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14 billion years is a ball park figure for the age of the universe not the solar system. Depending on who you talk to, ages for the universe range from 11.3 billion to 13.7 billion depending on whose theory you accept. Oldest rock on the surface of the Earth date around 4.3-4.4 billion. Geologist use 4.5-4.6 billion as the age of the earth which becomes the bottom limit for the age of the Solar System. The age of the Solar system can be defined as when the Sun became hot enough to ignite, starting the fusion process. The elements of the Solar system existed long before the event of 1st light for the Sun, as the dust cloud which became our Solar System contracted forming the planets and Sun. If you call the birth of the Sun when it first gave off light-started the fusion process astrophyscists, astronomers and nuclear physicists using the law of conservation of energy and nuclear energy working backwards from calculating the mass of the sun sort of thing come up with varying answers depending on the assumptions you use. My personal guess is 5-6 billion for the Sun since 1st light.

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