Planet X would be the hypothetical planet of the Solar System located beyond Neptune, or even beyond the Kuiper belt. Recent observations of orbital disruption from trans-Neptunian objects have led astronomers to seriously consider its existence. However, despite the relative robustness of the theoretical models, it has never been observed. So for what reasons, if it exists, has this planet X still not been detected?
The notion of magnitude is essential. Each object has an intrinsic luminosity representing the amount of light an observer receives from that object. For the stars, this light comes from themselves, since they produce their own energy and emit its radiation in all directions. For most other objects, this is reflected brightness, since they only reflect the light produced by other objects.
However, other parameters come into play. For example, inherently, the Moon is the faintest object visible to the naked eye, of anywhere on Earth, due to its very low magnitude. Yet it appears brighter than all other objects except the Sun. This is because the Moon is near and its intrinsic luminosity is different from its apparent luminosity.
The farther away an object is, the less bright it appears. The relationship b =~ 1/r 2 shows that the brightness of an object decreases with the inverse square of the distance. These two parameters overall determine the type of telescope that should be built or used to observe an object. To see a very faintly luminous object, it is necessary to collect a lot of light; either by building a larger telescope, or by observing the same portion of the sky longer.
Without the technical or financial considerations, building a bigger telescope would always be the best option. By building a telescope twice as big, it is four times more light collected and a doubled resolution. Today's largest telescopes are able to observe objects with the highest possible resolution and resolve their details in the least amount of time.
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It is also necessary to determine the desired field of view:observe a small region with high precision, or observe a larger region with less precision. Just as a telescope increases its precision by reducing its optical diameter, a telescope can observe the Universe more precisely by reducing its field of view. There are thus different telescopes for different purposes. But the obstacle always remains the same:to observe with great precision, the observation area must be small.
This image is the Hubble eXtreme Deep Field . A very small region of the Universe imaged in several wavelengths for 23 days. It contains 5500 galaxies, and the faintest objects in this image are 10 billion times dimmer than the limit of brightness perceptible to the naked eye. Thanks to the large diameter of its mirror, its position in space and its reduced field of observation, Hubble has revealed the faintest galaxies ever discovered. But that has a price:the image, which took 23 days to pose, only covers 1/32,000,000th of the sky.
In contrast, it is possible to obtain images like this, taken by the Pan-STARRS telescope which can observe the entire sky every night from its terrestrial location. Its size is comparable to Hubble, but it is optimized for wide-field observation, around 75% of the sky. It is particularly useful for detecting changes between light points. It can detect comets, asteroids, Kuiper belt objects and more.
However, it can only detect objects thousands of times brighter than the faintest objects observed by Hubble. It is therefore not possible to observe the entire sky in the hope of discovering all the objects hidden there. A telescope that can simultaneously cover a large portion of the sky while having extreme precision is technologically impossible to build.
There are many telescopes that can detect very faint objects, but you need to know where to point them. And there are plenty of telescopes that can cover large swathes of the sky, but they can only detect the brightest objects. And for objects in the Solar System, since they only reflect light from the Sun, the more distant ones simply cannot be observed. This is the case, if it exists, of planet X.
