# Earth-like planet which is smaller but has the same gravity

If there were a planet similar to earth where the lines of latitude and longitude were half as far apart (about 35 miles instead of about 70), but the planet's density were increased to compensate for lost gravitational force, how similar to earth could it really be?

Would it be possible for weather and seasons be essentially the same or would they have to be altered? Would the horizon be visibly different to the naked eye? Could air pressure be essentially the same at the same measurements from sea level? Would there be any other significant, unavoidable changes to that world?

The goal is to try and keep the planet as earth like as possible while shortening the distance between equatorial lines (bringing the arctic circle closer to the equator, so it would take only half the time to walk between them)

As a bonus question, what would that planet's radii be? I was thinking 0.5 but my mental math for 3d space isn't too great.

• Radii means "rays" (plural). The singular is radius; yes, the radius needs to be half of that of Earth. Surface gravity scales linearly with the radius, so all you need to do is to make your planet twice as dense as Earth; this is not that easy, because the average density of Earth is a whopping 5.5. You need to have a lot more iron and a lot less silicon and aluminum. The horizon would be quite conspicuously closer. (Edit: as @Ummdustry says, not even 100% iron is enough.) – AlexP Sep 2 '18 at 16:12
• Even if your planet was entirely iron it would only be 7.9 i.e. not high enough – Ummdustry Sep 2 '18 at 16:14
• @Ummdustry, isn't Earth's core already like that (made of iron)? – rus9384 Sep 2 '18 at 18:49
• Earth is only 32% iron while its core is 89% iron. We say its an iron core simply beacuse it's easier than saying "the core is a mixture of elements, predominately iron" – Ummdustry Sep 2 '18 at 19:03
• Related, maybe duplicate: worldbuilding.stackexchange.com/q/76107/809 – Mołot Sep 3 '18 at 0:10

The length of a circumference is given by $L=2\pi r$, while the length of an arc of circumference is given by $L=\alpha r$, with $\alpha$ measured in radians.

So, if you want a certain arc to be half the length of another, the radius has to be half of that other.

You can get the same gravity by using a more dense material, but, considering that you are also closer to the center of mass, the change is not as dramatic as one can expect.

The problem is that, halving the radius, you are reducing the solar harvested energy by $1/4$, but the volume available to absorb that energy reduces by $1/8$, thus you actually have twice the energy per unite volume we get on Earth.

I suspect this would make the climate a bit more extreme.

• Why is the power / volume ratio relevant? Seriously asking. – AlexP Sep 2 '18 at 16:14
• @AlexP, the incoming energy is absorbed by the available mass. The available mass is proportional to the volume. You end up having a lower thermal inertia (warp up and cool down faster). – L.Dutch Sep 2 '18 at 16:17
• "I suspect this would make the climate a bit more extreme." - this planet could be closer to a star than the Earth, or the star could be brighter/larger than the Sun. That would also require faster spinning for the planet so that it does not overheat locally. – rus9384 Sep 2 '18 at 18:43

This would be accomplished with a planet with half the radius and double the density. This would easily be attainable with a core rich in denser metals like uranium, osmium or plain old lead (though how likely a core like that is to form is up for debate.)

The air pressure could be tailored to your needs simply by adding or taking away air, leading to whatever air-pressure you desire. however you will have a significantly slower escape velocity of just eight kilometres per second meaning you will loose that atmosphere MUCH faster (but perhaps you simply had a larger atmosphere in pre-history).

I am assuming you are trying to keep day length the same, which is easily doable though will lead to a slower tangential velocity and thus a smaller Coriolis effect, meaning less intense hurricanes and winds.

Your moon will be orbiting something significantly less massive and thus you will either need longer months, a closer moon or some combination of the two. Either way this will effect tides though not to an unlivable extent, just like "hey look the tides are quite wacky today".

You will be getting the same sunlight per unit area, which is the important thing for climate (the earths internal volume being mostly dominated in geo-thermal activity, being well insulated from the sun-lit surface by many kilometres of rock). You'll notice i disagree on L.dutches answer here. I would say that this planet would have similar climate, with the exception of less wind + waves. due to the lower Coriolis effect and smaller distances over which such phenomenon can build up.

All in all such a planet could be almost arbitrarily earth-like in most important ways, but would be highly improbable to occur naturally. (ignoring the incalculable vastness of the universe)