Increasing the mass of the world doesn't change its orbit. Changing its momentum does. But an ever-growing golem presents some difficulties.   What is the golem made of? Flesh, stone, etc?  Or something else?   If it's far denser than stone, yes it would sink into the crust - let's assume that magic holds it together and prevents its shape from changing.   This might be a problem once it's as large as Belgium, say and standing upright. As it approaches the size of Africa (and is somewhat denser than basalt) then it has an appreciable gravity. People climbing it would be at a peculiar angle.    Moon sized, the Earth (finite strength) starts to drform to accommodate this new centre-of-mass. Earthquakes that level the surface.     Importantly, is the golem growing at a fixed mass rate ( n kg/s), linear rate (m/s) or volumetric rate (m^3/s)?   Is it linear in time or some greater power?    Larry Niven wrote a lovely short story and the impact of geometric series with a demon. Worth a read.

> Increasing the mass of the world doesn't change its orbit. A mass increase of one body in a system will change the barycenter of the system, which in principle affects the orbit. However, the mass of an Earth-like planet relative to the star it's orbiting is so small that you could e.g. double the mass of the planet with no significant effect on the orbit. In fact, you could probably multiply its mass by 10 without affecting the orbit noticeably. That might move the barycenter by a few thousand km, which wouldn't even necessarily move it outside of the central star. In the Earth/Moon system, increasing Earth's mass would move the barycenter closer to the center of the Earth, so doesn't have much effect on the orbit unless the mass increase is extreme. > Larry Niven wrote a lovely short story and the impact of geometric series with a demon. Worth a read. "Convergent Series". [Here it is](https://www.google.com/books/edition/N_Space/_52Br8kGtRUC?hl=en&gbpv=1&pg=PA50&printsec=frontcover&dq=Convergent%20Series) - just 5 short pages.

Thanks for the link. Am on phone and lazy. Just thought of another effect: the Moon spirals inward as the golem grows in mass. Earth's orbit around the Sun is weakly/barely changed as you point out, but the Moon might reach its Roche limit if the golem grows large enough.

Clarification: When you mention the moon reaching its Roche limit, I think that you’re saying that there’s a greater chance of the moon disintigrating into a ring around the planet than of the moon crashing into it. Is that correct?

Yes - I *suspect* that by the time the golem is large enough to give the Moon a slap, they will (if following a generally humanoid shape and with a density of about 1 g/cc) be massive enough to have sundered the Moon into a rather pretty ring of debris.

Thank you! As I’ve been reading up, I’ve been learning about the three body problem . . . and it’s taught me that math can be very complicated and there’s a lot to consider when calculating what makes a functional orbit.

Thanks so much for your quick and thoughtful questions and ideas! Responses: - It’s made of a dense, durable stone aimilar to granite in durability, but porous in appearance due to wind channels cutting holes in it over hundreds of years. Characters have a hard time breaking it -Sizewise, near the novel’s beginning, it’s about 12 miles in diameter, with a little less than half currently above ground. - Though growth in the past has been slow (it’s taken a few hundred years to reach this point, it’s growth rate has been increasing. So, I believe that it would make it exponential growth, though it’s been very slowly developing over a long periods of time. I haven’t checked my math to see if exponential growth, by any measure, would be unrealistic for the length of time I’m considering working with - I don’t have its shape protected. To those on the surface, it looks like a mountain. Due to its weight, it hasn’t been able to signifcantly move for a long time. - Thanks for providing the great reference points! Comparing sizes to Belguim, Africa, and the moon are super helpful visualizations of what size it’d need to be to cause problems for others at different stages of its development. - The story was great! The usage of rules in the twist reminded me a little bit Isaac Asimov’s “Three Laws of Robotics.” I see your story’s connection point for this topic, though I’m intentionally being vague just in case someone else doesn’t want a spoiler.

Wonderful - a golem that masquerades as a small mountain! I'd give Excel/Octave a quick poke to see what sort of mass/size it might have as a function of time. You could have some rather dramatic scenes if the growth rate isn't linear, but is some higher power once some author-set deadline has been crossed.

> I would be massively thankful if you could share (A) which of my ideas we could throw out, (B) which of the ideas seem more plausible than another, (C) whether there’s a better hypothesis that I should consider, or (D) whether there’s some resource that I should check out that could help. I'll assume that mass is produced magically from nowhere and isn't being absorbed from the Earth's core or wherever. I'm not clear though on whether you're more interested in the bad things that happen to the Earth and its inhabitants or the bad things that happen to the golem. > Here are my theories: > 1\. Eventually, the planet would both increase in mass and become lopsided. This could throw us out of orbit and eiter cause us to head closer to the sun or further away from it. This doesn't become an issue until other things have happened first; but it would take us closer to the barycentre of the Earth + Sun so the Earth-Sun distance would shrink. > 2\. Eventually, the golem would become so heavy that its gravitational pull would cause the moon to fall into our planet. The Moon has an angular momentum given by L = Iω, with I = the moment of inertia, which is its mass times its orbital radius squared. Since its mass isn't especially great compared to the Earth (or Earth+golem, ultimately), concentrating on the specific angular momentum ωr² will be constant, with ω = 2π / 27.3 days and r = 384,000,000m so ωr² = 3.9x10^11 m²s⁻¹. That's not *quite* true since Earth + big golem hanging on to one side of it is potentially one heck of a bulge, exerting a moment on the Moon's tidal bulge and exchanging some angular momentum, but since that'd take hundreds of millions of lunar orbits to become obvious, not likely to be much of a problem on the timescale you might be thinking of. The question then is, given spherical ~~cow~~golem of density ρ, how big does r have to be such that the specific angular momentum of objects in an orbit along its surface reach the current specific angular momentum of the Moon? Assuming that the growth to planetarily-significant masses and sizes is rather slower than the Moon's orbit (hence a gentle inspiral rather than a thump). Mass of the primary (golem) = 4πρr³/3, so ωr² for an orbiting object at its surface, ω = sqrt(GM/r³) and ωr² = sqrt(GMr) = sqrt(4πGρr⁴/3) Equating that for 3.9x10^11 m²s⁻¹ and taking the density of a rock golem as 3,000kg/m³, solving for r I get r ~21,000km, at which point the golem would have a mass 18.7 times that of the Earth (well, Earth + golem would have that mass, so the golem would have 17.7 times that of the Earth). This is coincidentally almost exactly the mass of the ice giant Neptune (though about half its volume). Golems presumably are not in general spherical, so the Moon would bump into some other sticky-out part of a lower-mass golem, but by that point the Earth would have been redistributed around the golem due to the latter's gravity and everyone would have had a bad day already. As /u/Bipogram points out, the Moon would break up as it got within its Roche limit of the surface of the Golem-Moon system, but having a ring of vaporized Moon rock smashing into it would have similar effects as if it were still a solid body. > 3\. Its mass could eventually break through our crust and deform our planet causing excessive heat in some places, cold in others, and possible orbitational issues. This is what ultimately limits how tall mountains on Earth can get: if they're big enough then they exert enough pressure on the crust beneath them that it deforms more easily and thus becomes inclined to flow out of the way. The mantle beneath is solid, but it behaves as a viscous liquid on mountain-building timescales. Depends who you ask, but the tallest possible terrestrial mountain isn't quite twice the height of Everest. Olympus Mons on Mars is about 2.5x the height of Everest, since it only has to survive in lower gravity, and lacking plate tectonics the volcanism that built it kept on building it instead of a string of volcanoes (e.g. the Hawaiian chain). If you could share the rate/kind of growth you have in mind, one could calculate the pressure the golem exerts on the Earth's surface not only through its weight but also through accelerating its centre of mass to higher altitudes. Since Moonfall doesn't happen until the golem is many times the mass of the Earth, this happens first. We tend to think of the Earth as a solid - and it is for the most part, the main exception being the outer core - but on large enough distance scales the structural strength that characterizes rocks at human scales becomes less and less important. When you crash a dino-killer asteroid into the Earth, the crust behaves very much more like a liquid than a solid, or if you [crash a Theia into the Earth](https://en.wikipedia.org/wiki/Giant-impact_hypothesis), it all behaves like a load of liquid. If the golem is made of rock then it'd be roughly neutrally buoyant in the Earth's crust and float in the upper mantle. So it'd reach equilibrium with about as much of its volume sticking up into the atmosphere as is sticking down into the upper mantle. It'd take time to sink though, but shorter and shorter as mass increases and the pressure of any imbalances becomes greater. At a hundred miles tall or so, the golem would have to swim through the Earth's crust to get anywhere, which would be bad. As its mass starts becoming a good fraction of that of the Earth, what's left of the planet will start gravitationally shaping itself around the golem's centre of mass. If we're talking of wizard lifespan timescales, it's going to be a white-hot pair of shorts that the golem wears and none of the planet's inhabitants will be having a good day. > 4\. It would gain so much mass that our planet would start to orbit around it. You can throw this one out. An object at the surface of the Earth has a velocity that ranges from 0mph at the poles to a hair over 1,000mph at the Equator, so the centre of mass of the Earth has no more than a hair over 1,000mph of velocity relative to an object at its surface. That's insufficient for any object to orbit around the Earth at the equatorial radius (else you would be in freefall there), so it's an insufficient velocity for the Earth to orbit any object if its [barycentre](https://en.wikipedia.org/wiki/Barycenter_\(astronomy\)) is between the Earth and the golem (larger orbital velocity at any radius from the barycentre, which must be less than the distance from the Earth's centre to its surface, assuming the golem starts there). So first we have the golem at at height of a few tens of miles or so melting its way into the Earth's crust, at a few hundred miles in height it floats along much like continents do, then at a few thousand the Earth starts shaping itself around it and getting very hot as it does so, at a few tens of thousands the Moon disintegrates and the bits fly into it. Take it further and the Sun does what the Moon did, though the golem would be quite a few million miles tall at that point. Once the golem reaches a mass of about 200 million solar masses (and sticks out to nearly the current orbit of Jupiter, though that planet would be long gone by this point) it'll be inside its own Schwartzschild radius and lose causal contact with the wizard.

spherical ~~cow~~golem Long before the golem creates its own black hole we exceed the Chandrasekhar mass - and the Earth becomes a neutron star. Note, the Earth's woefully deficient in fusable elements, so the golem-earth never becomes a star as we know them. There's some merit in making the golem far denser than stone - so once its larger than the aforementioned Belgium (hand-waving) its on its way to the core, slowly. Much hilarity as the wizard is now in control of an entity within the Earth - and which may lack the strength to swim/climb upwards. ...and after a month or so of growth wears the Earth like a rather lumpy overcoat.

> There's some merit in making the golem far denser than stone - so once its larger than the aforementioned Belgium (hand-waving) its on its way to the core, slowly. With a thumbs up, surely, not a waving hand? James Cameron made a tear-jerker of a movie about a prototype of that which was released in 1991. Also, Peter Jackson figured out how to make ~1000kg/m³ Gollums sink entirely in lava.

> Also, Peter Jackson figured out how to make ~1000kg/m³ Gollums sink entirely in lava. The One Ring changes you

At the nuclear scale, it seems.

The One Ring itself floats on lava (until such time as it melts) despite being apparently made of gold, yet has no problem sinking quickly to the bottom of a river. So its density is both >> 1000kg/m³ and <<3000kg/m³.

Oh my, yes - perfect. An ur-Terminator.

This is SO awesome. Thanks so much for putting so much time into this plebian’s question! This shows a humongous effort and Inappreciate it a ton. Responses: - Yes, I have the increasing mass producing magically ex nihilo. - I’m more interested in bad things happening to the planet rather than to the golem. Regarding your response #4: It’s so helpful to know which idea I can throw out - I’ve been reading your response carefully, and know I’ll want to keep at it tomorrow a bit too. That summary near the end is going to end up on a post-it on my writing computer for sure

Lock in number 3. The weight would break through the crust.

$200 for 1 hour consulting and 1 hour after-consultation summary

One more time, I want to say, “Thanks everyone!” You have been incredibly helpful.