I have a planet in earth's solar system that is on a comet's orbit rather than like the orbits of the planets we have. I need some help picturing how this would work to meet a few requirements for the story.
Requirements in order of importance
The planet needs to be visible to the naked eye for years. Currently I have it being discovered about 16 years before it reaches it's closest point to earth (It's x times further than the moon so that it appears to be bigger than the moon noticeably while being about earth sized in absolute terms, I have some handwavium for the tidal effects that would cause). It doesn't need to start out as visible as a planet rather than a star to the naked eye but needs to be visible to the naked eye as a distinct planet for several years prior to the closest point.
The planet needs to be visible opposite/across/not right next to the full moon in the night sky in the northern hemisphere. It needs to 'rise' the night of its closest pass but what this looks like can be changed. This orbit should be primarily or entirely so that it's visible at night and during the spring/summer months.
It needs to be close enough for probes to be sent by NASA (etc) in a reasonable time frame. This is set in current times with current technology but I specify 'reasonable' because the probes keep failing and I want NASA to be able to send multiple ones for pictures between when it's first discovered and when it's at it's closest. I know it takes time for probes to be built and launched and longer still to reach things because they can't often do a straight shot.
Be on a stable orbit that would allow it to come into earth's proximity every once in a while (how often can be changed) but preferably in such a way that there is no historical accounting of it. Like there is of the once in a generation comets we get where we can look at the records and guess as to what specific object they meant. (This can be discarded if it's not feasible given that it is more important that the planet be visible in the night sky for years). Edit Per a comment suggestion below this point should read; it has appeared in the past at least semi-regularly but if the orbit calls for it, the planet's apparent size need not be consistent through history.
Something about the orbit needs to explain why it wasn't discovered before now in an official sense, the way we know about Neptune for example. This planet is bright enough to shed light on the earth with this orbit so I don't see it just being mistaken as a star before.
My understanding of the answer
The way I picture this planet is that it's on a very oblique angle compared to the earth's orbital plane and it has a very elliptical orbit so that while it would fit inside of earth's orbit at it's narrowest point, it would also extend way beyond it for at least part of the orbit. My thinking is that the oblique angle makes it looks like it is essentially coming towards the earth for years, narrowing missing it, and then doing it the same many years later coming from the opposite direction. On some passes it wouldn't be visible in the sky (either because it's opposite of earth's orbit or mostly on the day side and not noticeable in the sun's light) accounting for it being missed by history. Or else on some sort of orbit that means it doesn't always cross earth's path even when in proximity to the sun. However I don't know if this is correct thinking.
The question; what would the orbit I described look like? Is there anything wrong or inconsistent with those requirements that makes this an unreasonable orbit.