Continuing on the failure of my concept of turning Jupiter into a sun, I’ve been considering other means of terraforming Ganymede. One way I thought of was to use steered asteroids to “nudge” Ganymede into a closer orbit, so tidal flexing from Jupiter would heat the surface and melt the ice. I got the idea because io, the farthest in of the Galilean moons, is very geologically active and hot because of this phenomenon. Would this work?
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2$\begingroup$ Simple answer: Sure. More Complete Answer: changing the orbit of one moon changes the orbits of other (if not all) moons with very difficult to determine consequences. Complete answer: No, we do not have that tech today and by the time we have it the simple answer wins. My point... Why are you asking? From a suspension-of-disbelief perspective, this is a great idea. But, like each and every idea that's beyond the scope of current tech, we can always point out reasons why you can't do it. Does that matter to you? What's the real question? $\endgroup$– JBHCommented Oct 14, 2022 at 19:05
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1$\begingroup$ I understand completely that this will require more advanced technology than we have so far (given that we haven’t personally gone beyond the moon) I’m focusing on the method. If this is okay with future technology, then that’s goo enough for me. Thanks! $\endgroup$– user98816Commented Oct 15, 2022 at 11:10
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1$\begingroup$ As you use the Stack, please note Arthur C. Clarke's third law: "Any sufficiently advanced technology is indistinguishable from magic." That's why I asked what your real question is, because anything in your imagination is possible given Clarke's third law and time. There are many reasons why an idea won't work, my personal favorite is economics. (Can you do it? Sure! With enough time and a mountain of money. Don't have the money? Then you can't do it.) So it's only worth asking "would this work?" if you can explain limitations and conditions. Without them, the answer is always "yes." $\endgroup$– JBHCommented Oct 15, 2022 at 17:58
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$\begingroup$ You so lusty for Io, @user98816. All her flexing and hotness. And I heard she likes you too. Why not just plant your base on Io? Wink, wink, say no more, but no nudging necessary. Ganymede can do her Ganymede thing in peace. But before you make the first overtures you might consider changing your username to something that rolls off the tongue. I suggest BULCAN because he is god of the forge, and big. $\endgroup$– WillkCommented Oct 15, 2022 at 21:04
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1 Answer
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Several issues here:
Scale
Ganymede is $1.4819*10^{23}\text{ kg}$. For comparison, the total mass of the Jupiter L4 Trojan asteroids is $6*10^{20}\text{ kg}$.
Assume for a moment that we're using a 1km radius M-class asteroid. Density of $5 \text{g}/\text{cm}^3$, so total mass of $10^{13}\text{ kg}$ or so.
Ignore Jupiter for a moment, and just look at Ganymede and said asteroid. Ditto, ignore orbits for a moment. Consider what would happen if we somehow held said asteroid just above Ganymede's surface, to maximize gravitational acceleration. Ganymede has a radius of 2634.1 km, (+1km additional for the asteroid of radius 1km), so the resulting acceleration is about $10^{-11} \text{m}/\text{s}^2$. This gives the absolute best-case resulting acceleration.
This is decidedly outside the range where a Hohmann transfer is appropriate, so we have to do a circular transfer. The cost of a circular transfer between two circular orbits, is, to a first approximation, just the difference in velocities of the two orbits.
Say we wanted to move Ganymede into Europa's orbit (ignore for a moment that you'd have to do something with Europa in the process). Ganymede's orbital velocity is 10.88km/s. Europa's is 13.74 km/s. So a difference of 2.86 km/s.
How long would this take? Well, 2.86 km/s at $10^{-11} \text{m}/\text{s}^2$ is about... oh. Just under a million years. And again, this is under unrealistically optimistic assumptions. You can't hold asteroids right above the surface. You have to have them in (unbound) orbits, which means they will be on average further away. And gravitational acceleration is an inverse-square with distance...
Resonances
The inner Galilean moons are in a stable 1:2:4 orbital resonance. It is not clear what would happen if you tried to nudge one of the moons out of its orbit; I suspect this would perturb the other moons, or would cost more delta-v than expected, or both.
Energy Output
Ganymede is currently tidally locked with Jupiter, and hence rotates once every 7.15 days. If it was dropped into Europa's orbit, it would then try to tidally lock into a 3.55 day rotation.
Time for tidal locking is roughly given by $t_{lock} \approxeq \frac{0.4 \omega \alpha^6 m_s R_s^2}{3 G m_p^2 k_2 R_s^5 }$. Note that this scales with the orbital radius to the sixth (!) power. $k_2 \approxeq \frac{1.5} {1 + \frac{19 \mu} {2 \rho g R_s}} \approxeq 0.003737$ (link), so $t_{lock} \approxeq 7.4*10^{15}\text{ years}$ (link).
The energy output by tidal heating comes from the difference in rotation rates, and hence is upper-bounded by the rotational kinetic energy.
The energy to go from a 7.15 day rotation to a 3.55 day rotation is approximately $6.7*10^{25}J-1.7*10^{25}J$, or about $5*10^{25}J$. (link) $5*10^{25}J$ in $7.4*10^{15}\text{ years}$ is about 215 W. 215W across an entire moon is... effectively negligible.
(Why, when Io is affected so much by tidal heating? Partially because Io's tidal heating is largely driven by orbital eccentricity not rotation speed, and partially because Io is so much closer - and tidal locking time scaling with orbital radius to the sixth power implies tidal heating scaling with the inverse sixth power of orbital radius. Unfortunately, moving Ganymede closer takes even more time, and deflecting Ganymede into a non-circular orbit isn't really possible via asteroid deflections.)
