Only if you bother to look, which wasn't necessary to do their assigned task. They were not there to survey the system, just check out if Ceti Alpha VI really had no life on it so it could get blownup and rebuilt into a proper M-class planet.
That makes no sense, because it's not exactly something you'd have to go out of your way to spot. Even today, we can detect planetary systems around stars thousands of light-years away. And we know that Starfleet has faster-than-light sensors. An event as massive as the destruction of an entire planet would've been detected by Federation scientists almost as soon as it happened. Even if they hadn't spotted it, even if they were limited to speed-of-light sensors, then the
Reliant's sensors would undoubtedly have detected the explosion as soon as they passed within 15 light-years of the system.
That's the "Atomic Rocket" theory of sensor detection: if your most sensitive instruments are capable of detecting something at a distance, then your instruments WILL see it at that distance.
The picture just isn't as simple as people like to think, and detection systems screw up all the time. The main reason for this is that as far as sensor instruments are concerned, the sky is FAR from empty: You might look at a solar system and see "Lots of empty space and eight planets in there" but your sensors look at the same area and see "Four hundred and seventy nine discrete heat sources, nine hundred and twelve UV sources, two thousand one hundred objects magnitude +10 or brighter." Sorting out terrestrial planets above a certain size from that huge data set takes TIME. The time required to sort that out is exactly why survey missions exist, and is exactly what Reliant was NOT there to do.
A solar system that can contain hundreds of comets, thousands of asteroids and dozens upon dozens of dwarf planets, and this for a system that hasn't even been charted in detail, whose planetary orbits haven't been observed for any length of time, and for which only basic data exists for any of the planets that ARE known...
Not to mention that in order to reach a planet in the first place, you need to know exactly where it is and what its orbital parameters are, because -- despite the tendency of a lot of mass-media sci-fi to forget this -- planets are constantly moving.
You don't need to know that ahead of time, though, which they probably didn't. Once you enter the system, you scan the region around you and figure out where everything is, find one that matches the description of the planet you're looking for, and fire up the warp drive and GO there. The planets aren't actually moving fast enough for you to have to plot a Hohman transfer with a fixed delta-v budget, and even if they WERE, that's exactly why "midcourse corrections" exist.
There is simply no realistic way they could mistake one planet for the other, even if, by some incredible coincidence, they had the exact same mass.
Sure there is, especially if they don't KNOW the mass of those planets, and also do not actually know beyond vague generalities what those planets even look like. Which, in the case of Ceti-Alpha VI, they did not.
Ask yourself if you can tell the difference between Vesta and Pallas if you've never actually seen either of them and don't know what their orbits look like. Now ask yourself if, having found what you think is Vesta, you are in a position to notice that periapsis -- which is still six months away -- has shifted half an AU closer to the sun.
No matter what the orbital parameters were, even if they got stupid lucky and got there at the exact 3 seconds when 5 looked JUST like 6 would have...
It wouldn't be 3 seconds, actually. If V was "beneath" VI in their orbits when it exploded, its apopsis would have raised and its periapsis would have lowered by the same degree. Assuming those planets were pretty close in their orbits, separated by only half an AU (they'd pretty much have to be for one's destruction to effect the other) then a shift of a little more than half an AU in either direction would mean V would swing out to if not past the former orbit of VI on one half of its revolution, then way the hell closer to the sun on the other half. It could be as much as 3 or 4 months that V's position is out near the former orbit of VI.
If Reliant identifies it as "Planet VI" just by virtue of its distance from the sun, it would take them a couple of days to notice that the planet's orbit is a lot more elliptical than they expected and that it won't retain this distance for long. For the moment, they're' operating on the assumption that "Ceti-Alpha VI" has been found in a stable orbit around its sun, an assumption that, just this once, is far from the case.
they should still notice that there's only 4 planets closer to the sun than the one they are on.
That, again, would take them a while to notice, assuming they bothered to look.
It wouldn't matter if they traded distances occasionally; any astronomer observing their motion for any length of time could tell that their other orbital elements were different.
Exactly. All of the things we're assuming they "should" have noticed would only have become apparent WITH TIME.
Reliant didn't spend that kind of time. They warped into the system, found a planet at the right distance and beamed down to check it out, probably all in the space of two or three hours. Somewhere on Terrel's desk is a preliminary report from the head of his Astronomy department that at least one planet in the system isn't where it's expected to be and he wants a couple of days to turn the ship's telescopes on them and computer their new orbits and, if possible, figure out what caused the anomaly.
By the time Terrel gets that report, there's a Ceti Eel in his brain.