well folks I've finally managed to come up with a formula composed of 4 small other formulas which you can use in order to see how a star has to act in order to replace our Sun, without changing our life conditions so basically it can really replace teh Sun without us knowing it
That star has to :
1) be situated at a distance = 13000000000 kilometers for every E surface ( where E is the size of 1 Earth )
2) have a temperature = 0.004 Celsius degrees for every kilometer of distance ( where the distance is the one calculated above )
3) have a luminosity = 26000000000000000000000 Watts for every kilometer of distance ( where the distance is the one calculated above )
4) have a gravity = 0.0000186 g ( where g is the gravity of 1 Earth ) for every kilometer of distance ( where the distance is the one calculated above )
I hope this comes handy for anyone who wants to see if a certain star would fit as a new Sun
NOTE : in order for a star to be able to do such a thing, ALL of the above 4 mentioned have to be satisfied simultaneously else God forbid !!!