Describing a planet on a comet like orbit

Question

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

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

Answer 1

You Can't Have It All

Needs to be visible to the naked eye as a distinct planet for several years prior to the closest point.

It appears to be bigger than the moon noticeably while being about earth sized in absolute terms

Be on a stable orbit that would allow it to come into earth's proximity every once in a while... but preferably in such a way that there is no historical accounting of it.

These are in conflict.

We have records of comets, much less striking than your proposed object, going back 2000 years from the Chinese, Greeks, Babylonians, etc... Such an event as a second moon would be recorded. We need a highly elliptical orbit where it's last pass was before we have written records, probably more than 4000 years. Such an orbit is "near-parabolic" meaning it has almost enough energy to escape the gravity of the Sun.

C/1823 Y1 or Comet De Bréauté-Pons or The Great Comet of 1823 will serve as an example. It was much, much smaller than your object, and had an orbital period of about 2300 years. As it fell towards the Sun it accelerated. As it passed the Earth at 1 AU it would be doing about 40 km/s. At its closest it got within 0.5 AU of the Sun doing close to 50 km/s. If we assume an average of about 45 km/s inside Earth's orbit, then it could be in and out of Earth's 150,000,000 km orbit in about 6 or 7 million seconds or 77 days.

$$\frac{150,000,000 \text{ km} \times 2}{45 \text{ km/s}} \times \frac{1 \text{ day}}{60 \text{ seconds} \times 60 \text{ minutes} \times 24 \text{ hours}} = 77 \text{ days}$$

And that's roughly what was seen. It was visible to the naked eye in Dec 1823 and by April 1824 it was no longer detectable by 19th century astronomers.

"Earth sized, but appears noticeably bigger than the moon"

Totally doable, but not for long, and it's not predictable nor stable nor good for the Earth.

As we showed above, this thing will come screaming in from the outer solar system at a very high velocity. It's possible it could coincidentally cross the Earth's orbit at just the right distance to appear larger than the Moon.

As it relies on the Earth just happening to be in the right place relative to the object's orbit, and they would not be in resonance, this would not be a regular occurrence in its orbits. It wouldn't last long as both the Earth and the object move relative to each other.

The angular diameter of the Moon, how big it is in the sky, is about 1800 arc seconds, or 0.5°. Angular diameter in arc seconds is

$$206265 \times \frac{\text{actual diameter}}{\text{distance}}$$

Note that it's a simple ratio of actual diameter to distance, so if we want something bigger to remain the same size it has to be further away by the same ratio. The diameter of the Earth is about 3.7 times the diameter of the Moon, so for an Earth-sized object to appear about the size of the Moon it needs to be about 3.7 times further away. The Moon is about 400,000 km away so our object is about 1.5 million km away.

But it can't stay there for long. Since it's moving towards (or away from) the Sun at about 45 km/s it won't stay that apparent size for long. In an hour it will have traveled about 160,000 km and in a day it would have moved 3.9 million km.

Best we could get it for it to grow menacingly and recede over the course of a few nights.

But that's also really close such that it would effect both orbits so this is not a stable situation. At their closest approach they'd be putting about $1^{21}\text{ N}$ on each other or about 5 times the force of the Earth on the Moon. This would be bad.

What Could Make This Work?

Drop the historical stability. Make this a one time orbital change.

I'll draw inspiration from $\text{2015 BZ}_{509}$. This is an asteroid in a retrograde orbit (it's orbiting the other way from everything else) near Jupiter. It's gotten attention recently because of a paper claiming it may be an extra-solar object captured by Jupiter. Scott Manley has a great video explaining why this is so significant and with some excellent animations.

You could have a low-albedo Earth-sized object in an eccentric and very high inclination orbit. Since it's at a high inclination it whips down through the solar system every few hundred years. Since it's so far off the plane of the rest of the planets, it normally interacts with little on it's trip through the inner solar system. Since its albedo is so low and it doesn't come close enough to the Sun to vaporize gases and leave a noticeable trail, it normally isn't noticed by historical astronomers.

Modern astronomers see it coming this time. But this time it's different. This time it gets a bit too close in front of Jupiter. This interaction puts on the brakes and whips it into a new less eccentric and lower inclination orbit.

Suddenly there's a new Earth-sized planet zipping around through the inner solar system, crossing everybody's orbits. If you play a bit, you can find an orbit that's elliptical, inclined, but still passes close to Earth every once in a while.

Just how close it would have to get to Jupiter for this to happen I'll let somebody else figure out. I will note that capturing an asteroid and capturing an Earth-sized planet probably a million times more massive (and with a million times more momentum to overcome) are rather different matters.