In the movie Independence Day, the alien mother ship is said to be 500 km in diameter and have a mass 1/4 that of earth's moon. If the mother ship were a sphere, what would its density be? (The volume of a sphere is 4/3 pi radius^{3})

1/4 moonmass / (4/3 pi (500/2 km)^3) -> water 280.68

This makes the ship 280 times denser than water. This is 36 times denser than iron and more than 12 times denser than any known element! As the ship is actually more a thin disc than a sphere, it would actually be even denser. Since it contains lots of empty space, parts of it would have to be much, much denser.

If the object is this dense and has such a large mass, what is its surface gravity? Surface gravity is given by G mass / radius^{2}, where G is the gravitational constant (which Frink knows about):

G 1/4 moonmass / (500/2 km)^2 -> gravity 2.000079

The surface gravity of the spaceship is thus at least twice earth's gravity--and that's on the rim where gravity is weakest. It would actually be much higher since it's much, much flatter than a sphere. I hope you're not the alien that has to go outside and paint it.

Posted on Thursday, August 5, 2010 9:02 AM | Back to top

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