Thursday, May 15, 2014

So You Think You'd Like to be a Planet

Suppose, for example, that you are one of those 100 nanometer sized particles of rocky materials that populate the galaxy as a result of Supernovae and other major Stellar events. It's lonely out there in the cosmic void, so you would like to get together with friends to form a planet. How does one go about this?

First thing is, you've got to hang where the cool crowd does - in a large, cool (say 10 C above absolute zero), cloud of gas and dust. There's usually a bunch of them around the plane of the disc of any respectable spiral galaxy. You and your cloud may need a little push to get started - a nearby supernova or a density wave in the spiral galaxy, for example, but once your local cloud is gravitationally bound, you're on your way.

Once the cloud starts contracting, it begins to break up into small pieces. It's important at this point to stay in the thick of things, since the early stars get the gas - and dust. Be cool though, and hang on to some of your angular momentum, otherwise you just get sucked into the star and re-vaporized. At this point, you and your homies will be circulating about the protostar, with a lot of bumping and jostling which will circularize and flatten your orbits.

At this point, the trick is for you and your posse to stick together. Gravity can't do that job for you yet, though the combined gravity of zillions of little particles can help you all clump into a rough disc, so actual sticking has to depend on chemical forces between surfaces. How big do the lumps have to get for gravity to start to be important?

Consider a sphere that has grown to 1 cm in radius - you and a few million-quadrillion other dust grains lumped together, maybe. The surface gravity of your little ball is given by G*M/r^2, where M = 4*pi*rho*r^3/3 where rho is the density. G = 6.67 x 10^-8 in cgs units, so if we assume rho = 1 g/cm^3, the density of water, surface gravity becomes about 2.8 x 10^-7 cm*s^-2. Note also, that for constant density, surface gravity scales with radius, so for an Earth sized planet of radius 6.4 x 10^8 cm, surface gravity would be 178 cm/s^2. Earth is about 5.5 times as dense as our hypothetical planet, so it's surface gravity is about 5.5 times as large, or 980 cm/s^2.

Another interesting parameter for you and your fellow dust grains is the escape velocity at the surface, given by Sqrt(2*G*M/r). For our 1 cm radius dust ball, it works out to about 7.5 x 10^-4 cm/s. Note that it too scales like radius, but only like the square root of density. Clearly that's a small speed, even by snail standards - so gravity isn't really any help at that scale. By the time you get to Earth size and density, though, the numbers get kind of big, 11.2 km/s.

How about a stadium sized fluffy rock of 100 meter (10^4 cm) radius? Escape velocity is still small - 7.5 cm/s, and you could definitely jump off. Scale that up to 10 km, and escape velocity becomes 7.5 m/s, and you would need to be fairly athletic to make the leap out of the gravitational field, so gravity is now a major player.