These entities are the input to an inverse problem solved by Binet’s equation. Using Delaunay variables to parametrize these entities, one can show the conservation of Tisserand’s parameter. The shape of these entities may be described by the Laplace–Runge–Lenz vector. Bertrand’s theorem states that these entities are only necessarily closed for two power-law potentials. The vis-viva equation describes bodies moving along these entities, which are classified as hyperbolic when the dimensionless parameter epsilon is greater than one. An object’s period is proportional to the three-halves power of these entities’ semimajor axis by Kepler’s third law. For 10 points, name these trajectories of objects experiencing an attractive central force. ■END■
| Eastern Canada | Main | Y | 13 | 92% | 0% | 8% | 74.00 |
| Upper Mid-Atlantic (1) | Main | Y | 10 | 100% | 0% | 0% | 81.80 |
| Lower Midwest | Main | Y | 3 | 100% | 0% | 33% | 85.67 |
| Upper Midwest | Main | Y | 10 | 100% | 0% | 30% | 68.10 |
| Northeast | Main | Y | 11 | 100% | 0% | 0% | 70.73 |
| South Central | Main | Y | 8 | 100% | 0% | 0% | 63.75 |
| Southeast | Main | Y | 8 | 100% | 0% | 0% | 70.63 |
| UK | Main | Y | 14 | 93% | 0% | 14% | 65.15 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Akshansh Chauhan | UTD A | Iowa | 24 | 10 |
| Matthew He | Texas A | Arizona State A | 27 | 10 |
| Yrwin Batan | MIT A | Amherst A | 35 | 10 |
| Ben Richards | Sheffield B | City St George's A | 35 | 10 |
| Will McCurley | Auburn A | Bruin A | 37 | 10 |
| Benjamin Chapman | Toronto A | Toronto B | 38 | 10 |
| David Bass | Johns Hopkins A | Maryland A | 38 | 10 |
| Alex Akridge | Indiana A | UIC | 38 | 10 |
| Ezra Santos | Chicago A | Notre Dame D | 39 | 10 |
| Shardul Parthasarathy | Illinois A | Louisville B | 39 | 10 |
| Alec Riso | Cornell-UG | Dartmouth | 39 | 10 |
| Philip Yao | Brown A | Harvard | 39 | 10 |
| Matthew Sumanen | Georgia Tech A | Georgia Tech C | 39 | 10 |
| Kevin Flanagan | Bristol A | Warwick B | 39 | 10 |
| Gus Redding | Imperial B | Bristol B | 39 | 10 |
| Asha Basu | McGill A | Guelph A | 40 | 10 |
| Braxton Davis | Missouri A | SIUE | 41 | 10 |
| S. A. Shenoy | Georgia Tech B | Vanderbilt B | 41 | 10 |
| Rohit Chintala | Maryland C | George Washington B | 42 | 10 |
| Sharath Narayan | Northwestern A | Alberta B | 44 | 10 |
| Collin Leck | UCO | Northwestern B | 44 | 10 |
| Jacob Finley | Notre Dame A | Chicago D | 45 | 10 |
| Will Zhang | Tufts A | Tufts B | 53 | 10 |
| Sidarth Erat | MIT B | BU | 55 | 10 |
| Mia Clark-Webb | Oxford B | Durham A | 55 | 10 |
| Kai Madgwick | Manchester A | Oxford A | 56 | 10 |
| Agnijo Banerjee | Cambridge A | Edinburgh B | 57 | 10 |
| Oscar O'Flanagan | Imperial A | Birmingham A | 59 | 10 |
| Ethen Sun | Toronto D | Ottawa | 61 | 10 |
| Mats Miller | Chicago B | Michigan C | 62 | -5 |
| Fern Fang | VCU A | George Mason B | 62 | 10 |
| Anirudh Terdal | LSE B | Manchester B | 62 | 10 |
| Raymond Jiang | Illinois C | Louisville A | 66 | 10 |
| James Xiao | Toronto E | Western Ontario | 67 | 10 |
| Kevin Le | Carleton | Toronto H | 67 | 10 |
| Aryan Desarapu | Michigan B | Indiana B | 67 | 10 |
| Matthew Kohn | Williams | Yale A | 67 | 10 |
| Oliver West | Cambridge C | Lancaster A | 67 | 10 |
| Brendan Bridle | Queen's A | McMaster C | 70 | 10 |
| Samir Sarma | Georgia Tech D | Vanderbilt A | 70 | 10 |
| James Windle | Purdue C | Notre Dame B | 71 | -5 |
| Denali Tran-Le | McGill B | Toronto K | 71 | 10 |
| Yashwanth Bajji | Michigan A | Purdue B | 72 | -5 |
| Caleb West | Kentucky | Michigan D | 76 | 10 |
| Joel Dicker | Southampton A | Sheffield C | 76 | -5 |
| Abdelrahman Elsisi | Sheffield A | Warwick A | 79 | 10 |
| Felix Garrett Johnston | Huntsville A | Auburn B | 81 | 10 |
| Camden Walker | WashU B | Truman State | 85 | -5 |
| Max Kolda | Notre Dame E | NYU B | 87 | 10 |
| Shreyas Sinha | Texas B | McGill D | 89 | 10 |
| Jakub Hel | UAB A | Mississippi State A | 89 | 10 |
| Oliver Rothnie | Durham B | Imperial C | 90 | -5 |
| Platon Gorokhov | Toronto F | Toronto G | 92 | 10 |
| Vincent Zhang | Penn A | George Mason A | 92 | 10 |
| Leonard Castine | Penn B | Georgetown A | 92 | 10 |
| Franklin Wu | Toronto C | McMaster A | 92 | 10 |
| Lesley Kwarteng | Johns Hopkins C | UMBC A | 94 | 10 |
| Sarah Khan | Queen's B | McMaster B | 94 | 10 |
| Zaire Gibbons | Toronto J | Toronto Metropolitan | 94 | 10 |
| Eames Weeks | Brown B | Brandeis Lloyd George | 94 | 10 |
| Jeremy Mau | Northwestern C | Rose State | 94 | 10 |
| Nolan Travers | Tulsa | UTD B | 94 | 10 |
| Henry Jameson | LSE A | Edinburgh A | 94 | 10 |
| Young Fenimore Lee | Ohio | Arizona State B | 94 | 10 |
| Gavin Ge | Waterloo | Guelph B | 95 | -5 |
| Misty Chen | Purdue B | Michigan A | 97 | 10 |
| Adil Soubki | Cambridge D | Southampton B | 97 | 10 |
| Christopher Dech | Brandeis Wilson | Brandeis Orlando | 98 | 10 |
| Sam Kemeny | Brandeis Clemenceau | Brown C | 99 | 10 |
| Andres Cordoba | Yale B | BC A | 99 | 10 |
| Ian Parsons | Maryland D | Johns Hopkins B | 100 | 10 |
| Graham Lucas | Bowdoin B | BC B | 100 | 10 |
| Davin Sivertson | Alabama B | Alabama A | 100 | 10 |
| Luke Sloan | McGill C | Toronto I | 102 | 10 |
| Gabriel Avrahami | Georgetown B | Maryland B | 103 | 10 |
| Phillip Jordan | Imperial C | Durham B | 103 | 0 |
| Matthew Wozniak | Michigan C | Chicago B | 106 | 10 |
| Donal Ryan | Truman State | WashU B | 108 | 10 |
| Sophie Lyman | WashU D | William Woods | 108 | 10 |
| Adrian Dooley | Notre Dame B | Purdue C | 108 | 10 |
| Stephen Pace | Guelph B | Waterloo | 108 | 0 |
| Dillon George | Catholic University | George Washington A | 108 | 10 |
| Alex Irvine | Sheffield C | Southampton A | 108 | 10 |
| Ethan Burks | Huntsville B | Sewanee A | 108 | 10 |