Looking from the shots in space in the movie, Melancholia is around 4 times the diameter of the earth. This makes it around 64 times the volume of the earth. We'd need the density to work out the actual mass, but Melancholia in the movie did seem to be portayed as a solid rock planet similar to earth. Even if we say that Melancholia has only one third of the density of the earth, this would still make it 20 times more massive.
And has anyone considered the speeds involved. I already just posted this on another forum, but here are my thoughts:
John mentions, prior to Melancholia boomerang move to smash into the earth, that it is travelling away from the Earth at 60,000 mph. Now, in cut scene at the start we see the planet, upon impact, consume the entire diameter of the Earth in around 20 seconds. That's around 8000 miles. In 20 seconds!
Even if we charitably assume the collision with Earth did not slow Melancholia down at all, AND don't consider that the Earth is moving away from Melancholia in its own orbit from the sun, it still meant Melancholia was travelling towards the Earth at around 1.44 million mph at the point of impact. That's around 1/465th LIGHT SPEED (186,000 mps * 60 secs * 60 minutes / 1.44 million mph = 465).
Please someone correct if my maths is way off, but the numbers look approximately correct to me!
What kind of gravitational force is required to make something considerably more massive than the Earth (maybe 20 to 60 times), travelling at 60,000 mph away from it and getting it to travel at 1.44 million mph towards it? My humble guess is that it would take a lot more than the Earth's puny 1G. A very close fly-by would probably hardly bend it's trajectory at all with Melacholia being so massive by comparison. Quite the opposite, the tidal forces exhibited by its mass would probably rip the earth apart!