Gravity.
Planets orbit around the Sun because of Gravity – the Sun pull them in, while inertia has them trying to “escape”. Without the Sun, they would each just fly in a straight line right out of the Solar System.
But gravity happens between all objects, not just planets and the Sun. Planets’ gravity also affect each other.
So, after astronomers discovered Uranus, they tracked its orbit around the Sun and realized that it doesn’t quite orbit the Sun predictably as you would expect. At that point Newton’s laws of gravity were already known for nearly 200 years, so you were able to predict an objects orbit around another object with a high level of accuracy. Uranus’s orbit however didn’t look right, it had some irregularities. These irregularities could only be explained if there was some other massive object nearby. They looked at where this object might be, and found Neptune.
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