We’ve observed that the universe is expanding, and this expansion is accelerating. We know this because of the Doppler effect. Basically, when something moves quickly away from you, the wavelength of their light gets stretched, giving off a red-ish appearence. We can use this red shift to figure out roughly how fast the universe is expanding. If the universe is expanding now, perhaps it’s always been expanding, so we work backwards to predict how long it would’ve taken for the universe to go from 0 size to how it is today.
There’s multiple different ways to calculate the appropriate age of the universe. A very simple method would be to calculate the acceleration of stars in our own local group and see how far/fast they are moving apart over a set time frame. With that knowledge we can reverse the math and get a very rough time frame of when our system was created. However the real answer is quite more complicated than that. I’ll place a nice info graphic below.
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