets sucked straight inward, as is the spaceship in which the humans are trying to escape.
In "The Name of The Doctor" The TARDIS drops like a stone towards the planet Trenzalore the very second The Doctor turns off the anti-gravs.
An example of failing to recognize what an orbit is shows up in Stargate Atlantis. In "Inferno", they jump a ship to "orbit" using the hyperdrive and magically going into orbit (their sublight propulsion/maneuvering system was inoperable at the time). In reality, the ship would start to fall. Fast. Usually the problem of orbit vs. altitude is handwaved via the same mechanism which brakes the ship as it goes sub-light. That's the kind of thing which makes it so hard to make an actually realistic space simulator appear as realistic to the layman.
In an early episode of Mystery Science Theater 3000, a number of space dog skeletons (or whatever they were called) were piling up onto the space station in such numbers that they were weighing the station down to the point where it was dropping the orbit. Remember the MST3K Mantra.
Averted in the Star Trek: The Original Series episode, "Courtmartial". Finney sabotages the Enterprise, causing it to lose power. The Enterprise remains in orbit and they have time to correct the issue before it decays.
In the Star Trek: Enterprise episode Breaking the Ice, Reed and Mayweather are taking mineral samples on the surface of a comet. Mayweather injures himself when a slope gives way underneath him and he falls several feet. It would be a rather nasty fall on Earth, but they're on a comet and probably weigh all of six ounces. They later seriously damage their shuttle when it falls through weakened ice on the comet's surface...twice.
Mega Man 5 and Mega Man X3 actually avert this with the Gravity Hold and Gravity Well- both of them affect the entire screen. Played straight with Black Hole Bomb from Mega Man 9 and Squeeze Bomb from Mega Man X8- only enemies near the black hole get sucked in.
Unreal features Na Pali, a planet that is notorious for puling ships into its gravity field.
The actual phrase appears as a graffiti in a prison cell in Space Quest 6.
As in the Film examples, Star Destroyers in the Star Wars Rogue Squadron series are prone to make sudden vertical 90-degree turns as soon as they're critically damaged; Rogue Leaders who aren't careful during the Battle of Endor will suddenly find the Star Destroyer they'd disabled swooping forward to crash into them.
Touhou has Suika and her ability to manipulate density. As this includes the creation of Black Holes, this trope is naturally present in the games she appears in.
Also Utsuho and her last spell card in TH 11. Koishi of the same game has a similar spellcard, but it pushes you away instead — to a wall of danmaku with KILL written all over it.
Koishi's Suppression "Superego" spellcard in 13.5 plays it straight. Get too close to her and you get damaged.
Recca has this boss◊ who fires out two kinds of gravity wells, blue ones which suck your ship towards them and white ones that repel your ship. This is an NES game...
In Halo, Pelican dropships are shown dropping like a stone the second they are released from the ship suspending them above the surface of the planet below. Possibly justified if the parent ship deliberately flies low enough before releasing its cargo, but that's certainly not how it looks in the game. Like a lot of Halo, it is cribbed from Aliens.
Justified in that the dropships aren't just released, there is a minor propulsive force to put distance between the Pelican and the ship. Even then, they don't fall - they drift along until they engage their own propulsion. A more extreme mechanism is used for the ODST drop pods - they aren't dropped, they're shot out of the ship.
Final Fantasy X has multiple cutscenes of Sin manipulating gravity. One of them is actually listed as "Gravity Sucks" if you view it again in the Sphere Theater in Luca. Rocks are actually shown floating off of the moon in a roughly straight line toward Spira, implying this trope is somewhat in effect.