Is Melancholia's orbit impossible?

Question

In the recent movie "Melancholia", a planet, also called Melancholia, enters the solar system and hits the Earth. I want to leave aside the (also unreasonable) aspect that planet "hides behind the Sun" and is undetected until it's a few weeks from Earth. I want to focus on the final stages. In the movie, the planet passes close to the Earth, starts receding, doubles back and hits the Earth, all in a few days. My question: Is that physically possible? I guess not, but I was never good at orbital mechanics.

Assume the givens are as in the movie. One of the main characters finds on the internet a path for the planet that seems to what it eventually does. Mass of the planet is four times that of the earth?

Answer 1

A planet that was four times the mass of the Earth would tend to drag and/or slingshot the Earth out of its orbit; multiple interactions are possible depending on the details of the first pass, but any further interactions would take place around the center of mass of the Earth-Melancholia system, which you would find by adding their initial vectors weighted by their mass (assuming that we can neglect the sun, which we can't, but it gives you a very approximate idea of what would happen).

Answer 2

It seems to me that if Melancholia were four times the mass of the Earth, and passing behind us in our orbit, its gravity would have sling-shotted us backwards into a retrograde orbit while changing the path of Melancholia into a prograde orbit at a similar distance from the Sun as is the Earth. The planet would appear to recede from us leaving the Earth "spared." However, in six month's time Melancholia would barral down on us at a combined speed of 132,000 miles per hour (37 miles a second!).

For a simmilar celestial game of "planet pool" I suggest that you look up the H.G. Welles story, "The Star". It predicts nicely the effects of a small star which wanders through the Solar system.

Answer 3

Melancholia seems to be much larger in mass than 4x. This website allows you to simulate the setup in the movie. It suggests that the earth would come out of its orbit and smash into Melancholia without any full orbits at all.

http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

Answer 4

I am not an expert but I believe that, having in mind the earth's orbit around the Sun during Summer is closer than winter. Therefore there could be some time of the year that Sun could block our view of what might be behind the Sun, more or less time depending on our position. According to the movie plot the planet called melancholia was moving away from the Sun, but Sun being a much heavier object affects the path of the melancholia in a way to hit the earth. It is a matter of calculation to find what is going to hit, which means huge changes in the solar system and long time to regain balance.