section_path: Newton's laws of motion/Approaches to many-body problems
section_name: Approaches to many-body problems
paragraph_text: Approaches to many-body problems
  
  Rather than an exact closed form solution, orbits with many bodies can be approximated with arbitrarily high accuracy. These approximations take two forms:
  
  Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large assemblages of objects have been simulated.