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Hi I am a bit of a science noob but anyway I'm writing a little Sci-fi story and I just want to know if there is a substantial difference in perceived time passed at point A and point B if Point A is on the tip of our galaxies outer edge and point B is say two thirds of the radius in (from the outer edge of the galaxy)?

Just because I was going to have two alien factions fighting over outer territories for research purposes (There home worlds are closer to the center of the galaxy so if they conduct research out there on weapons and stuff they can get a leg up on the competition because they have more time to do research, IDK if I'm explaining it well but I think you'll get what I'm Saying).

DonaldPepe
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Yes. At the center of our galaxy, there is a black hole with a mass of roughly 1300 times the mass of our sun (known as Sagittarius A). As you near a massive body, time proceeds at a different rate when compared with another observer, that is at a different distance from the massive body.

In the weak field limit and in our galaxy you can roughly use the following formula to calculate the difference between two observers in the same gravitational field: $$ \frac{t_0}{t_f} = \sqrt{1 - \frac{10^6}{r}} $$

Here, $t_0$ would be the time percieved by an observer inside the gravitational field of our galactic center and $t_f$ would be an observer so far away from it that it's effects are basically non-existent.

In the case of the earth, we are approximately 10^20 meters away from the center of our galaxy and thus we feel effectively zero time dilation when compared with an observer much further away than us and thus, we can use $t_0$ to mean the time experienced on earth.

So, in order to feel a significantly different amount of time pass relative to those on earth, your alien planet would need to be very close to the center: it would need to actually orbit the black hole at the center of our galaxy.

Note: this is a very rough calculation, since I have assumed that mass of the center of the galaxy is basically all from the black hole and that the black hole is non-rotating and charge-neutral.

Akoben
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