What is the biggest a comet could theoretically be?

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United States Roadster Tracker -Ben Pearson
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How big could a comet really be? With the recent excitement about the confirmed largest comet in our solar system, Bernardinelli-Bernstein, let's talk a bit about what the largest theoretical comet is, and a bit about what actually makes a comet.

The distinguishing feature of a comet is it needs an unbound atmosphere, in other words, the tail. This will happen when an object is close to the Sun and contains ice, or some other similar material that can produce a comet. Bernardinelli-Bernstein has one made of ammonium and nitrogen, for example.

The key thing is that there must be some particles, likely dust or water, that will be able to escape the gravitational influence of the planet when it flashes. Earth has the composition of a comet, but clearly isn't one because it holds on to its water long term. Mars is similar, although it does slowly let go of the water. Let's go with a definition where the average particle of water will be moving over the escape velocity at 0C as an arbitrary definition of a comet. The speed of a water particle at that temperature is 565 m/s. The density of the largest Kuiper-Belt objects is around 1.5 g/ml. At that density, the escape velocity is achieve around a size of 600 km. That seems to be a reasonable upper bound, although more work would need to be done to ensure it is reasonable.

https://www.omnicalculator.com/physics/sphere-density

https://www.omnicalculator.com/physics/escape-velocity

https://www.verticallearning.org/curriculum/science/gr7/student/unit01/page05.html

https://arxiv.org/abs/1311.0553

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