2021-P2 Best Solutions and Final Results

Problem 2 – Comet’s orbit

By 7th March 2021, there are 992 registered participants from 71 countries (the list of countries is given below). During the five weeks, 151 solutions were submitted for problem 2, out of which 95 were correct.

This problem was clearly a big success as there was a big number of correct solutions with completely different approaches which showed that the problem was a great source of inspiration for the contestants. As usual, the main contenders for the best solutions were the solutions submitted before the publication of the first hint – there were 65 such solutions. Out of those 65 solutions, I picked 11 well-documented not-too-long solutions which demonstrated different approaches. The ranking list gives preference to the shortest solutions and to creative ideas.

  1. Lotus Chen, 45% of the bonus – by far the shortest solution, not surprisingly based on the eccentricity vector.
  2. Eddie Chen, 25% of the bonus – also a very short solution, bypasses the eccentricity vector, mostly geometrical.
  3. Sangyul Lee, 15% of the bonus  – an analytical solution based on the formula of the ellipse in Cartesian coordinates and generalizing the result.
  4. Nguyen Manh Quan, 15% of the bonus – a solution bypassing the eccentricity vector and using a series of clever geometrical constructions, and application of Apollonian circles.

Apart from these, there are solutions that are also very interesting and deserve publication, hence earning the publication bonus factor of 1.1. Jianzheng Deng and Oliwier Urbanski – solutions that start with the eccentricity vector and then make use of clever geometry. Yu Lu – a mostly analytical solution based on the formula of the ellipse in polar coordinates and making use of the Lagrange multiplier. Absur Khan Siam and Fang Tzu, Hsu – solutions making use of the fact that the locus of the intersection point of two mutually perpendicular tangents to an ellipse is a circle. Arhaan Ahmad –  a solution making use of the fact that the locus of the intersection point of a tangent to an ellipse with its perpendicular drawn through a focus is a circle. Ricards Kristers Knipsisa nicely written solution based on the fact that the hodograph is a circle (which, as a matter of fact, has been used in many solutions and follows immediately from the eccentricity vector, here proved in a different way).

Finally, we are publishing here the solutions by the author of the problem, Thomas Foster, and by the academic head of Physics Cup, Jaan Kalda.

Final results for Problem 2

Pre-university students

First nameSurnameCountrySchoolDateTimeScore
EddieChenUnited StatesWest-Windsor Plainsboro High School North31.01.2114:412.752
Manh QuanNguyenVietnamHanoi – Amsterdam High School for the Gifted31.01.2114:392.740
ThanadisCharoenrujijinThailandSuankularb Wittayalai School31.01.2113:592.594
Bayram AlpŞahinTurkeyAnkara Science HS31.01.2114:561.949
ArhaanAhmadIndiaKrishna Public School31.01.2116:271.949
ZheningLiCanadaSir John A. Macdonald Secondary School31.01.2117:451.611
LotusChenChinaNo.2 High School Shijiazhuang01.02.216:221.568
Cristiana AndreeaMurgociRomaniaInternational Computer Highschool of Bucharest31.01.2117:491.464
Vlad-ȘtefanOrosRomania“Grigore Moisil” Informatics High School31.01.2118:541.331
Absur KhanSiamBangladeshNotre Dame College31.01.2120:031.331
VukHipSerbiaMathematical grammar school31.01.2123:211.100
JianzhengDengChinaShenzhen Senior High School02.02.212:521.100
YuLuChinaSuzhou High School of Jiangsu Province03.02.2115:121.100
OliwierUrbańskiPolandLiceum Ogólnokształcące nr 7 w Poznaniu03.02.2112:231.045
DušanBegušSerbiaMathematical Grammar School31.01.2123:441.000
Wesley AntonioMachado Andrade de AguiarBrazilMilitary School of Manaus01.02.213:591.000
JiaxiSuChinaNO.1 Middle School attached to Central China Normal University01.02.219:211.000
MinhTrang DaoVietnamHus highschool for gifted students01.02.2110:071.000
AmeyaDeshmukhIndiaSt. Joseph’s Convent High School01.02.2115:111.000
AnantLuniaIndiaDelhi Public School RK Puram01.02.2121:561.000
JoshuaTeoSingaporeNUS High School02.02.218:281.000
AnastasiaPozharkovaRussiaMBOU “Gymnasium 91 named after M. V. Lomonosov”02.02.2111:361.000
XuanyuLinChinaShenzhen Foreign Languages School02.02.2114:531.000
PriteshMehtaIndiaAllen04.02.2118:041.000
JózsefGurzóHungaryBudapesti Fazekas Mihály Gyakorló Általános Iskola és Gimnázium04.02.2119:171.000
M. SubhiAbo RdanSyriaKnowledge private schools05.02.2118:451.000
Arturo Francisco RuizMercadoBoliviaHno. Felipe Palazón05.02.2121:271.000
BalázsKovácsHungaryHatvani Bajza József Gimnázium05.02.2122:301.000
DengJinqiuChinaGuangdong Experimental High School06.02.2110:581.000
DmitryKhvatovRussiaLyceum “Vorobyovy gory”06.02.2118:211.000
MartinVassilevBulgariaSMG “Paisii Hilendarski”07.02.219:521.000
AdamDžavoronokSlovakiaGymnázium Poštová 907.02.2119:181.000
CristianArdeleanuRomaniaInternational Computer High School Bucharest09.02.2115:241.000
Sebastián AndrésArévalo AguirreEl SalvadorInstituto Emiliani10.02.2113:371.000
AbdullahAlHussniSyriaAl Saade HS, Syria11.02.2122:301.000
TimothyHoSingaporeGap Year13.02.2115:061.000
NitheshSanjeevi SaravananSingaporeIn gap year13.02.2117:301.000
PhatthanonPattanakanvijitThailandSuankularb Wittayalai School13.02.2118:411.000
GigiTsirekidzeGeorgiaLEPL Kutaisi Phys. Math. Public School N4113.02.2118:501.000
AbdalazeezJerbySyriaAl-Basel high school14.02.210:351.000
Gyan Seah;TJ Wei & P SeowSingaporeNUS High School of Mathematics and Science14.02.218:481.000
Je QinChooiMalaysiaKolej Tuanku Ja’afar02.02.212:430.950
Gia HiểnNguyễnVietnamHUS High School for Gifted Students04.02.2112:330.950
DutaKartvelishviliGeorgiaLEPL KUTAISI ANDRIA RAZMADZE PHYSICS AND MATHEMATICAL PUBLIC SCHOOL N4110.02.2116:090.950
SarthakpandaIndiaFiitjee Bhubaneswar14.02.215:000.950
Caio AugustoSiqueira da SilvaBrazilColégio Objetivo Integrado12.02.214:460.900
AntoniaGhitaRomaniaInternational Computer High School of Bucharest14.02.2112:150.900
AlessandroMenegonBrazilColégio Objetivo Integrado16.02.2118:340.900
JiuyunCheungChinaHuaiyin Middle School19.02.2116:110.900
LanTianyiChinaBeijing Academy20.02.211:450.900
EvanKimUnited StatesTesla STEM High School21.02.219:110.900
Minh HoàngVietnamHUS High School for Gifted Students15.02.213:060.810
JieWangChinaZhangjiakou No.1 Middle School16.02.2113:420.810
AlexandarRoussevBulgariaFirst Language School17.02.2110:320.810
Ameya VikramaSinghIndiaFIITJEE Junior College19.02.2113:250.810
Huy PhuongDangVietnamHigh School for Gifted Students25.02.210:010.800
JozefCsipesSlovakiaGymnázium, Grösslingová 18, Bratislava27.02.2116:370.800
GolamIshtiakBangladeshKushtia Government College15.02.218:510.729
AshmitDuttaUnited StatesWayzata High School20.02.2120:300.729
郑智豪Zhihao ZhengChinaHuaiyin High School23.02.217:030.720
JeffreyShiUnited StatesPhillips Academy Andover06.03.2123:130.700
ViníciusFerreira RodriguesBrazilColégio Master06.03.2123:590.665
幻夜Zhuang YichengChinaUrumqi No.1 Senior High School04.03.2117:550.630
Chin PengTanMalaysiaKolej Matrukulasi Melaka04.03.2118:210.630
TasnimulJishanBangladeshNotre Dame College, Dhaka06.03.2111:120.630
DivyanshPandeyIndiaKV Picket26.02.214:260.583
DženanMidžićBosnia and HerzegovinaJU Gimnazija “Bihać”06.03.2118:340.567

University students

First nameSurnameCountryUniversityDateTimeScore
NikitaSemeninRussiaMoscow Insitute of Physics and Technology31.01.2114:292.594
HuiyuanWangChinaUniversity of Cambridge31.01.2122:482.358
PieterVan SteenweghenBelgiumImperial College London31.01.2123:182.144
Fang TzuHsuTaiwanNational Taiwan University01.02.211:362.144
YuechenZhuChinaPeking University01.02.2110:411.683
JanisHunsLatviaUniversity of Cambridge01.02.2111:161.611
QianLinChinaUniversity of Oxford01.02.2122:391.464
SangyulLeeKoreaSeoul National University03.02.2118:421.406
BatuhanKeskinTurkeyBoğazici University03.02.2118:031.331
PrakharSinghIndiaIIT Kanpur04.02.217:071.100
RicardsKnipsisLatviaUniversity of Manchester13.02.2114:111.100
TevžLotričSloveniaUniversity of Oxford04.02.219:271.000
VineetGuleriaIndiaSri Chaitanya10.02.2121:081.000
ElioMoreauItalyÉcole Polytechnique Fédérale de Lausanne (EPFL)12.02.2116:581.000
AlessandroRezziItalyUniversity of Padova13.02.2111:511.000
JaroslavHermanCzechiaCharles University, Prague13.02.2122:021.000
HugoBäckmanSwedenChalmers University09.02.2122:150.900
DaoxinZhongSingaporeUniversity of Oxford15.02.210:120.900
JamesWalklingUnited KingdomUniversity of Cambridge15.02.2110:400.900
Masuk RidwanSaumoBangladeshBangladesh University of Engineering and Technology15.02.2111:390.900
PhungMinh HiepViet NamTHPT Chuyên Vĩnh Phúc15/02/2112:380.900
星宇 姜Xingyu JiangChinaTongji University20.02.213:450.855
LeonardoWimmerJapanOsaka University22.02.2114:090.800
NguyenTanVietNamHong Kong University of Science and Technology24.02.217:160.800
YiChenZhuChinaNanjing University27.02.2111:580.720
LuoLongChinaUniversity College London28.02.2114:310.700
YanjunZhouUnited KingdomUniversity of Oxford01.03.2120:210.700
AlfianGunawanIndonesiaUniversitas Indonesia06.03.2122:030.700

Participating countries: Algeria, Azerbaijan, Australia, Bangladesh, Belarus, Belgium, Bosnia and Herzegovina, Bolivia, Brazil, Bulgaria, Cambodia, Canada, China, Croatia, Czechia, Egypt, El Salvador, Estonia, Finland, Georgia, Germany, Greece, Hungary, India, Indonesia, Iran, Israel, Italy, Japan, Kazakhstan, Kenya, Korea, Kyrgyzstan, Latvia, Lebanon, Lithuania, Macedonia, Malaysia, Mexico, Moldova, Mongolia, Nepal, Nigeria, North Macedonia, Pakistan, Peru, Philippines, Poland, Romania, Russia, Saudi Arabia, Serbia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Syria, Taiwan, Thailand, Turkey, Turkmenistan, United Arab Emirates, United Kingdom, United States, Uzbekistan, Vietnam.