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SPOILERS FOR "INDEPENDENCE DAY: RESURGENCE" ABOUND.

I just watch ID:R and had a question about a plot point. In the movie, a large alien ship, which looked to be about 10-20 percent the size of Earth lands/parks on Earth. It's not solid through and through, so its specific gravity wouldn't be identical to the mass per volume of Earth, but it would still have an enormous mass nontheless. Wouldn't the increased mass cause a change in the gravitational pull between Earth and the Sun, and eventually cause Earth to spiral in and collide with our star?

It's hard to say how long the ship stayed on Earth (it left). But would a few hours be enough to affect the gravitational pull and start the inward spiral?

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  • $\begingroup$ Since Earth is in solar orbit and the ship is in the same solar orbit, they are both falling freely in exactly the same way and neither feels the attraction of the sun, at all (except for tidal forces). Such a body could, however, change the orbit of the planet gradually by making many passes inside or outside of earth's solar orbit. This is usually used to accelerate or decelerate spacecraft around the sun, but it can, in principle, be used to "drag" a planet to a farther orbit or to move it closer to the star. $\endgroup$ – CuriousOne Jul 12 '16 at 7:03
  • $\begingroup$ Oh ok. I had a thought years ago where maybe eons of meteors, meteorites, and other galactic dust entering our atmosphere and not leaving made our planet heavier, and the planet would spiral in toward the sun. But that would be the same scenario of the ship parking here. Thanks. $\endgroup$ – user38537 Jul 12 '16 at 8:25
  • $\begingroup$ The Earth is not spiraling inwards. Actually, its orbital distances are slightly increasing because the sun is slowly moving mass to the solar wind and its radiation. The effect is very small, though. $\endgroup$ – CuriousOne Jul 12 '16 at 18:40
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If you add mass to the Earth, or the "Earth system", it makes not the slightest bit of difference to the orbit unless you also change the Earth's angular momentum around the Sun.

That is because the basic dynamical equation controlling the orbit is that the inward gravitational force due to the the Sun is equal to the mass times centripetal acceleration.

Since the mass of the "Earth system" appears on both sides of th is equation it cancels out and nothing changes.

On the other hand, if you add angular momentum to the Earth then its orbital radius will increase, and vice versa. In principle this could be achieved by the close approach of another massive body to the Earth that did not have a matching orbital speed.

There is no scenario where the Earth spirals in to the Sun.

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  • $\begingroup$ You want to maintain the ratio of earth(+ship) mass to angular momentum constant to not perturb the orbit. This is the same as maintaining velocity. $\endgroup$ – Ross Millikan Jul 12 '16 at 14:20

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