How Hard is it to Find Planet 9?

A collaboration with Ella Alderson

An artist’s depiction of Planet 9 as an ice giant.

Since the early 90’s, humanity has exhibited an astounding skill for identifying planets outside of our solar system. To date, we have confirmed the existence of 3,946 such worlds, spread among nearly 3,000 different planetary systems. Using various discovery methods, we have been able to accurately deduce the radii and masses of many of these objects, some of which even bear a striking resemblance to the pale blue dot we call home. In our quest for exoplanet discovery, we have learned that planets in the galaxy are more common than grains of sand on the beaches of the Earth. With the addition of the Kepler space telescope to our exoplanet hunting arsenal, it seemed as though no planet residing in our cosmic backyard could remain hidden from humanity for long.

Then, a study in 2016 proposed the existence of a planet that was much, much closer to home. Based on the highly unlikely aligned orbits of several Kuiper Belt Objects (KBOs), two astronomers from Caltech conjectured a new planet; not one in our cosmic backyard, but rather one right on our very own doorstep. Dubbed Planet 9, the proposed object would require a mass ~10 times that of the Earth, and a highly elliptical orbit for it usher the KBOs into the trajectories we observe today. Because it would require thousands of passes for such a planet to kick that many KBOs into elliptical orbits, it is hypothesized that Planet 9, if it exists, still lurks silently in the Kuiper belt, far beyond the orbit of tiny Pluto.

A diagram of the orbits of the aligned KBOs, the proposed orbit of Planet 9 shown in orange.

However exciting it is to speculate about the existence of another large planet in our own solar system, a perhaps more prudent question which begs answering is: why haven’t we found Planet 9 yet? The last planet to be discovered, Neptune, was done so nearly two centuries ago using an archaic 4.3 meter long refractor telescope; a magnification no greater than 20. Though a fair bit closer to us than Planet 9 should be, Neptune still yields a similar radius to the newly proposed planet. Surely 200 years of advances in science and technology would allow us to spot a planet only marginally smaller than Neptune a little farther out in the solar system, so what gives?

The level of difficulty for the discovery of new solar system objects can be chiefly attributed to four major factors about the object:

  1. Angular diameter — How large the object appears from Earth
  2. Apparent magnitude — How bright the object appears from Earth
  3. Relative motion — How fast the object appears to move from Earth
  4. Orbital characteristics — Where the object appears in the sky from Earth

In this article, I will use these factors to discern exactly how hard it would be to spot Planet 9 using modern technology, and speculate on why we haven’t been able to find it as easily as other bodies, like Neptune and Pluto. This will allow a conclusion on whether the world could still be hiding in the outskirts of our solar system, or if its existence can be ruled out entirely. Finally, this article is done in conjunction with Medium space writer extraordinaire Ella Alderson, who has prepared her own article about the latest updates on the current status of Planet 9 in the astronomy community. I highly encourage you to check our her article, which I will link at the bottom.

So, how hard is it to find Planet 9?

1. Angular Diameter

Imagine trying to spot a soccer ball on the Earth from a commercial jet at cruising altitude. This is how large Neptune appears in the sky from the Earth. Neptune averages more than 27 times Pluto’s angular diameter, making Pluto the proverbial equivalent of a pea in the example above.

How large each planet appears from Earth on average, with a comparison of Pluto to Neptune on the right.

Determining the angular diameter of Planet 9 requires us to consider a few different possibilities. Firstly, though the mass of Planet 9 has been somewhat reliably estimated, determining the radius of the world is a bit more equivocal. This is because Planet 9 falls into a size category between Earth and Neptune referred to as the “Super Earths”. We do not know enough about the evolution of this foreign class of exoplanet yet, because no such analog exists in our solar system. Planet 9 could be a compact, monster rocky planet, or it could be a diffuse gas world, similar to a mini Uranus or Neptune. This discrepancy allows its estimated radius to swing between 2 and 4 times that of the Earth’s; a noteworthy variance when it comes to spotting a world as distant as Planet 9.

And that brings up the second difficulty of determining Planet 9’s angular diameter; distance. Most planets orbit in nearly circular orbits, their distance from the Sun largely unchanging over the course of the planet’s year. Planet 9, however, is estimated to swing out as far as 1200 AU from the Sun, only to plunge back inward to a distance of just 200 AU. This means Planet 9 will appear 6 times larger at its perihelion than at its aphelion. Because we don’t know where Planet 9 is in its orbit, nor have we any means of determining its true radius, we will have to take every possibility into account to determine how difficult the world may be to detect with modern technology.

Strangely, Planet 9 averages an angular diameter quite similar to Pluto’s. On the optimistic side, the world may appear more than 4 times larger Pluto’s diameter, or as tiny as just 1/3. It is interesting to note that the optimal angular resolution of the Hubble Space Telescope would only allow Planet 9 a maximum resolution of just a few pixels on its CCD camera. The world could still be confirmed, however, if it’s bright enough…

Photos of Pluto from the Hubble (like this one) are actually a compilation of many tens if not hundreds of stacked images to obtain a resolution of this quality. In reality, Pluto only appears about 2.4 pixels across on Hubble’s CCD.

2. Apparent Magnitude

In the domain of astronomy, size isn’t everything. If something shines bright enough, even if it is too small to resolve, we can capture its light and determine something about it. For stars, this is easy. Intense light is emitted from stars’ surfaces, where it then travels largely unperturbed to our eyes or telescopes for us to observe. For planets, the process is not so straightforward. Light leaving a planet’s host star decreases exponentially with distance as the light spreads out through space. By the time this light reaches a far away planet, its intensity has diminished vastly. The planet’s atmosphere then absorbs a fraction of this light before the rest is allowed to reflect back out into space. The light is again exponentially dimmed on its return voyage before it can finally reach our eyes and telescopes.

Neptune averages an apparent magnitude comparable to spotting a 60 Watt light bulb atop the Willis Tower in Chicago from the Empire State Building in New York (ignoring terrain). Pluto is 800 times less luminous than this, relocating the aforementioned 60 Watt light bulb to Geosynchronous orbit, over 30,000 kilometers away. When it comes to detecting Planet 9, an object that averages nearly 18 times farther away than Pluto, apparent magnitude may prove to be a significant hurdle.

Even exhibiting its largest possible radius during its closest pass to the Sun, Planet 9 would still be multiple times dimmer than Pluto. The distant world would average less than 1/700th of Pluto’s brightness, with its most pessimistic characteristics granting it a luminosity ~15,000 times less than the little former planet. The brightness of this last scenario is just marginally above the limiting magnitude of the Hubble itself, and is in fact dimmer than 70% of all the stars in the Milky Way galaxy from Earth! Even if we were lucky enough to capture it in Hubble’s frame, Planet 9 would likely be drowned out of an image by a brighter background star.

There is, however, another form of light which planets can emit; not light reflected by their surfaces, but rather light which is generated deep within the planets themselves. Gas giants are massive worlds, their insides compressed by enormous gravitational pressures. This, combined with the dynamic nature of gas worlds, grants many giant planets bright emissions in the infrared spectrum of light. Most of the gas and ice giants in our solar system are actually a few times brighter in the infrared spectrum than in the visible spectrum, making them easier to see with long wavelength telescopes.

Jupiter in infrared light, from the Gemini Observatory.

One blatant exception for this trend is Uranus. For reasons still unknown, Uranus seems to exhibit almost no internal heat. It is possible that Planet 9 is similar to Uranus, in which case we will have to rely on visible light in order to discover it. If it is more like the other 3 gas planets in our solar system, Planet 9 could be generating infrared heat at a rate 500 times the average intensity it receives in visible light from the Sun. If this is true, spotting Planet 9 would become much more feasible.

3. Relative Motion

Watching distant solar system objects move is a tedious task. It takes 3.4 minutes for sluggish Pluto to traverse the relative distance of 1 pixel on the Hubble CCD. For scientists to actually verify motion of the tiny world, Pluto has traverse the distance of its angular diameter, fully moving out of the way of its own cross section. Because Pluto is about 2.4 pixels in diameter, two photographs would need to be taken more than 8 minutes apart to confirm that Pluto is indeed a mobile, solar system object. Imagine the example from before of seeing the pea from the commercial airliner, only now the pea is moving… at a rate of 0.0000062 meters per second… and you have to see it move.

Though similar in angular size to Pluto, Planet 9 would move much, much slower in the sky. At perihelion (the most rapid point in its orbit), Planet 9 would still take several hours to move out of the way of its own silhouette to discern its motion. At aphelion, this same phenomenon could take more than a day!

4. Orbital Characteristics

One last difficulty of finding Planet 9 would be its atypical orbital characteristics. Pluto may have been found by accident, but its discovery was not completely by chance. When searching for new solar system objects, scientists tend to observe near the solar system’s orbital plane, because most objects which orbit the Sun do so within just several degrees of this plane. On the date of its discovery, Pluto was almost exactly on this plane; a phenomenon that only happens for it roughly once every century or so. Planet 9, which would also have an inclination high above the plane of the solar system, may have an orbital period in excess of 18,000 years! This gives it a minuscule probability of being near the ecliptic today, likely ruling out an accidental discovery.

The orbital plane of the planets. Note Pluto’s proximity to the orbital plane in 1931; just 1 year after its discovery.

Conclusion

Alas, discovering distant solar system objects is rigorous any way you slice it, and Planet 9 would be no exception. Based on these numbers, it is entirely possible that we haven’t discovered the giant world yet simply because we haven’t looked in the right places, we haven’t looked in the right wavelengths, or that we’ve looked and missed it entirely. As our observation technology grows and evolves, we will eventually reach a point where Planet 9’s existence could no longer remain ambiguous. It will be at this moment that we either discover the long lost ninth planet of our solar system, or point our telescopes elsewhere in search of the next great mystery.

As promised, here is a link to Ella’s article! I strongly urge you to check it out, and thanks for reading!