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In the movie Melancholia, one of the characters finds this diagram on the internet showing the planet approaching, passing, and then slingshotting around to hit earth. In the end, that seems to be exactly what happened. Does this make any sense from a physics point of view?

enter image description here

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This may be more appropriate for Physics.SE. –  gnovice Jun 25 '12 at 14:48
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Actually, this was already asked on Physics.SE, and Rex Kerr below gave the accepted answer there as well. –  Mark Beadles Jun 25 '12 at 16:04
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Although what about this screen grab from the movie, which is different? i.stack.imgur.com/4Ww2o.jpg –  Mark Beadles Jun 25 '12 at 16:07
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@MarkBeadles: That image shows the movement of both planets around the sun. The image above shows the movement of Melancholia around the Earth. –  gnovice Jun 25 '12 at 16:25
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Already asked and answered on Physics(physics.stackexchange.com/questions/15083/… it is about) –  KHW Feb 28 at 21:51
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closed as off-topic by KHW, Richard, Monty129, Kalissar, DVK Mar 1 at 2:45

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7 Answers

It's not possible as shown for multiple reasons. The main one is conservation of momentum: initially, Earth is moving left while Melancholia is moving up. When they collide, the total momentum vector (speed*mass for Earth + speed*mass for Melancholia) must remain the same. So the Earth would have to be well off its orbit and heading up-and-left with Melancholia coming in behind it.

Also, conservation of angular momentum around the Earth-Melancholia system would mean that given how close Melancholia passes the second time (so close that it hits Earth), it would have to be traveling extraordinarily fast--but then there is no way for Earth's gravity to turn it around at point (6).

So, no. Not physically plausible; you need to get other bodies involved for such gymnastics (e.g. the Sun), and here there was neither space nor time for that to happen. (A passing black hole that nearly collided with Melancholia at point (6) would do the trick, I guess....)

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Not even slightly possible. Not even after point 2. As mentioned above, let's assume Melancholia is a rock like planet. The graphics indicate it is when the Earth smashes into it near the beginning of the movie.

According to the path, Melancholia is moving away from the Sun across Earth's orbit. So the Sun's gravity is already out of play. When Melancholia passes behind Earth (between points 2 and 3), Earth's mass would slightly pull Melancholia left, but after that, it would continue on in a straight line out of the solar system. What could happen on a such a close pass is that tidal forces from Melancholia could rip the Earth's crust.

But anyway, anything after point two could never happen. It would be like rolling a marble in front of a bowling ball and expecting the bowling ball to not only move towards the marble, but to speed up so it catches it.

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This is, as displayed by the graphic, patently impossible. With Melancholia supposedly a planet equal to or larger than Earth, there is no way it could ever be in a position to chase down the Earth after passing around it that manner AFTER coming around the sun, as it does in position two.

enter image description here

Let's assume it could come around the sun slowly enough to track around the Earth as it does in positions 3, 4, 5, being a planet equally as large as Earth would require a very close passage to the surface of Earth (far inside the orbit of the moon) in order to slow down enough to even consider reaching position 6.

There is no way any position after position 6 could take place unless there was something for Melancholia to bounce off of. The gravitational effect required to draw such a massive body back toward the Earth would require a mass many times the mass of the current Earth, given the incredible mass Melancholia would have. Objects in motion tend to stay in motion. Gravity is definitely not the force for attracting an Earth-size body toward another Earth-sized body once they are moving AWAY from each other at decent speeds.

This story could have still taken place, albeit some years later if the orbit of Melancholia moved around position 5 and had the planet share the same kind of orbit as the Earth. Eventually moving counter to the movement of the Earth, it could possibly, eventually intersect the orbit of the Earth, catastrophically.

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Well I am no scientist, but for starters let's look at the speeds involved and the likely size and mass of Melancholia.

Firstly, its size and mass. The planet looks from the shots in space to be about 4 times the diameter of the Earth, and therefore if my maths is right, around 64 times the volume of the Earth. Of course we don't know its density, but it certainly looks to be a similar style solid rock planet.

If the density is the same, we have an object around 64 times the mass of the Earth. Ouch.

Next, its speed. John mentions, prior to Melancholia's boomerang move to smash into the Earth, that it is travelling away from the Earth at 60,000 mph. Now, in the 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 of 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 (64 times is my ballpark guess), travelling at 60,000 mph away from it and getting it to travel at 1.5 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 its trajectory at all with Melacholia being so massive by comparison.

An exo-planet being tossed out of its solar orbit and eventually finding our solar system is exceptionally improbable, but certainly not impossible. But I think the science of its orbit could have been worked better. Maybe initially passing the Earth and moving away, and then some months later meeting the Earth again after a trip past the Sun (something as massive as the Sun could certainly bend the planet's trajectory if it got close enough, as it was supposed to have done in the movie before reaching Earth).

Another couple of scientific flaws I have noticed:

1) In the scene where they are on the balcony at night viewing Melancholia's moon-style rise, we hear the planet rumbling away. How would that sound travel through the total vacuum of space to the ears of the observer? We'd hear nothing, because there would be nothing for it to travel through.

2) Does anyone else but me think the planet is a bit too beautiful and blue and swirly considering it's been travelling through space at temperatures of near absolute zero for probably tens of thousands of years at least, then gets cooked by our Sun on its way past? :)

3) Wondering if tidal forces would have ripped the planet and final scene apart long before impact given the mass difference as things started to "fall" towards the massive planet at 64G?

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1) I think the sound is probably related to tidal stress on the earth, sea and atmosphere, not travelling through space from Melancholia itself 2)&3) - yes –  zipquincy Aug 13 '12 at 15:29
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Well we're talking about the science of what is a metaphor in the movie, there was no actual planet as such.

Even still it's more likely such a thing would throw earth out of it's orbit, as it is far bigger the earth would be in the sling shot, not melancholia. Secondly a near miss would be enough to kill us all, with the sheer power of it's gravity tearing at tectonic plates causing catastrophic earthquakes and volcanic activity. If not close enough for that it would cause massive king tides that would devastate coastal cities across the planet.

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The Dance of Death, as diagrammed, wouldn't happen:

  • Melancholia would not slingshot around the Earth between points 2 and 5 as it is much larger and so shouldn't be affected by Earth's gravity in that way.
  • If somehow it did then it would also have to gain a tremendous amount of speed to catch up with the Earth in order to collide with it.
  • What is it slingshotting around at point 6??

The Path of Melancholia diagram also looks very odd: - Look at the path before it turns. Why is it straight then turning suddenly? Surely it would be affected by gravity before then; the shape should be elliptical.

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The image and screen grab are compatible (within the confines of the movie's suspension of disbelief). The black-background screen grab shows Melancholia's swing around the Sun and how it just misses the Earth, which is what the father in the movie wanted everyone to believe, and apparently what mainstream scientists were predicting. The white-background image above was a kind of conspiracy theory being circulated around the internet picked up by his wife, which eventually played out in the movie, namely that after Melancholia's "flyby" past Earth, it swung around and again to hit it. So there is no incompatibility here. One is a continuation of the other. I would be interested in reading what would really happen to Earth if such a huge planet flew past it at such close range. People have mentioned tides and volcanos... would anyone have survived?

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As it stands, this answer is largely a response to the comment by Mark Beadles. With some edits, this could probably be turned into an answer of its own - though, you'd need to leave out starting a new discussion regarding what would happen to Earth and ask your own question if you feel so inclined. –  phantom42 May 20 '13 at 14:46
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