Timeline for If a massive object like Jupiter flew past the Earth how close would it need to come to pull people off of the surface?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2020 at 8:21 | comment | added | Pere | That's the reason the answer starts with "about". | |
| May 29, 2019 at 14:42 | comment | added | David Tonhofer | "The Roche Limit" does not exist for a single body. One could define "A Roche Limit" for a Jupiter-Earth system, but not for a Jupiter. And it would be different for a Jupiter-Mercury system etc. | |
| May 28, 2019 at 21:48 | comment | added | Pere | @mistertribs - Interestingly, that article states that "If the planet passes within the Roche limit at periastron, however, mass can be stripped from it". Likely, that mass would include some people standing on the planet. | |
| May 28, 2019 at 20:04 | comment | added | user24157 | A quick search for the Roche limit for planet-planet scattering Faber et al. (2004), who consider the Roche limit for objects on near-parabolic orbits (their Appendix A gives a brief overview). This situation is probably more relevant to the encounter case discussed in the question than the usual formulation of the Roche limit. | |
| May 28, 2019 at 8:54 | comment | added | Pere | The actual Roche limit for Earth over Jupiter would be way larger, because such a big body like Earth wouldn't behave like a rigid body. | |
| May 28, 2019 at 4:54 | comment | added | Peter Cordes | BTW, in my first comment about being deformed before coming apart, I was referring to the "fluid" Roche limit. Once I looked up the wiki article, I realized that the "rigid" Roche limit is exactly what we want here. That's the assumption of rigid but no tensile strength, which works perfectly for loose objects pulled off the surface. For the integrity of Earth itself: it's squishy long-term (molten rock), and in a close orbit would deform like for the "fluid" Roche limit (which has a much larger radius). Tidal drag speedup up our rotation = catastrophic tsunamis! | |
| May 28, 2019 at 4:49 | comment | added | Peter Cordes | Or the "more accurate" formula for a tidally locked body (including the body's rotation) gives us 62 709 km. But Earth isn't rotating that fast. (The orbital period for a circular orbit just skimming the surface of Jupiter is ~2.86 hours, which is a lot faster than 24 hours, and why this Roche limit formula predicts a body can be torn apart so much farther away than if it's not rotating. | |
| May 28, 2019 at 4:35 | comment | added | Peter Cordes |
@HenningMakholm: I think this answer accidentally took Jupiter's actual radius as its Roche limit!, because the Wikipedia page has a table of density and radius for objects in our solar system at the top of the section for Roche limits for pairs of bodies. The actual rigid-body Roche limit (where objects are pulled off the surface by tidal forces) is $R_m * (2 \rho_M / \rho_m) ^ {1/3}$ = 71493000 * (2 * 1326/5513)^(1/3) = 56 018 km using the "fully rigid-satellite" formula from Wikipedia.
|
|
| May 28, 2019 at 4:18 | comment | added | Peter Cordes | The wikipedia article shows the elongation as part of the torn-apart effect right at the Roche limit. See also video animations like youtube.com/watch?v=tGS_gZm6HxI and youtube.com/watch?v=6e5yyIcq40o. And remember, it's the radius where a rigid or fluid body can't exist long term in a stable circular orbit. An elliptical orbit that just dips in at perigee could conceivably let an aggregate body re-form itself when farther out. See How fast does Roche limit disintegration proceed? on space.SE | |
| May 28, 2019 at 4:10 | comment | added | Peter Cordes | At just inside the Roche limit, the math in @uhoh's answer shows that loose objects aren't literally ripped off the surface. I think the mechanism is more gradual even for a totally non-rigid aggregate of gravel: with its own gravity being unopposed in the other directions, it would elongate in the tidal-force direction. This puts the ends farther and farther from the centre of mass, and increases the distance for the gravity gradient. This eventually leads to it being torn apart, but one quick pass wouldn't rip loose objects off the surface (esp for a stiff / viscous object like Earth) | |
| May 27, 2019 at 21:13 | comment | added | EvilSnack | To this layman it seems obvious that Jupiter's gravity would make life unpleasant (if not impossible) on Earth at a much greater radius than 70Mm. | |
| May 27, 2019 at 13:59 | comment | added | J... | @NuclearWang But... people are held to the earth purely by gravitational forces. Being within the roche limit would not pull humans apart but we would still act like those pebbles in the sense that individual humans would not be stuck to the earth by gravity any longer. | |
| May 27, 2019 at 13:44 | comment | added | Nuclear Hoagie | People aren't held together by gravitational forces, so being inside the Roche limit won't pull them apart like it would for a planet. In that regard, people on the surface do behave differently than rocks - a pile of gravel will separate into individual pebbles as it gets sucked into Jupiter's gravitational well, but a person will remain intact. | |
| May 27, 2019 at 12:53 | history | edited | Pere | CC BY-SA 4.0 |
can't
|
| May 27, 2019 at 11:14 | comment | added | Pere | @HenningMakholm - Starting the answer with "about" was intended to deal with variation of Roche limit due to a lot of factors. However I edited the answer to make it more clear. | |
| May 27, 2019 at 11:13 | history | edited | Pere | CC BY-SA 4.0 |
(although its actual value varies a lot depending on the other involved body)
|
| May 27, 2019 at 11:03 | comment | added | hmakholm left over Monica | Note that 70,000 km also happens to be Jupiter's radius, so the planets would need to be touching. (And there's not a "the" Roche limit; it depends on the density of the secondary object, that is, Earth in this example). | |
| May 27, 2019 at 9:52 | comment | added | uhoh |
I didn't even think to mention the Roche limit; very good point! +1
|
|
| May 27, 2019 at 9:16 | history | answered | Pere | CC BY-SA 4.0 |