Far-field approximations in multipole expansions allow for sub-quadratic complexity in this system, such as in the Barnes–Hut treecode algorithm. Small perturbations in this system lead to large changes in motion in the first-studied “small denominators” problem, which in simulations can be adjusted by applying a “softening parameter” to the potential. The Jacobi integral is an invariant for a form of this system that is “restricted,” which produces five equilibrium points named for Lagrange. In the simplest form of this system, one can fix a reference frame about the center of mass and use the reduced mass, allowing one to derive Kepler’s three laws for a form of this system. For 10 points, name this system concerning the orbits of objects in gravitational central force problems. ■END■
| Great Lakes | 2025-02-01 | Y | 6 | 100% | 0% | 17% | 89.67 |
| Lower Mid-Atlantic | 2025-02-01 | Y | 1 | 0% | 0% | 100% | 0.00 |
| Midwest | 2025-02-01 | Y | 1 | 100% | 0% | 0% | 100.00 |
| Northeast | 2025-02-01 | Y | 3 | 100% | 0% | 0% | 67.67 |
| Overflow | 2025-02-01 | Y | 4 | 75% | 0% | 0% | 67.33 |
| Pacific Northwest | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 75.50 |
| South Central | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 87.50 |
| UK | 2025-02-01 | Y | 1 | 100% | 0% | 0% | 64.00 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Nathan Sheffield | MIT A | Brandeis B | 52 | 10 |
| Stan Melkumian | Purdue | Northwestern A | 55 | 10 |
| Aditya Patnaik | Ohio State B | Carnegie Mellon B | 64 | 10 |
| Agnijo Banerjee | Cambridge A | Oxford A | 64 | 10 |
| Joy An | Harvard A | Brown A | 72 | 10 |
| Michał Gerasimiuk | Stanford B | Iowa | 72 | 10 |
| Catherine Welch | UW A | UW B | 72 | 10 |
| Karan Gurazada | Texas A | Texas B | 72 | 10 |
| Stephen Heritage | Notre Dame A | Georgetown A | 75 | 10 |
| Angelo Pan | Case Western B | Michigan B | 79 | -5 |
| Andrew Harms | Michigan State | Case Western A | 79 | 10 |
| Isaac Meredith | Tufts A | Brandeis A | 79 | 10 |
| Matthew Wang | UBC | Alberta | 79 | 10 |
| David Nieman | Carnegie Mellon A | Michigan C | 90 | 10 |
| Yashwanth Bajji | Michigan A | Kenyon | 90 | 10 |
| Calvin Bostleman | Ohio State A | Michigan D | 90 | 10 |
| Ezra Santos | Chicago B | Missouri | 100 | 10 |
| Bryan Ugaz | ASU | TAMU | 103 | 10 |
| Noah Chin | Virginia Tech A | Virginia A | 105 | -5 |
| Mitchell Indek | Michigan B | Case Western B | 125 | 10 |
| Joseph Chambers | Virginia A | Virginia Tech A | 125 | 0 |
| Christopher Joseph | Notre Dame C | Georgetown B | 125 | 0 |
| Amanda Zhao | Georgetown B | Notre Dame C | 125 | 0 |