In this inverse of the Round Table Shot, there is only one subject around whom the camera circles (usually on a dolly track), so as to provide a rotating view from all sides. Sometimes gives the impression that the subject is spinning.
This was a particularly common shot in music videos during the 1980s.
Orbital Kiss is a common subtrope. The Orbital Shot is often used in Bullet Time. See also Dizzy Cam, which is an Orbital Shot done with a handheld camera at a distressing speed.
Not to be confused with Kill Sat or Orbital Bombardment, both an entirely different kind of orbital shot.
Examples:
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Anime & Manga
In the final episode of Steel Angel Kurumi 2, the animators' virtual camera does an Orbital Shot around Nako as she performs in the cello competition.
This happens in Death Note, during a personal confrontation between L and Light.
There is one in Ouran High School Host Club around Renge, when she accuses the members of the male club of not being good enough.
In the opening of the second season of K-On!, there is an orbital shot around the whole band as they're playing in the music room.
This is seen in the first episode of Fate Zero, as Kirei is told about the Holy Grail War.
Film
In Bad Boys 2, when the villain calls the heroes to inform them that he holds the lead girl (who happens to be one hero's sister and the other's girlfriend) hostage, the camera does a dramatic Orbital Shot as one of them delivers the punchline "Shit just got real!"
Sent up in Hot Fuzz, where the camera spins around the protagonists as they deliver these immortal lines:
Angel: You're a doctor. Deal with it.
Danny: Yeah, motherfucker.
Parodied in Superhero Movie: Dragonfly and the Hourglass confront each other while the camera spins around...making both of them rather dizzy.
In the Twilight film, this happens whenever Bella and Edward stand beside each other, to denote the seriousness of their conversation. It got really annoying, really fast.
Done to excess in the final rendition of 'This Is Me' in Camp Rock when Shane and Mitchie meet on the middle of a catwalk-esque podium to sing.
The Joker and Rachel in The Dark Knight "You wanna know how I got these scars?"
In the just-begging-for-a-Rifftrax horror film Darkhunters, there is a scene where a demon is holding Carol Miller by her jacket and pulling her up to his face, and while they talk the camera is constantly panning around them. It's not a continuous shot but a series of half-orbits around the two of them, zoomed in close to their faces. Watch it here starting at 51:50. It lasts nearly three minutes, so have a bucket handy...
Dizziness exacerbated by forcing you to read subtitles during the whole thing!
A fairly brilliant one in Murder in the First, orbiting a cell set in the middle of a room. Thanks to flyaway walls, the camera appears to move in and out of the cell.
Rick Astley's Lights Out music video makes EXTENSIVE use of the orbital shot, with mind-dizzying action lasting for almost the entire video.
Lindsey Stirling uses this in her The Lord of the Rings medly. She stands in the wind on a hill by the sea, and the shot goes around and above/below her.
Video Games
Used in one of the later conversations with Jack in Mass Effect 2, when the camera rotates around her as she tells Shepard about her boyfriend's sacrifice and the effect it had on her.
MegaTokyo did this in five panels, in the middle of a fight in a crowded nightclub. It's about as confusing as you'd expect, and it's entirely possible to miss the fact that it's the camera that's rotating, not Kimiko.
Western Animation
In the finale of Danny Phantom, Danny and Sam get one during a romantic moment.
Used forebodingly in Watership Down, when Hazel's group are inside Cowslip's warren. They're bunched up in the middle of a large chamber with multiple entrances, and the perspective rotates around the room, looking at them through each entrance in turn. It's creepy, because two or three resident rabbits crouch anxiously inside each tunnel, out of the newcomers' view, and are eavesdropping on their conversation.