# Is this planet possible in real life?

In the Halo series there's a habitable planet called Harvest with a diameter of 4,012 kilometres, and gravity 99% of Earth's, though the planet only has 9% of Earth's mass. If such a planet is possible, what are some factors that might lead to its formation?

Doing a simple density calculation, I get $$\rho=\frac{0.09M_{\oplus}}{\frac{4}{3}\pi R^3}\approx15.97\text{ grams/cm}^3$$ For comparison, here's a list of the average densities, $\bar{\rho}$, of the planets in the Solar System: $$\begin{array}{|c|c|c|} \hline \text{Planet} & \bar{\rho}\text{ (g/cm)}^3\\ \hline \text{Mercury} & \text{5.4}\\ \hline \text{Venus} & \text{5.2}\\ \hline \text{Earth} & \text{5.5}\\ \hline \text{Mars} & \text{3.9}\\ \hline \text{Jupiter} & \text{1.3}\\ \hline \text{Saturn} & \text{0.7}\\ \hline \text{Uranus} & \text{1.3}\\ \hline \text{Neptune} & \text{1.6}\\ \hline \end{array}$$ This means that your planet would have a density much greater than any of the planets in the Solar System. I looked up some mass-radius curves from Seager et al. (2008). Your planet is fairly low-mass, and so it's possible that their models fail in that regime, but your world ($0.09M_{\oplus}$ $0.315R_{\oplus}$, still falls on the pure iron track.

• Look at a planet composition more like Ceres. Rocky with a large quantity of water/ice. Since you won't get a lot of core compression, the composition needs to be about 50% rock and 50% water or ice. – Jim2B Mar 17 '16 at 2:24

The gravity seems right. I'll focus on the other side: density. It should be obvious that such a planet has to be very dense - but how dense, exactly?

First, specific figures on the gravity: Earth's diameter is about 12740 km, so the gravity of Harvest as compared to Earth would be about 0.09*(12740/4012)^2... since 12740/4012 is approximately 3.175, this comes to (roughly) 0.91.
For a result of 0.998 (as in the wiki), we need the mass to be 0.998/(3.175)^2, or about 9.89 percent Earth's. This can be easily rendered as "9 percent" if rounded down to the nearest integer (where's that figure from anyway? I couldn't find it in the linked article); I will use this figure in the following calculations (the other figure makes the density about 10% less, but doesn't change the conclusion much).

Now for the density. A planet the same density as Earth and 3.175 times smaller diameter would have a mass (3.175)^3 times smaller; combining with the previous, the density needs to be about 3.17 times larger than that of Earth, or 3.17*5.515 - that is to say, about 17.5 - grams per cubic centimeter.
This is an extremely high density for a normal planetary object... for anything, really: that's over 1.5 times the density of lead (11.3 g/cm^3), and only 10% less dense than tungsten and gold (19.3 g/cm^3). It is also about a third more dense than Earth's inner core (13 g/cm^3).

Can a planet with such a high density exist? In principle, yes, but it would pretty much have to be formed artificially. (The Halo universe being what it is, that's not that much of an impossibility.)
Metals so heavy and dense as to create such a planet form naturally almost only in supernovas, and not in especially huge amounts, so they're not particularly common (or, at least, much rarer than the less dense metals). Thus it is unlikely that a planet could have naturally formed consisting of them only (or mostly).
Whether such a planet, once created, could have been habitable is a separate hard question; IMHO, probably not if it somehow formed naturally (or generally if left alone for a long enough time), and all bets are off if it was created artificially and geologically recently (i.e. within the last several million years).

It can't hold an atmosphere. Atmospheric retention is based on escape velocity, not on surface gravity.

For those who want the math:

First, escape velocity Calculator: 5.98 km/sec

Second, to convert this to what can be held:

Light molecules such as any hydrogen-bearing one are soon lost. This world holds an atmosphere about as well as Mars--and note what it's like there.

• sometimes short and sweet is all you need :) – EveryBitHelps Aug 10 '18 at 21:47
• So calculate it. – Spencer Aug 10 '18 at 22:13

In a word.

## Yes.

It's probably a bit less than 0.98 Earth gravity. It's closer to 92%.

Trivial to test for if you know the laws of gravitation.

• Well, yes, but could a planet with such low density exist? That's the question that's being asked. – HDE 226868 Mar 17 '16 at 1:45
• @HDE226868, I think it's more dense than Earth. – user6511 Mar 17 '16 at 2:39
• You forgot to put the meters inside the square, this resulted in the wrong units. Also, Gauss's law is quite unnecessary for this, Newton's law is directly relevant. Also, you know what the first comment meant, there is no reason to be pedantic about a simple error. – k-l Mar 17 '16 at 12:07
• I'm working on a calculation about the density right now. (The 92% figure is approximately correct, incidentally.) – January First-of-May Mar 17 '16 at 12:09
• Fixed calculations for gravity and density. Earth's density is ~5.5 g/cm^3, this planet is ~16 g/cm^3, and natural osmium is ~22 g/cm^3. So this planet is pretty feasible. – Lacklub Mar 17 '16 at 12:34