One of the consequences of Newton's Law of Gravitation is that every object with mass is attracted to every other object with mass by some measure of force.
You are attracted to the Earth just as the Earth is attracted to you. This is not necessarily obvious but it is easy to demonstrate. Just jump in the air and you will fall back down to the ground. Gravity will bring you back down to Earth.
What is not so easy to observe is that from the Earth's perspective, it will "fall" up to meet you. That is, the gravitation attraction you exert on the Earth will pull it towards you when you are in the air. It is just that the difference in masses between you and the Earth make the Earth's motion virtually imperceptible.
The universal law of gravitation holds. Newton's equations tell us that everything in the universe is attracted to everything else. (If you are ever feeling blue just remember that the whole universe is attracted to you!)
This is true for the Earth and the Moon, the Earth and the Sun, and the Earth and all of the other planets. They are all caught in a gigantic mutually interactive gravitational field which encompasses the whole solar system. As they are all large objects, each affects the other and is, in turn, affected by all of the others.
The effect of gravity on objects is one of the ways we have learned about the solar system.
In 1846, Johan Gottfried Galle was guided by the perturbations in Uranus's orbit to the discovery of Neptune. The gravitational influences on Uranus dictated that something else must be present in the solar system. It turned out to be another gas giant.
Studies of Neptune's orbit revealed small perturbations which did not arise from all of the other known planets. The gravitational influences of the other planets were not enough to account for the deviations. These calculations led Percival Lowell in the early 1900s to start the hunt for a "Planet X" which he predicted would lie beyond Neptune just as Neptune was beyond Uranus.
Ironically, his calculations led astronomers at the Lowell observatory to discover Pluto in 1930. But rather than being a gas giant, Pluto turned out to be a disappointingly small, rocky planet. (Or at least it was until Mike Brown led the charge to have Pluto declared not a planet by the International Astronomers Union. Pluto is now classified as a "dwarf planet" along with a number of other objects in the solar system.)
In 2014, Chadwick Trujillo and Scott Sheppard published the results of their studies of a Kuiper Belt object, 2012 VP-113. It joined Sedna as only the second known object with a very distant orbit. Their work suggested the possibility of another object larger than the Earth orbiting well beyond Pluto.
Trujillo and Sheppard noted that Sedna, VP-112, and several other Kuiper Belt Objects all shared a peculiar property: their point of closest approach to the Sun lay in the plane of the solar system. Further, they all moved from north to south as they passed through the plane.
But could this be another failed attempt to find the mystery planet at the edge of the solar system? Could there be an alternative explanation?
That is what Mike Brown and his colleague Konstantin Batygin suspected. They set out to prove another planet didn't exist. Instead, in a twist of fate, they may have found the telltale fingerprints of Planet 9.
The mystery planet has yet to be observed with a telescope or measured by any other method. All they have right now is a prediction of a massive planet orbiting beyond Pluto and Neptune which may exist due to gravitational perturbations in the Kuiper Belt Objects.
In their efforts to discount the possibility of another planet, Brown and Batygin analyzed the orbits further and included a number of other Kuiper Belt Objects. They discovered that the long axes of their orbits aligned. Something appeared to have nudged these Kuiper Belt Objects into occupying the same space around the Sun. That something would need to be large enough for its gravity to influence other bodies in the solar system. It would need to be a massive planet.
Using the gravitational data, they calculate that if Planet 9 exists, it will be about 10 times the size of Earth with an elliptical orbit that takes between 10,000 and 20,000 years, and never getting closer than 200 AU to the Sun.
No one has seen Planet 9 yet but the gravitational data makes a strong case for it being there. A century after Percival Lowell began looking for it, a gas giant beyond Neptune might finally have been found.