# Simulation of Planetary Accretion Formation

Team: 47

School: LAS CRUCES HIGH

Area of Science: Earth and Space Sciences

Interim: Problem:
Given a set of initial accretion disk conditions, i.e. a sun and a circumsolar disk, what planets and objects will form? How long will it take and what are the distributions of different planet types?
This question is essential to the astronomical community because as awareness of extrasolar planets and the capability to detect them increases, an accurate prediction for where to search for earth-like terrestrial planets will greatly increase the detection rate and decrease the cost of locating near-undetectable worlds.

Plan:
The core program is a basic dynamics simulation based around the application of Newton's Law of Universal Gravitation, using a given array of particles with randomly generated masses, positions, and rotations about one or more central stars. Output will be in the form of a series of arrays recording the x, y, and z positions of each particle at each time step. An animation will be generated based on these arrays. Particle collisions will cause individual particles to merge, gaining mass and eventually forming into protoplanets and planets.

Progress:
Our program has reached a good testing bed, but have few concrete results. We have routines set up to calculate velocity, acceleration, and position, write a given number of points at a given frequency into a file, plot with gnuplot, and create animations of the points. Within the program we have control over structural and scientific variables, such as the number and attributes of particles, and the 'timestep' between iterations. However, while two particles orbiting around a common center of mass should form ellipses retracing their paths, our particles do not, but rather experience a number of phenomena that make for interesting screenshots but have no scientific value. We have yet to create an algorithm for combining the particles as we are more interested in their motion.

Expected Results:
At some point in time, when we can get two particles to move properly, we will expand the program to run using more realistic parameters, showing the development of planet bodies. More efficient algorithms should greatly increase the number of particles the computer can handle. Following this, we will attempt to adapt the program for parallel processing, time permitting, however, given the complexity of porting a program into an unknown interface, we may also explore options to make the current program scientifically beneficial on a desktop machine.

Referenced Sources:
Note- several of these deal with planetary formation regarding accretion disks as a fluid. We are not implementing this model due to the complexity of the science and coding involved.

Giant planet formation by gravitational instability. Boss, Alan P. Science, June 20, 1997 v276 n5320 p1836(4).

Chambers, J.E. 2004. Planetary Accretion in the Inner Solar System. Earth and Planetary Science Letters, 223, 241-252.

Chambers, J.E. 2003. Symplectic Integrators with Complex Timesteps. Astronomical Journal, 126, 1119-1126.

Planetary Systems: Formation, Evolution, and Detection. Weidenshilling, Stuart J. Science, Jan 20, 1995 v267 n5196 p395(2).
Formation of giant planets by fragmentation of protoplanetary disks. Mayer, Lucio; Quinn, Thomas; Wadsley, James; Stadel, Joachim. Science, Nov 29, 2002 v298 i5599 p1756(4).
http://www.amara.com/papers/nbody.html
Special thanks to Dr. Anatoly Klypin of NMSU's Astronomy Department for helpful tips on how to program particle-based planetary simulations.

Team Members:

Andrei Klypin
Jonathan Lee Annua
William Downs
Vincent Mestas

Sponsoring Teacher: Gregory Marez