# Maximum size of an Earth-like planet that's as close to reality as possible

EDIT: by 'larger' I meant a larger radius

EDIT 2: Relaxed the elemental similarity criteria, as that is incompatible with the 1G criteria

I wanted to have my story take place on a huge, alternate reality Earth; The issue being that from all the research I did online, it seems like it isn't possible for such a planet to exist and have the same attributes that our planet has at the same time. I would appreciate it if anyone could tell me the next best alternative, or if it is possible for an Earth-like planet to exist and possess the following traits:

## Criteria

1. Possesses 1G of gravity ($$9.8 m/s^2$$)
2. Receives a similar amount of sunlight as Earth does
3. Has a solar year that is either the same as, or could be translated to in some way or fashion, Earth's solar year
4. Possesses a somewhat or vaguely similar elemental composition in it's "solid earth"
5. Possesses the same habitability as Earth does in regards to temperature, but perhaps with a more diverse distribution of biomes
6. Has orbiting celestial bod(ies?) that can perfectly or nearly replicate The Moon
7. LARGER THAN irl Earth (in terms of radius/surface area)

TLDR -

Is it possible for an Earth in a different reality to both have the near similar surface level properties as irl Earth and be larger at the same time

if it isnt, can you please recommend an alternative

• What do you mean by "larger than Earth?" In terms of volume, radius, or mass?
– stix
Aug 1, 2022 at 20:39
• I should have been less vague haha, I meant radius, but with a similar density as well if possible Aug 1, 2022 at 20:41
• Without a density or mass change the only option I can see is to go hollow earth on it. Aug 1, 2022 at 20:47
• By definition you're not going to get 1G in a larger volume (radius) with the same density.
– stix
Aug 1, 2022 at 20:50
• Yeah, something's gotta give. $g \propto \frac{4\pi r\rho}{3}$, where g is surface gravity, r is planetary radius and $\rho$ is average planetary density. Can't change one without changing another. Aug 1, 2022 at 20:54

# You really can't do it

The criteria that are incompatible are:

2. Similar Density / Similar elemental composition
3. 1G gravity

The volume of your planet will be given by the radius $$\Large \ V=4\pi R^3/3$$

The Mass, given the density $$\large\rho$$ and volume $$\large V$$ will be $$\Large\ M=\rho V$$

The gravity on your planet will be $$\large g= GM/R^2$$, substituting we get $$\large g= 4\pi\rho GR/3$$

The only ways around this are:

1. Allow your density to be lower as you increase the radius (hollow places, different composition, etc.)
2. Change the gravitational constant of the universe (at least on or near your planet)
3. Relax the 1G requirement for your planet. 30% more gravity for a planet that's 30% larger should be tolerable.
• If we get rid of the density criteria and elemental composition of "solid earth" entirely, what would that change, and would it still work? Aug 1, 2022 at 23:53
• Another criterion to govern the size of such a planet is whether it can accrue hydrogen from outer space, in order for a rocky planet to remain rocky, this state should be false. This depends on insolation in terms of spectrum, atmospheric density/height and gravity Aug 2, 2022 at 6:11
• You've missed out the G-constant from your final algorithm, so the = is inappropriate. That's why I used ∝ in my comment on the OP ;-) Aug 2, 2022 at 7:56
• You could get slightly bigger by using a rocky core. From the surface-dweller point of view it is the same material (but no magnetic field). Hollow Earth or a special density-of-water core needs magic. Aug 2, 2022 at 11:02
• @StarfishPrime Thanks, I've edited to correct Aug 8, 2022 at 15:21

## A Ring World

Since naturally occurring is not on the list of requirements, I'm going to go ahead and say that a ring world is your maximum size. A ring world is a megastructure built around a star (similar to a dyson sphere but only a ribbon instead of a whole sphere). While a ring world is a bit of a stretch of the definition "planet", it gives you about 8 million times as much livable surface area while closely replicating the living conditions on Earth.

Possesses 1G of gravity (9.8m/s2)

The actual gravity in any part of a ring world is negligible, if not negative. It uses rotational forces to simulate gravity.

Receives a similar amount of sunlight as Earth does

The ring is large enough that the whole thing encompasses a circle around the sun inside the goldilocks zone. Between the sun and the ring world would be a slower orbiting ring with plates that block/let through the sun giving you night and day.

Has a solar year that is either the same as, or could be translated to in some way or fashion, Earth's solar year.

Years on a ring world are not about revolutions around the sun, but about an up and down motion as it bobs between above and below the sun. As it reaches an Apex the ring experiences winter and as it lines up with the rest of the solar system it has a summer.

Possesses a similar or equal elemental composition as Earth

The ring world would need a surface area with elements designed to replicate soil conditions so that the species who made it can use it for agriculture needed to support thier population.

Possesses the same habitability as Earth does in regards to temperature, but perhaps with a more diverse distribution of biomes

The whole place is designed to be a giant terrarium so to speak. Everything about it will be focused on habitability. There will likely be a wide range of biomes made by artificial means if need be that support all the life forms native to the builder's home world

Has orbiting celestial bod(ies?) that can perfectly or nearly replicate The Moon LARGER THAN irl Earth (in terms of radius/surface area)

Depends on what aspect of the moon you are trying to replicate. If you are looking for tidal forces, those can be achieved by giving the ring a slight wobble. If you want a bit of light at night, you can make the sun blocking ring slightly translucent so that it only blocks 99.99975% of the sun light. This way the sun would shine like the moon through it.

• Would it still classify as a planet? It seems to violate the hydrostatic equilibrium condition. Aug 1, 2022 at 21:43
• @Mathaddict depends on how pedantic you get with your definitions, but the flattening effect of the rings rotation on the soil and oceans should likely count as a form of hydrostatic equilibrium. Aug 1, 2022 at 22:03
• @Mathaddict when you're a K2 civilization capable of building ringworlds, no-one questions your terminology if they don't want to find out what the business end of a Nicoll-Dyson beam feels like. Aug 2, 2022 at 7:55

If you assume that the planet composition instead of being mainly iron is a mix of magnesium, aluminium and silicon you could reduce the average density to a little bit more than a half of the earth density. Maybe the core has a lot more heavy elements than we think, so you could take the average density exactly the half of the Earth density. That would allow a radius of about 7800 Kilometres. So such a planet could be a little bit more than 20 % bigger than the Earth.