# Mars sized planet with 83% Earth gravity?

For one of my stories I’ve developed a planet with approximately the same total surface area as Mars. This planet has high quantities of heavier metals/elements (especially silver) and it has roughly 83% earth gravity. It’s very earth like in terms of environment (a little cooler but the temps and atmosphere are well within human limitations. Is this planet feasible?

• It would be much easier to dunk. – Willk Feb 11 at 2:07
• (continued) So, you'd need to replace most of the planet's iron core with something exceptionally dense like platinum or gold to make it happen. So, it's feasible in the sense that the physics works but such a planet is not likely to come into being naturally or to be practically constructible short of outright magic. – GrumpyYoungMan Feb 11 at 3:39
• The gravity is achievable, yes by adding a lot of more dense elements. This would have the side effect of making the surface utterly toxic to all life. And I don't mean just Cyanide-on-anthrax biscuits level toxic, I'm talking arsenic floating on Mercury with Cadmium sprinkles on top toxic. – PcMan Feb 11 at 4:48
• Re: heavy metal toxicity, in terms of density, gold and platinum are near the top and both are nearly chemically inert, see thoughtco.com/elements-listed-by-density-606528 – GrumpyYoungMan Feb 11 at 5:25
• @GrumpyYoungMan there is no conceivable stellar process that would generate VAST quantities of Silver, without also creating huge quantities of Cesium, Polonium, radium, lead, and a host of the higher heavy metals and radioactive elements. Nucleosynthesis simply is not that selective! Your planet with a silver core will also have many other undesireable heavy elements in it. – PcMan Feb 12 at 18:51

So you want have Mars sized planet to have gravity equal to 0.83 the gravity of the Earth.

Some facts and figures:

• The diameter of Mars is 6779 km
• The volume of Mars is 163.116 x 10$$^{\sf9}$$ km$$^\sf3$$
• The gravity of Earth is 9.78 m/s$$^\sf2$$
• 83% of the gravity of Earth is 8.12 m/s$$^\sf2$$
• The bulk density of Mars is 3.934 t/m$$^\sf3$$ (or g/cm$$^\sf3$$)
• The bulk density of Earth is 5.514 t/m$$^\sf3$$

For your Mars sized planet to have a gravity of 83% that of Earth, 8.12 m/s$$^\sf2$$, the bulk density of the planet would have to be 8.57 t/m$$^\sf3$$, which is 1.554 times the bulk density of Earth.

Given that the density of iron is 7.874 t/m$$^\sf3$$, that level of increase cannot be achieved with a larger iron core.

Nickel has a density of 8.908 t/m$$^\sf3$$, which would help, but as @L.Dutch suggests, for your Mars sized planet to have a gravity that is 83% that of Earth's would require an anomalously large amount of scarce very heavy metals.

For reference, Earth has the highest bulk density of any planet in the solar a system, followed by Mercury (5.427 t/m$$^\sf3$$) and Venus (5.243 t/m$$^\sf3$$).

Edit 1

I've done a partial simulation, using several rare, valuable and heavy metals to get an idea of what metals and their amounts would be required on your planet to get the criteria you specified.

As can be seen from the table below the amounts more than what they would be on Earth huge by comparison.

As another perspective, nickel has a density of 8.91 t/m$$^\sf3$$ and your planet needs a density of 8.57 t/m$$^\sf3$$. You planet could almost be just nickel, with some lighter elements to reduce the overall density.

I very much doubt such a planet is possible

Edit 2

After additional research, prompted by a comment from @J... and a question from the OP in a comment, "Could such a neutron star collision have occurred near enough to the system (black hole + star binary) that a sufficient amount of heavier metals were caught by the star to create the anomalous planet?". Planet K2-38b has one of the highest densities of any planet so far discovered, at 11.0 t/m$$^\sf3$$.

A neutron star collision near a "black hole + star binary" is unlikely to accumulate the material necessary for such a planet.

Instead the most likely scenario is,

The best description for the composition of K2-38b comes from an iron-rich Mercury-like model, while K2-38c is better described by a rocky-model with H2 envelope. The maximum collision stripping boundary shows how giant impacts could be the cause for the high density of K2-38b.

Your Mars sized planet with 83% Earth gravity would most likely be the resultant core of a larger planet that was stripped of its outer layers by meteor type bombardment.

It is thought Mercury is a resultant core of a planet that was bombarded. The size of your planet, with a diameter of 6779 km, lies in between the size of Mercury, which has a diameter of 4879 km and K2-38b, which has a diameter of 19,622 km.

• My understanding (absolutely correct me I’d I’m wrong) is that metals such as iron are produced in supernovas while silver, gold, platinum, and others of the more rare variety are produced when two neutron stars collide. The former being more common than the latter, those metals prevail. Could such a neutron star collision have occurred near enough to the system (black hole + star binary) that a sufficient amount of heavier metals were caught by the star to create the anomalous planet? – Samuel Hope Feb 11 at 6:31
• @SamuelHope absolutely. And it would satisfy the density requirements. The only problem is that the planet would consist of a reasonably normal distribution of these heavy metals, rendering the surface composition extremely toxic to any protein-based lifeforms. (also dangerously radioactive) – PcMan Feb 11 at 13:51
• would require an anomalously large amount of scarce very heavy metals. Space is vast. Anomalous for our little backwater solar system is not necessarily anomalous for Space. K2-38b, for example, is thought to have a density around 11g/cm3 (=t/m3), which is more than sufficient for this case. – J... Feb 11 at 15:25
• In fact, this list has exoplanets of known true mass and there are seven exoplanets in that list with density higher than 8.6g/cm3. – J... Feb 11 at 15:27
• @Rekesoft Sure, but it exists is the point. And if it exists and WE, in our stupendously tiny smallness, have seen it, then it is most likely not rare at all in the universe. Maybe a passing system comes by and kicks K2-38b out of that tight orbit where it settles over billions of years into a goldilocks orbit. Now OP has a story. – J... Feb 12 at 14:50

Having high quantities of heavier metals/elements is rather implausible: the heavy elements in the periodic table take a long time to be produced

Elements heavier than iron are made in energy-absorbing processes in large stars, and their abundance in the universe (and on Earth) generally decreases with increasing atomic number.

In the Milky Way 10 elements, of which the heaviest is iron, account for 99.95% of all the elements, so you see that a very high concentration of heavier elements is unlikely.

It might still happen that a rocky planet is stripped from the lighter crust and retains a large core made of iron, like it's the case for Mercury:

Mercury consists of approximately 70% metallic and 30% silicate material. Mercury's density is the second highest in the Solar System at 5.427 $$g/cm^3$$, only slightly less than Earth's density of 5.515 $$g/cm^3$$

Therefore, for it to have such a high density, its core must be large and rich in iron.

Mercury's core has a higher iron content than that of any other major planet in the Solar System, and several theories have been proposed to explain this. The most widely accepted theory is that Mercury originally had a metal–silicate ratio similar to common chondrite meteorites, thought to be typical of the Solar System's rocky matter, and a mass approximately 2.25 times its current mass. Early in the Solar System's history, Mercury may have been struck by a planetesimal of approximately 1/6 that mass and several thousand kilometers across. The impact would have stripped away much of the original crust and mantle, leaving the core behind as a relatively major component.

But again, we are still talking about an iron core.

## Turns out, it really is Definitely Realistic

The raw numbers given on the other posts are correct, but they ignore gravity, i.e. pressure. The density of Earth's inner core is around 12 tonnes per cubic meter even though it is mostly composed from iron.

Curiously, the maximum gravitational acceleration – around 11 $$m/s^2$$ – of Earth is reached at the boundary of the outer core at roughly 3480 kilometers from the center of Earth. This is almost equivalent to the radius of Mars, 3390 km.

The actual composition necessary would necessitate solving an equation state which is beyond me but, for reference, the densest exoplanet is K2-38b with a mean density of 11 tonnes per cubic meter.

Figures taken from Gravity of Earth wiki-page.

## UPDATE

Someone at NASA has actually done some calculations. Earth mass planet made of iron would have a diameter of roughly 5000 kilometers. This is less than the diameter of Mars (~6800 km). More importantly, the gravity on the surface of the Earth mass iron sphere would be around 7 times higher than on Earth.

This means that 83 % Earth gravity at surface of Mars sized planet sounds plausible and would not even lead to a solid iron sphere.

• Very interesting! But K2-38b has many times more mass than Earth. That helps it maintain a larger density. I don't think this would work for a planet that has less mass than Earth. (But figuring out the calculations is beyond me also, I'm just thinking.) – Daniel Darabos Feb 11 at 17:02