# A planet in the center of the system

In most star systems, planets orbit around a star. Is it possible for a planet to be so massive/heavy/dense that a star(and other planets) orbit it instead? Bonus points if the planet is also reasonably life-bearing and rocky.

Largely inspired by this question over here.

Some notes:

• Someone will probably provide a better answer but there is a transition between terrestrial planets and gaseous planets at a certain mass. Maybe at around 10 earth mases? Beyond that point, it becomes a gas giant/ ice giant. Eventually the gravity will be strong enough so the star can start combustion to become a brown dwarf (80 times the mass of Jupiter). If the size increases further, then it will begin fusion as a red dwarf. About the question you linked, the author only mentioned size and not the mass. White dwarfs can be really compact especially compared to the ice giants. – Vincent Apr 26 '15 at 15:42
• I suppose that in a sense you could consider a neutron start to be a planet of sorts, since it's not undergoing fusion. But AFAIK there's really no way to get to the neutronium stage without having previously been a star. Also, since there's an upper limit to the mass of a cold NS (en.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limit ), it and your star would orbit a common center of gravity. – jamesqf Apr 26 '15 at 17:49
• Jupiter is just short of being itself a star, but nowhere near big enough to be at the center of its own solar system. I think you'll really struggle. – theonlygusti Apr 26 '15 at 18:45
• en.wikipedia.org/wiki/Brown_dwarf#Sub-brown_dwarf, en.wikipedia.org/wiki/Rogue_planet - depends what you call planetary system – Mithoron Apr 26 '15 at 19:07
• I'm afraid that solid bodies must be relatively cold (i.e. heat does not alter their state - many white dwarfs are really white because they are hotter than the Sun) and cold bodies with big mass collapse into white dwarfs. Hotter bodies are gaseous stars. No cold body can be much bigger than Jupiter, greater mass means smaller size. – BartekChom Apr 26 '15 at 20:06

For the purposes of this question, a planet is a planet if it is not a ball of nuclear fire [...]

Then you're in luck! Your "planet" could be a white dwarf star, an ultra-dense ball of electron-degenerate matter. No fusion occurs in a white dwarf: its radiative output comes entirely from stored thermal energy.

The radius of a white dwarf of $1~M_\text{Sun}$ is around $0.008~R_\text{Sun}$. The surface gravity of such a star "planet" would be around $400\,000~g$, and the surface temperature would be $1000~\text{K}$ to $10\,000~\text{K}$, depending on age.

A short aside: this assumes the white dwarf composed mainly of carbon and oxygen, which is the case for naturally-existing white dwarfs. But what if the "planet" were composed of iron as WhatRoughBeast suggests?

The upper limit on the mass of a white dwarf (the Chandrasekhar limit) contains a factor of $\mu_e^{-2}$. The quantity $\mu_e$ is the average atomic mass per electron. For light elements which contain the same number of neutrons and protons, this number is very close to $2$. However, for a heavy element like iron, we have something like $\mu_e=56/26\approx 2.15$, so $M_\text{limit}$ drops from $1.4~M_\text{Sun}$ to $1.2~M_\text{Sun}$.

Although you wouldn't be in danger of immediate supernova, you should be wary of accreting too much matter onto the surface. In particular, you'd want to avoid a main-sequence star as your companion star orbiting "sun." When it reaches red giant stage, your white dwarf would begin to pull off the expanding outer layers. When it reached the mass limit and electron degeneracy pressure could no longer support the star, it would immediately collapse (until stopped by neutron degeneracy pressure). The amount of gravitational potential energy released would be enough to blow apart the star in a classic type Ia supernova.

But seriously here: there is no way a planet can be larger than a star. Anything that is large enough to ignite fusion in its core has three options:

• Generate enough pressure by fusion to hold itself up.
• Support itself by becoming a form of degenerate matter.
• Collapse into a black hole.

None of those are planet-like possibilities. Going the other way, even if you use the largest possible planet, any smaller collection of gas will not be massive enough to ignite fusion, so no star can be smaller (in terms of mass) than the largest planet.

## A Possible Way Out

We've firmly established that you can't have a star more massive than a planet. This means that your planet has to orbit around the star. However, from the point of view of the planet, the star is orbiting around it! It's easy for us to see that this is not really the case since all the other planets are seen to orbit around the Sun.

However, imagine a solar system consisting of a single large rocky planet (a super-Earth) with an extensive system of satellites like Jupiter or Saturn. From the point of view of the planet, all the bodies in the solar system (moons and star) would seem to orbit around it. The implications for the cosmology of the beings living there would be interesting to explore!

A central planet is possible (with a LOT of handwaving) but not likely to be habitable.

Let's start with an object with the mass of the sun and the density of earth.

This is actually a decent start, since the Earth's core is iron, and if the object is not to spontaneously become a star, it needs to be made of something that will not support fusion, and iron is the obvious candidate. Since the mass of the sun is about 330,000 times that of the earth, the object's diameter will be the cube root of 330,000 or 69 times that of the earth. You can't get much larger than this without becoming a neutron star, so an orbiting star will have to be considerably smaller, like white dwarf. There is a limit to this, though, since the lower limit on white dwarf size is about half a solar mass. Any smaller, and it can't become a star - not enough core pressure to start fusion.

Why is this a problem? Surface gravity. Surface gravity is proportional to radius (or diameter, if you prefer) times density. Since the density of our object is equal to that of earth, the surface gravity will have to be 69 times greater. If that's acceptable, you're in good shape.

EDIT - The assumption that density similar to earth's is possible was made on the basis of various articles I've run across which discuss the density of iron vs pressure; that is, not much. Further thought suggests that this may not be true at stellar core pressures. So, it's entirely possible that the density of the planet is greater than earths. If so, the greater the density the greater the surface gravity, with an exponent of 2/3. That is, for an increase in density of a factor of 8 you get a quadrupling of surface gravity. END EDIT

The handwaving comes on two fronts - object formation and companion capture.

If the object is (essentially) pure iron, it had to form from a cloud of iron, and there is no known way to do that. Iron is formed in the cores of supernovas and explosively dispersed. And if the object formed from an iron cloud, how did the white dwarf form from the hydrogen which was not present? And if it did not form as a companion to the object, how did it get captured? The last is not a trivial question.

• Actually a Sun-sized iron planet would collapse into a white dwarf or go supernova, since you can't generate enough pressure to suppert a solar mass of material without fusuion. – 2012rcampion Apr 27 '15 at 4:04
• As long as the mass is above the Chandrasekhar limit, the star will not drop into neutron star status. Since it's already iron, it cannot support fusion of any sort, and so cannot become a supernova. It's part of the handwaving that it is created rather than accreting, so there is no gravitational potential energy to convert to heat, so it is cool. However, you have pointed out a flaw in my density assumptions, and I've edited my post to reflect it. Thanks. – WhatRoughBeast Apr 27 '15 at 4:38
• You're thinking of type I supernovae. Core collapse (type II) supernova get their energy from gravitational potential energy. The star will have the same amount of gravitational potential energy no matter how it's constructed. Depending on the collapse mechanism (electron capture or photodisentigration) a white dwarf remnant will form. A white dwarf is a star less massive than the Chandrasekhar limit (1.44 Msun), and is a form of electron-degenerate matter (a neutron star is more massive than the limit and is composed of neutron-degenerate matter). – 2012rcampion Apr 27 '15 at 11:32
• Also, stars less massive than 0.5 Msun become white dwarves after main-sequence evolution. Brown dwarves can get lower than 0.01 Msun while still fusing in their cores. – 2012rcampion Apr 27 '15 at 11:41

Are you limited to a single star?

• Imagine a dual star system, with both components orbiting around the common center of gravity.
• Next, imagine the planets in orbit around this common center of gravity.

There are examples for this. The wikipedia article states that

Because of the short orbits of some binary stars, the only way for planets to form is by forming outside the orbit of the two stars.

The explanation is a paper called Long-Term Stability of Planets in Binary Systems with plenty of maths in it. (Disclaimer: I didn't read all of it.)

Would it be acceptable for your world-building purposes to assume either a highly improbable system or one which isn't stable on the long run? Then a planet might orbit the common center of gravity within the orbit of the stars. That orbit could be rather small -- the planet wobbles in the center of the system.