How big can a planet get?

The more mass the planet has the bigger it should be, right? Well, it turns out the answer is no! Let's take a look at why this happens. During the formation of a planet the size of its radius slowly increases as more more massive it gets. Once a rocky planets becomes heavy enough, it will attract a lot more hydrogen and helium gas due to its gravity, its radius now grows faster. However there comes a point when adding more mass compresses the gas more and the radius actually begins to shrink. So the answer to our question is that a planet doesn't get much bigger than Jupiter as we can see from this chart of simulated planet sizes along with some measured planets and exoplanets:

(Credit: Christoph Mordasini)

If we continue to add mass to a planet, it will keep shrinking turning into a brown dwarf until it reaches the critical point where fusion takes place, turning it into a real star. At this point the outward pressure from the fusion reactions will increase the radius again.

Kepler-36 and Its Two Unusual Planets

I was reading a recent article about the strange extrasolar system Kepler-36 which has two planets closely orbiting the star. The two planets come as close as 1.2 million miles (2 million km) of each other. If Mars came this close to Earth, we would be in trouble.

This got me thinking, is this even possible? Wouldn't one just orbit each another as a moon? Time to do some math.

In order for one object to be a moon of another it has to be inside of a Hill sphere of the larger object, an area where the gravity can hold on to satellite. According to Wikipedia the formula for to calculate a Hill sphere for planets with circular orbits is:

Where the mass of the smaller body (the planet) is m, and it orbits a heavier body (the star) of mass M with a semi-major axis a, and the the radius of the Hill sphere is r. Plugging in the values for the Kepler-36 star and its two planets we find that the Hill sphere for Kepler-36b is about 273,000km and Kepler-36c it is about 376,500km. Considering our own moon is 384,400 km away, none of these two planets would be able to hold on to it!

Conclusion:
As mentioned at the start of the post it since the orbits of these two planets are separated by 2 million km, that leaves us with about 1.35 million km of space between the two Hill spheres, meaning there is plenty of space between the two orbits. Here are the Hill spheres drawn to scale:

Both planets can have moons of their own, but they have to be closer than our own moon.

This still leaves us with some questions. How much closer can these orbits be? Surely their Hill spheres should not touch, but is that the limit?