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Just after the Big Bang all the matter that was created was dust and gas. This dust and gas started to create some little groups. (The reason why they started to group up is as followed: when two atoms meet each other, one of them may wrest an electron, which is not necessary, out of the other one. Let's call this atom 'Atom A'. When the atom with a spare electron (Atom B) touches another one, which has a lack on electrons, spare electron 'jumps off' from Atom A to Atom B. Nonetheless, Atom A still attracts this electron. What happens is that these two atoms just share it and so attract each other. You can see the same situation when using a glue stick.) Then these groups start to grow, and when they reach the size, where the gravity is strong enough to attract some smaller groups, they make these groups orbit them and so create a friction on themselves. The friction creates energy and rises the temperature. Through time the smaller groups finally join the bigger ones. In a couple of billions of years, one of the big groups reaches the size of the Sun. When this happens, it creates such a huge gravitational pull that it even makes another big groups of dust and gas orbit it. But because these groups are far enough, they do not create a friction. They continuously orbit the biggest group of dust and gas. We are used to call these groups 'planets' - they are bigger than an asteroid, but smaller than a star.

But they were completely different that time. There were about twenty of them. Ones were bigger, other ones were smaller. But the ones that were bigger attracted the smaller planets, which then joined together. And so on till there were only 8 planets left.

Another answer: The above answer is not completely accurate. For example

there may have been weak "van der Waals" forces involved in clumping matter together, but not the sort of chemical bonds described.

The hypothesis is called the "nebular hypothesis" because the solar system is believed to have formed from a "nebula" of gas and dust.

See the "related link" below for a more accurate statement of this hypothesis.

The link also gives details of the later evolution of the solar system.

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