Can Mars disintegrate entirely in this scenario?

Question

I have a hypothetical scenario in which Mars flies over Jupiter at close range. I want to make Mars disintegrate entirely in this scenario while keeping the scenario scientifically accurate (please ignore the part about why Mars leaves its orbit). The outline of my scenario is as follows:

• Mars goes deep into Jupiter's Roche limit. At the closest point, the surface of Mars can be as close as 1000 km from Jupiter's tropopause if necessary.
• Before the fly-over, Mars's rotation can be accelerated to up to 1 Martian day per hour if that helps Mars to disintegrate.
• Mars can fly over Jupiter with any relative orientation, i.e. it can have its pole or equator or anything in between facing Jupiter, whichever helps it to disintegrate.
• Mars has only one chance to fly over Jupiter. (It's okay if Jupiter captures Mars or all the remains of it in orbit. But if Mars survives this fly-over and escapes Jupiter, and encounters Jupiter again in the future, the outcomes of those encounters do not matter for this question.)
• You can use the gravitational slingshot effect of Jupiter if that helps Mars to disintegrate.
• You can use millions of super-deep drillings and nuclear bombs to introduce fractures in the Martian crust if that helps.

And my question is: Can Mars disintegrate entirely in this scenario, given the conditions above? Here, "disintegrate entirely" means that no fragments of Mars should have a mass greater than 1% Martian mass. Also, most of Mars' mass should not fall into (the atmosphere of) Jupiter.

Answer 1

Yes, and no need to introduce fast rotation, or nukes or anything similar.

The Roche limit for liquid bodies is $d=2.544R \sqrt[3]{\frac{\rho_M}{\rho_m}}$, where $R$ is the radius of the more massive body, and $\rho_M$ and $\rho_m$ are the densities of the more and less massive bodies, respectfully.

Using $R \approx 71,492 \text{ km}$, $\rho_M \approx 1326 \frac{\text{kg}}{\text{m}^3}$, and $\rho_m \approx 3930 \frac{\text{kg}}{\text{m}^3}$, I get $d \approx 122,187 \text{ km}$.

Shoemaker Levy-9 was shredded when it passed at about $96,000 \text{ km}$ and it was estimated at a tiny 1.2-1.7 km diameter sphere.

If Mars passed through an orbit at this distance, as it approached perijove the initial tidal forces would crack its crust like a pool ball in a vise. Those fragments would continue to break apart and separate until small enough that their cohesive forces outweighed the tidal forces. Mars' liquid core would separate into small droplets. It is doubtful that solid crust fragments much larger than Shoemaker Levy-9 would remain intact, which would be much, much smaller than 1% of Mars. Note that Mars's paltry radius of less than $3400 \text{ km}$ would mean the entirety of Mars would be within the Roche boundary, while not reaching the cloud tops of Jupiter at about $71,492 \text{ km}$. Similar to the fragments of Shoemaker Levy-9, most of the Martian fragments would not re-coalesce as their minor mutual gravitation would have negligible effects on their orbit compared to the close by and massive Jupiter. By the time they were out of Jupiter's Hill Sphere (assuming a sufficiently high velocity pass), the fragments' differential velocity would exceed mutual escape velocity and the Sun would dominate their resulting orbits.

The closer Mars passes to Jupiter, the smaller the resulting fragments!

Answer 2

One part of the question says:

Before the fly-over, Mars's rotation can be accelerated to up to 1 Martian day per hour if that helps Mars to disintegrate.

Would that help Mars break up into pieces?

It might.

Habitable Planets for Man, Stephen Ho. Dole, 1964, pp. 58-60, says that the lower limit for the length of day of a habitable planet would be when the planet rotates so fast that material on the equator reached orbital velocity.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

Dole also discusses how rotation rates can affect the shapes of planets on pages 41-48.

Mars has a mean radius of 3,389.5 kilometers and an equatorial radius of about 3,396.2 plus or minus 0.1 kilometers. Thus it has an equatorial circumference of about 21,338.935 kilometers. If Mars rotated once in one Earth hour of 3,600 seconds it would rotate at about 21,338.935 kilometers per hour or about 5.9274819 kilometers per second. That is larger than the orbital velocity at the Martian surface. In fact it is also larger than the Martian escape velocity (at the surface) of 5.027 kilometers per second.

So if Mars stars rotating that fast a lot of Martian material will fly away at more than escape velocity, and a lot of other material will start to orbit the planet.

But that would not be enough to make Mars entirely disintegrate. You want no chunks of Mars larger than 1 percent of the Martian mass to remain.

If all of Mars had the same density as its overall density a body with 0.01 the volume of Mars would have 0.01 the mass of Mars. According to my rough calculations the cube root of 0.01 is approximately 0.2154444. So a spherical object with the overall density of Mars and 0.01 Mars' mass would have 0.01 of Mar's volume and thus a radius of 0.2154444 of Mars' radius and thus a radius of 730.24843 kilometers. Such an object would probably be pulled into a spheroidal shape by its gravity, though it might take a long time for a jagged Martian fragment to do so.

Since the Martian crust, mantle, and core have different average densities, crust and mantle fragments with 1 percent of the mass of Mars would be larger, and core g fragments with 0.01 percent the mass of Mass would be smaller, than calculated above.

The Martian iron nickel sulfur core is quite large, believed to have a radius of 1,794 kilometers (1,115 miles) plus or minus 65 kilometers. The Martian core is partially fluid.

https://planetary-science.org/mars-research/internal-structure-of-mars/

The Martian core radius is more than half the radius of Mars and about half the size of the Earth's core. This is somewhat larger than models predicted, suggesting that the core contains some amount of lighter elements like oxygen and hydrogen in addition to the iron–nickel alloy and about 15% of sulfur.[36][37]

https://en.wikipedia.org/wiki/Mars#Internal_structure

Guessing that a chunk of Martian core that had 0.01 of the total mass of Mars might have a radius of only maybe 500 kilometers, twenty or thirty of them might fit within the core of Mars. Thus the Martian core might have to broken up into many smaller pieces so that none of the pieces had more than 0.01 of Mars's total mass.

There isn't much problem with breaking up the parts of the Martian core which are still fluid. If Mars spins rapidly enough, or passes close enough to jupiter, the fluid parts of the Martian core will find themselves in orbit around the remnant of Mars or even escaping from Mars.

But the solid inner core of Mars would be a problem. It would have originally been molten and gradually cooled to solid state over billions of years. So it would be essentially a single giant piece of solid metal and other materials. It would not be held together merely by its gravity but also by electrochemical attraction between its atoms and molecules. And those bounds might be harder to break than those of gravity and require greater stress.

If Mars does break up and the pieces go into orbit around Jupiter, it would become like a super asteroid belt for space mining.

Answer 3

Keeping in mind many of the theories of the Formation and evolution of main rings. And as you mentioned Mars could travels within the Roche limit, Édouard Roche himself proposed that the rings are part of a large moon or captured planet that simply got too close. The only question I would have would be the time frame of such an interaction would take place across and if it is within your criteria of the mass being disrupted down to %1 of Mars original mass.

Answer 4

Given

" ... You can use millions of super-deep drillings and nuclear bombs to introduce fractures in the Martian crust if that helps.."

then

Ender Wiggins and Dr Device can make it a certainty, with or without Jupiter.