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In Star Trek II: The Wrath of Khan (the one from 1982, not the recent remake), Khan yells "This is Tau Ceti Alpha V!" and they're all like this is a big surprise, we didn't know.

If they had previously charted the planet, wouldn't the computer have told them the planets weren't quite where they should be based on earlier visits? I mean, we can predict the next hundred transits of Venus, shouldn't 23rd century explorers be able to predict where the Tau Ceti planets are less than twenty years after their first visit?

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It's a definite plot-hole, that's for sure. I've always thought so myself. I think the best explanation is that the destruction of Ceti Alpha VI altered the orbit of Ceti Alpha V to the point where it occupied (roughly) the same space as Ceti Alpha VI would have, and Starfleet approached the system from a direction which would normally have obscured Ceti Alpha V - such as approaching from the opposite side of the sun - and therefore got a little careless. –  James Sheridan Aug 5 at 3:30

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We in the 21st Century care about ephemeris data because our current spaceships move among the planets using Hohmann transfer orbits. We need to know where the planets are going to be so we know when to launch. We need to know how fast the planet is moving in its orbit so we know how much propellant to carry to produce the delta-vee needed to get there. We need to know these things because if we don't the ship will miss its target, run out of fuel and then everybody dies.

A 23rd Century starship with antimatter-fueled faster-than-light maneuvering and FTL sensing capability doesn't need to keep track of that kind of detail. They arrive in the system, scan for the planets, find one in roughly the right orbit and with matching surface characteristics and then drive straight toward it. Reliant arrived looking specifically for a barren lifeless planet roughly X million kilometers from the star and they found one. It's sloppy navigation work by our standards, but we don't live in a world where space navigation is as easy as guiding a ship from continent to continent with GPS.

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Could it be because piloting a starship is significantly more difficult than other activities (such as dusting crops, for example)? –  Richard Aug 5 at 6:32
    
It's sloppy navigation work by our standards - So you mean the Reliant's crew was too reliant in that point? ;) It's still a bit odd, considering other episodes/movies where it's obviously pretty much standard to scan a system after arrival. However, at the same time we don't know how complex that system would have been. It's easy to notice pretty fast whether there are 6 or 7 planets, but if you're talking about 20+ it might get quite a bit more complicated. –  Mario Aug 5 at 7:03
    
@Mario: While at the time of production of TWOK, the producers may not have had any idea of that yet, 20+ is not any more complicated than 6 or 7 for a computer to distinguish. –  O. R. Mapper Aug 5 at 7:15
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I think this is just your typical TOS sending your ship's senior officers down to the planet nowhere close to fully informed. In Star Trek: First Contact, they're measuring space dust and radiation spikes per cubic meter. Surely in Wrath of Khan they would at least be aware of a whole planet not being where it's supposed to be. A TNG era captain would probably have had a meeting in the ship's conference room and someone would have mentioned the missing planet. –  Alonso del Arte Aug 5 at 13:47
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The planet was where Ceti Alpha VI should have been, not where it belonged as Ceti Alpha V. Its orbit had shifted and it could easily have been mistaken as Ceti Alpha VI if they were only judging by its orbit. Of course, all the other aspects would be wrong, like size, orbital speed, geography, and so forth. It was a science vessel. You'd think someone on board would actually be a scientist and notice. –  BBlake Aug 5 at 16:13

They reasonably thought they were on Ceti Alpha VI because that had been it's orbit. Space is a very large and busy place so obviously Stellar Cartography is kept very busy. A single planet taking another's place in orbit in a remote solar system could be easily missed.

It's possible also that the star chart could have mistakenly logged the surviving planet as Ceti Alpha VI and removed Ceti Alpha V as being destroyed. No one had been back to confirm this apparent fact since Khan and company had been placed there. They obviously had no idea that it was in fact Ceti Alpha VI that had been destroyed and it's orbit taken over by Ceti Alpha V. Who knew? Thinking that Ceti Alpha V was destroyed is reasonable due to it missing from it's orbit.

The kind of planetary 'musical chairs' that occurred is obviously very rare so their surprise by such an unusual/rare occurrence would be a reasonable reaction.

Chekov though, being there firsthand when Khan was marooned, was quick to put 2 and 2 together and recognized their danger after seeing the ship's name, 'Botany Bay'.

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Blake's comment on Kyle's answer brings up a couple of very good points. Maybe a Klingon crew wouldn't care about this sort of thing, but a Starfleet science vessel? As for Chekov "being there firsthand when Khan was marooned", that's a whole can of worms for another day. –  Robert Soupe Aug 6 at 3:38

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