If a massive object like Jupiter flew past the Earth how close would it need to come to pull people off of the surface?

  • I understand this is a silly hypothetical but I'm asking for a 7 year old so please bear with me.



    Imagine an interstellar stray gas giant comes flying through our solar system.



    If we were not concerned that it would also steal our atmosphere and create tidal forces that destroyed everything... How close would it need to come to us to exert enough gravity to lift people off the ground and pull them into its own orbit?


    The question would be more interesting with a rather small body (like a small, dense moon or even better, a small black hole) whose gravity field close by is stronger than the Earth's but farther away too weak to suck the Earth in.

    @PeterA.Schneider I'm not quite sure what you mean. If in the answers below you replaced Jupiter with a black hole of the same mass, there'd be no significant difference (initially at least): the gravitational force is more or less the same.

    @Chappo Not of the same mass but of a much smaller mass, and much closer, exploiting the inhomogeneity of its gravitational field. Imagine a black hole 10 km above us exerting 1g on us. (Its mass would be much smaller than Jupiter's.) The far side of the earth, being 12000 km away, would only experience (12000/10)^2 ~ 1.4E-6 g, i.e. almost no attraction. *That* black hole flying by at **9** km distance would suck us up, and some of the upper 1 km of earth's crust.

    That would be a cute story if one day, we wake up and we find out that birds disappeared, "stolen" by a planet passing by

    I think you could get a more "fun" answer if you wrote to what-if.xkcd.com.

    @Barmar: Assuming that's even still active - the last post there was months ago at least.

    This is the very definition of the Roche limit of the passing body.

    @LorenPechtel Which means that things like mountains and the seas get sucked up too.

    @Aron Correct. The planet is destroyed.

    @Barmar If Randall answered it, then, yes, it would. Sadly, Randall's last post on What If was a year ago last week.

    @reirab Yes, someone else already pointed out that he seems to have abandoned What If.

    @reirab No, it can't be! Surely he's just working on a new What-If book, keep the faith!

    @Aron If you were very, very careful, no. Mountains aren't held to the Earth's surface merely through gravity, while humans are. The same is true for oceans, though there the extra attractive force is much smaller. Of course, both planets would be rather disturbed anyway, but the OP explicitly said he doesn't want to consider those effects.

  • uhoh

    uhoh Correct answer

    3 years ago

    TL:DR Jupiter isn't dense enough for its gravity gradient over Earth's radius to produce a 1g tidal acceleration, even right at Jupiter's surface.




    thanks to PeterCordes






    Jupiter's gravity will pull on the Earth itself, as well as everything on it.



    It's not like a vacuum cleaner that selectively lifts small and light objects, the gravitational force will scale with the mass of each object; if the Earth is a zillion times more massive than we are, then Jupiter's gravitational force will also be about a zillion times larger.



    What that means is that Earth will accelerate towards Jupiter, and we will accelerate along with it, and so we won't "feel the tug" anywhere near as strongly as one might suspect.



    Instead, let's think about the size of the Earth, and the fact that people on the near side will be closer to Jupiter than the center of mass of the Earth, and people on the far side will be farther away.



    Since people nearer to Jupiter will feel a slightly stronger acceleration than the center of mass of the Earth, they will feel a quite gentle tug. We'll calculate that in a minute.



    But believe it or not, people on the far side of the Earth, feeling less of a tug than the Earth's center of mass, will believe they are being pulled in the opposite direction! They won't really be pulled away from Jupiter, but they will not accelerate towards Jupiter as fast as the Earth, and so it will feel like they are being repelled.



    This kind of force is called a tidal force and this is the picture that's often used with the concept:



    enter image description here Source Replace "Satellite" with "Jupiter"



    The acceleration we feel due to gravity is expressed as



    $$a_G = \frac{GM}{r^2}$$



    where $G$ is the gravitational constant and equal to about $6.674 \times 10^{-11}$ m^3/kg s^2 and M is each mass that's pulling on you.



    If you put in 6378137 meters and the mass of the Earth ($5.972 \times 10^{+24}$ kg) you get the familiar 9.8 m/s^2.



    If Jupiter were 114,000,000 meters or 114,000 kilometers away, the Earth would accelerate at 1 g towards it, but people on the close and far side would accelerate very differently. On the close side, being 6,378 kilometers closer, would feel an acceleration 1.2 m/s^2 greater, so they would feel that they weighed 12% less. And people on the far side would also feel about the same amount lighter because they felt less acceleration than the Earth.



    If Jupiter were so close that it were practically touching the Earth, it still wouldn't pull is off of Earth, assuming that Earth remained intact. But that wouldn't last very long!!! Earth would be accelerating towards Jupiter at about 20.9 m/s^2, and people on the near side would feel acceleration of 24.8 towards Jupiter, but relative to Earth that's only 3.9 m/s^2, so not enough to overcome Earth's gravity of -9.8 m/s^2.



    On the far side of Earth it's similar; the acceleration towards Jupiter would be 17.8 m/s^2 but minus Earth's acceleration of - 20.9 it's -3.0 m/s^2 away, but that's also not enough to overcome the attraction to Earth of in this case +9.8 m/s^2.



    When Earth touches Jupiter, we will feel about 40% lighter on the near side and 31% lighter on the far side of Earth, but we would not leave the surface.



    However, in just minutes we'd be pulled so deep into Jupiter that we would be crushed by Jupiter's internal atmospheric pressure.



    It would certainly be fun, but it wouldn't last long!


    @ShakesBeerCH it looks like your edit was rejected, but there was indeed an error in the arithmetic. $GM_J/(R_E+R_J)^2=20.9$ m/s^2, etc. Can you check again, thanks!

    Isn't the earth's momentum a zillion times larger, so its motion won't be perturbed as much as a person?

    @Barmar double check the second paragraph that begins with: "It's not like a vacuum cleaner that selectively lifts small and light objects..." The Earth's momentum does not affect the Earth's *acceleration*, and the acceleration of objects of different sizes near Jupiter will be (almost) the same because the force depends on the mass; $F_E=M_EM_J/r^2$ so the acceleration $a_E=F/M_E=M_J/r^2$ is independent of the mass. I say "almost" because the Earth is so big that it's gravitational effect on Jupiter is very small but can't be completely neglected.

    TL:DR Jupiter isn't dense enough for its gravity gradient over Earth's radius to produce a 1g tidal acceleration, even right at Jupiter's surface.

    @PeterCordes that's so much better than I could have done I've just quoted you, thank you. Please feel free to edit the answer further!

    Glad I could help, thanks for doing the math and writing it up, this is an interesting Q&A. :) I thought about adding in the phrasing "having the Earth pulled out from under them (even faster than the extra pull of Earth + Jupiter)" for the people on the far side, but I don't see a place to put it without being redundant or rewriting a whole chunk.

    Lighter on the far side?

    @mckenzm yes. Earth's center of mass is closer to Jupiter than the people on the far side, so *Earth experiences a greater acceleration* than the people do. That's why the diagram showing outward-pointing arrows on *both sides* of the Earth is always confusing at first.

    "On the close side, being 6,378 kilometers closer, would feel an acceleration 1.2 m/s^2 less" <- 1.2 m/s^2 _more_?

    @LoganPickup yep I think you're right, changing now. Thank you!

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