So, we have a captured planet/moon orbiting a gas giant in the habitable zone. It is akin to prehistoric Mars, its geological activity having been maintained by constant tidal flexing from the gas giant. It is half the mass of earth, but knowing that the volume of a planet affects its surface gravity, could it still experience surface gravity of 1 g?
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1$\begingroup$ I could be wrong, but I think this question has been asked. Or very nearly. $\endgroup$– Boba FitFeb 1 at 15:30
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$\begingroup$ IMHO, sometimes the magic of creating a new world is the newness of it. Having lower gravity creates difficulties, but difficulties are the things that make a story come to life. If you've never read Forever War, I highly recommend it. The author goes to some length in describing how the conditions on the planetoid they are on (low gravity, extreme cold) make life there... interesting. $\endgroup$– HimFeb 2 at 12:24
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2 Answers
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Yes.
Surface gravity depends on the mass of the planet and its radius, according to the formula $g=Gm/r^2$.
If you put half the mass of Earth in $1/\sqrt{2}$ of its radius, the surface gravity will be the same.
Of course this would alter the density of the planet significantly, needing complete different materials to make it possible.
The average density would increase by a factor $\sqrt{2}$, which is not out of the realm of physics: 7.7 $kg/dm^3$ is a bit less than the density of iron.
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1$\begingroup$ Or a larger core? Perhaps more similar to Mercury? $\endgroup$ Feb 1 at 14:17
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3$\begingroup$ In theory yes. But for that to be happening you would need to have abundance of elements heavier than Ni/Fe which seems improbable. AND you would need to have little additional material getting trapped in the gravity pit of the forming planet otherwise you may end up with a super Earth. Overall an improbable combination. $\endgroup$ Feb 1 at 15:54
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7$\begingroup$ @DuncanDrake on Physics it's improbable. On Worldbuilding where the question is not tagged science-based or hard-science, it's probable if the OP wants it to be. Remember our goal from the help center, "Worldbuilding Stack Exchange is a site ... to get help creating imaginary worlds. World building includes geography, culture and creatures for the world, not to mention magic and planetary physics, in short, everything from the physics underlying your reality to the entire universe you want to build." $\endgroup$– JBHFeb 1 at 22:33
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4$\begingroup$ @ZeissIkon I'd skip osmium and go with a near-pure iron/nickel planet. Iron (and nickel) are way more abundant than osmium or even lead; nickel is a bit denser than iron. Iron meteorites are known; osmium is a big handwave. Iron is the 2nd most abundant solid element in the solar system by mass, half as abundant as carbon. Solid carbon is rare, as it tends to form CO2 gas. Oxygen is 1.5 times as common as carbon and tends to react chemically with everything. Next most common solid element is silicon; rocky planet's crusts are mainly SiO2. wikipedia.org/wiki/Abundance_of_the_chemical_elements $\endgroup$ Feb 2 at 0:56
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2$\begingroup$ Questions without those tags might not require scientifically plausible answers, but surely it's still useful to say if something is scientifically implausible, so that the OP can know that and make an informed choice. (And if we don't care about scientific plausibility then why care that osmium is chemically analogous to iron in the first place?) $\endgroup$– N. VirgoFeb 2 at 4:58
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L.Dutch's answer gives you the basic idea. At half the mass with a surface gravity of approximately Earth normal your planet has a radius of $2^{-1/2}$, a volume of $2^{-3/2}$ (0.35356) and a density of $(2^{-1/2+3/2}) = 2^{1/2}$... all as multiples of Earth's values. Since Earth has a density of approximately $5.495\ kg/L$ your planet clocks in at around $7.772\ kg/L$. That's a bit higher, but not unachievable.
Lots of comments about increasing the core size or density, but I think that's a non-starter. Earth's core accounts for only about $1/60$ of our mass, so your planet's core would have to be much larger by comparison and significantly more dense than our iron/nickel core to make much difference. The big payoff comes further up.
A little over 70% of the Earth's mass is in the Mantle, and the second most abundant element in there is magnesium. That's pretty wasteful considering that magnesium is a very light material. If we were able to removal all of the magnesium and replace it with more iron, the average density of our planet would increase quite a bit. What if we replaced most of the magnesium with manganese which is more than 4 times heavier by volume? OK the compounds aren't quite as much higher in density (some are lower, but we'll ignore those) so perhaps not. But you could simply siphon off all of those magnesium compounds to sell on the galactic gem market.
I'd say that simply changing the composition of the mantle can do most of what you need. Increase the iron in the mantle, add some more nickel in there too. Liberally sprinkle the crust with deposits of heavy metals. Maybe write in a collision with a heavy element asteroid in the planet's history - it's always fun to find new sources of Iridium for example.
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3$\begingroup$ Most of the iron in the mantle would have sunk into the core due to planetary differentiation, so that's a non-starter. Besides, it doesn't matter where the iron resides due to Newton's shell theorem. A smaller mantle and a larger core is exactly what is needed, and does so without resorting to uncommon elements. Iron and nickel are relatively common elements. Manganese is not. Iridium is even further from being common. If you want an uncommon dense element that doesn't sink to the core, I suggest uranium. Uranium coins would add a twist to the phrase "money burning a hole in ones pocket". $\endgroup$ Feb 2 at 15:32
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1$\begingroup$ Maybe a little tungsten would go a long way. Even its ores are heavy. Wolframite is >7kg/L. $\endgroup$– TheodoreFeb 3 at 15:55