Towards the beginning of Independence Day, one of the officers reviewing scans of the alien mother ship says about it:
We estimate it has a diameter of over five hundred and fifty kilometers and a mass roughly one fourth the size of our moon.
This has always bothered me, because the moon is has a mass of 7.3x1022 kg, meaning the alien mother ship would have had a mass of about 1.8x1022 kg = 1.8x1025 grams.
Meanwhile, a 550-diameter ball has a volume of 4/3 x 3.14 x (275 km)3 = 8.7x107 km3 = 8.7x1022 cm3
This means the ship has an average density of 212 g/cm3, which is five times denser than if it was made of solid osmium (the densest element known to mankind)! Not only that, but shots of the mother ship clearly show it's not spherical, and later in the movie we see that much of the interior is empty. So whatever material the ship is made out of must be even denser. Even assuming that the 550km figure is a significant underestimate (he did say "over 550", after all), this is an incredibly dense ship!
This raises all kinds of questions regarding the ship's composition, structural integrity, and gravitational pull, as discussed in this paper.
I'm sure this was just a casual oversight by the writers, but what in-universe explanation might there be for the mother ship's incredibly high density? Does the movie or its sequel give any clues as to what the ship could be made out of in order to be so dense, and how it holds its shape without collapsing into a ball?