How to prevent the effects on gravity, climate and day-night cycles on a "planet" with a surface area nth time as big as earth's?

Question

In my story, one key feature is that the earth-like planet or habitat has a surface area of earth > 10 times. However, as it is inhabited by pre-industrial humans that might have been brought on it thousands of years ago, it would need to have 1G of gravity, a hospitable climate, no extreme other-worldly storms or the likes, and a reasonable day-night cycle.

Unfortunately I am not well versed in physics, and this might even need an engineering perspective. I would like to give a hard science basis for my story to later highlight the implications on that world's science, astronomy and mythology.

But let me introduce some of my speculations: So, as for gravity, I imagined a hollow world. It most probably would have had to be created by the advanced predecessor civilization. I imagine an enormous skeleton holding the planet firmly together, or a sponge-like structural material in the center. It is important that the mantle itself creates enough gravity to achieve 1G. This may mean that we don't find any geologic activity, volcanoes and magnetosphere on that planet. The latter is a problem I would rather avoid.

If we want a 24 hour day-night cycle, I'd assume the Coriolis force would create an inhospitable climate, that is dangerous and persistent hurricanes. So in order to prevent that a day must be much longer than 24 hours. How much longer though? I haven't found a good equation for that. But to retain a 24h cycle in sunlight, I assume either one or multiple light-sources must rotate around the planet.

How big of a moon (or any) would be needed to exert enough tidal force on the planet?

And the climate itself should have somewhat of a variety, so a certain axial tilt is to be expected to create seasons. However, how does this work in conjunction with all the aforementioned variables?

I assume unbelievably large swaths of area to be basically the same climate and temperature, and there could even be an inhospitably hot and humid belt around the equator. If considering plate tectonics, there could be tens of kilometers tall mountains that pierce through the atmosphere. How would that effect the climate?

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So what I tried was to calculate the size of the sphere, I then used that data to generate a planet with climate in a computer program. That however yielded weird results that I knew ignores completely the fundamental problems. I tried to google my questions, that wasn't fruitful. It seems nobody has tried to expand a planet's surface in my fashion.

Unfortunately, on all the other things my imagination precedes my factual knowledge of astro-physics, meteorology and engineering. Hopefully you can help me, at least show me what to focus on learning to answer these questions.

Answer 1

You're very close in my opinion. A couple of things to consider to maybe help point you onto the right path.

Firstly, I agree with the ring world idea above given by LSerni, however, if you wanted a spherical world you merely need to work with a core that is less dense. Earth's core is predominantly iron and nickle, and produces the appropriate magnetic sphere to protect the plant from (most) cosmic radiation. If you assume liner proportions then increasing the size of the planet, would increase the size of the core, and produce an effect greater than the 1G you're looking for. As a result, I suggest having a metallic hydrogen core, similar to that theorized at Jupiter's center. The volume of the core would likely align with that of Earth's but be significantly less dense. Your crust and mantle would also likely have to be much thicker in order to produce the pressure needed to generate metallic hydrogen but those can still mostly consist of silicate and non-metals to increase volume and decrease density. The exact ratio you may need to calculate if needed.

Secondly, measurement of time is going to be tricky. You can either redefine the standard hour to align with that of the planet, such that 1 Earth hour!= 1 Nu hour, or you could play around with space-time density and have the planet orbit a star with more gravitational significance which may adjust the perception of time. You could maybe even have the star be of similar size to the sun, but me much more close to the galactic center where the super massive black hole is significant enough to adjust the perception of time.

Answer 2

A well-worn road to go is that of a ringworld. A hollow structure, more like a car tyre, as big as necessary. For a large enough radius, the spindle is invisible (not so the opposite section of the ring, which would reflect daylight).

You will need scrith - a material possessing the impossible tensile strength required to keep the ring stable and prevent it from exploding outward. Since the "weight" is generated through rotation, the spokes need to withstand, literally, the weight of ten times the surface of a planet.

The origin of the material is, if memory serves, left unspecified in Larry Niven's Ringworld series, but a handwavium process is described in some detail in Timothy Zahn's Spinneret - not too different from Van Vogt's ten-point steel.

You'll want at least twenty-kilometer mountains on the "walls" of the ring, to keep the atmosphere in (gravity will "fall off" more slowly on the Ring).

For the day, you need a ring 1.8255 million kilometers in radius, rotating once per day. This yields a surface "gravity" of Earth normal. The ring will have a surface of 11.47 million square kilometers per each kilometer in width; since the Earth has a surface of 510 M, and you want 5100 M, your ring needs to be 5100/11.47 = at least 445 km wide. Each 44.5 km of extra width add another Earth's worth of surface (note that inhabitable surface on Earth is 40% of that, because of oceans).

The ring will have a terrifying amount of momentum and will keep its orientation in space. You want it to be edge-wise to the Sun. For a G0 star like the Sun, at a distance of 1UA, its angular size is about 0.5 degrees, and a 445 km wide ribbon has an angular width of 0.007 degrees; there is no risk of an "eclipse", with the shadowed edge intercepting all the light of the illuminated edge.

If the ring has an angle, it will have seasons not unlike Earth, but at twice the speed (it will have a "year" of six months).

In the extreme case its axis of rotation lies in the same plane as the orbit (sort of like Uranus), it will have two "winters" each year, when the ring receives the light edge-wise: so, very little light, very little heat, and most of them intercepted by the sunward side wall (six months later, by the other). The light arrives at an angle of about 1.825:149, so in 445 km it will dip about 5 kilometers; that is to say, only the top five kilometers of the spaceward sidewall will get sunlight. Atmospheric diffraction should be more than enough to allow at least scotopic sight 24h/24 (in my own country there's a town, Viganella, in that situation due to having high mountains on all sides).

Climate variety: you can play with height and air currents. You can also play with the insulation of the ring bottom: the outside face of the ring is potentially exposed to the cold of space (every day), and can be insulated by mirrors, or not, during the "night". That's a significant source of either warmth (about 1200 W/square meter) or cold (about 315 W/sq m assuming a source at 0 °C).

You can have a sort of tectonic activity - it will be artificial, of course. There's something like that in John Brosnan's Mothership (all land very, very slowly migrates towards the sea, where it gets dissolved. The sea is continuously purified and dredged by hidden automatic machines, and the waste mass ejected near the walls).

Answer 3

Under your conditions a manufactured low mass core world would work with an internal ferro-magnetic shell of the core to provide a magneto-sphere and an internal thermal source a slow fusion reaction or the continuous gravitational change in pull of the three suns?

To be clear, such a planet must exist beyond the Goldilocks Zone. Thus the need for an internal heat source.

1G, 24 hour day and 10x Earth size is a problematic equation for a round world without certain conditions.

While short lived in small cosmic terms, a slow unstable three star(one major, two minor) elliptical system can provide a small variable 24 hours of daylight, extended sunrise and sunset by the minor suns, for a period of time(many generations).

This also opens up myths of a daylight period when the suns were out of sync. Both literal and symbolic enlightenment.

Tidal generation would be a function of the secondary suns relative positions. No need for large Moons.

As for seasons, tilt applies to a minor extent, due to the distance and internal heat. The winter and summer periods are caused by the passage or not of a much larger denser and slower elliptical planet in an outer orbit that transits the gravitational field for a small period of time, causing long Winters, and even longer Summers.

For an engineered planet, plate tectonics is up to you. The push and pull of gravitational forces could be mitigated by a flexible core shell. The magnetic implications are more far more interesting, through pole reversals each Winter. Even though minor, the repeated Summer/Winter cycles could have stretched and compressed the surface enough times to produce mountains and plains, and possible transit stresses like passing a black hole.

For weather: research the hairy ball theorem. Keep in mind the atmospheric pressure varies by season and rotation. The implication is that the weather follows Earth weather with a moving non-linear axis. Where the theorem's opposites are changes with the suns and seasons.

The same thing happens on Earth: El Nino, vs La Nina.

Extremely tall mountains, produced either in transit or evolutionary, provides a buffer to the extremes of seasonal pressure changes on one side: more pressure means more heat and an increase in the air's water capacity, and induce a desert on the other side.

The subject of water supply and cycle is assumed to be earth-like for this answer.