Stars occur where gravity causes gas and dust to come together in one spot and at a certain point the pressure and temperature get so high due to the mass of material gathered that nuclear fusion starts converting Hydrogen to Helium with light as a by-product!
Moons and planets form when the diameter of dust material build up more than about 1000 km in diameter and it has enough gravity to pulp all the dust and rock and form a spherical shape. If it gets even bigger the core gets hot due top pressure and the planer or moon distills the raw material so the heavy elements fall to the core and the light silicate minerals go to the surface, just like our moon.
Not only stars and moon, stars, planets, moons, galaxies or any other object in the universe are formed in a very natural way under fundamental laws of physics e.g. gravitational law, general theory of relativity and quantum mechanics. We draw a brief path of universe’s history, early universe was covered with dense electron and neutron clouds long back. Then electron and neutron were combined to form lightest atom called hydrogen. Hydrogen atoms came together due to gravitational pull to form giant hydrogen clouds. Inside the clouds hydrogen started convert itself into heavier atom called helium and radiated high amount of heat and energy. This is how stars were formed. The dust particles in the universe came close due to gravitation and form clouds. These clouds started spinning as its outer parts cooled down and inner part remained very hot. These started looking like a spinning disks. As disks got thinner and thinner, the particles at center of the disks came together and formed clumps of different sizes. These were planets and moons.
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