RSS feeds
РусскийEnglish
Issue 9, 2026
Volume year page
Issues Authors PACS Subscription For authors

Accepted articles
Methodological notes


The maximum range of a relativistic throw in a uniform force field

 a, b,  b
a N.E. Zhukovskii Central Aerohydrodynamics Institute, ul. Zhukovskogo 1, Zhukovskii, Moscow Region, 140180, Russian Federation
b Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russian Federation

The problem of relativistic physics is solved to find the initial angle of a maximum range throw in a uniform force field with a fixed initial velocity. Two physically different formulations are considered: the relativistic motion of a charged particle in a uniform electric field, and the motion of a particle in a uniform gravitational field in accordance with the general theory of relativity. It is shown that the maximum range throw angle in both cases monotonously depends on the initial velocity, increasing from 45 degrees for velocities small compared to the speed of light to approximately 56.5 degrees for motion in a uniform electric field and to 90 degrees for motion in a uniform gravitational field, at velocities approaching the speed of light.

Keywords: relativistic motion, uniform electromagnetic field, general theory of relativity, Rindler metric
PACS: 03.30.+p, 04.20.−q (all)
DOI: 10.3367/UFNe.2026.09.040198
Citation: Demyanov M A, Kondratenko N A "The maximum range of a relativistic throw in a uniform force field" Phys. Usp., accepted

Received: 20th, February 2026, revised: 26th, May 2026, 18th, September 2026

Оригинал: Демьянов М А, Кондратенко Н А «Максимальная дальность релятивистского броска тела в однородном силовом поле» УФН, принята к публикации; DOI: 10.3367/UFNr.2026.09.040198

Similar articles (20) ↓

  1. P.B. Ivanov “On relativistic motion of a pair of particles having opposite signs of masses” Phys. Usp. 55 1232–1238 (2012)
  2. A.A. Logunov “The theory of the classical gravitational field” Phys. Usp. 38 179–193 (1995)
  3. V.I. Ritus “Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry” Phys. Usp. 51 709–721 (2008)
  4. V.B. Morozov “On the question of the electromagnetic momentum of a charged body” Phys. Usp. 54 371–374 (2011)
  5. B.M. Bolotovskii, G.B. Malykin “Visible shape of moving bodies” Phys. Usp. 62 1012–1030 (2019)
  6. A.A. Logunov “The relativistic theory of gravitation” Sov. Phys. Usp. 33 (8) 663–668 (1990)
  7. G.B. Malykin “The Sagnac effect: correct and incorrect explanations” Phys. Usp. 43 1229 (2000)
  8. V.I. Ritus “Lagrange equations of motion of particles and photons in the Schwarzschild field” Phys. Usp. 58 1118–1123 (2015)
  9. S.I. Syrovatskii “On the problem of the ’retardation’ of the relativistic contraction of moving bodies” Sov. Phys. Usp. 19 273–274 (1976)
  10. V.L. Ginzburg, V.P. Frolov “Vacuum in a homogeneous gravitational field and excitation of a uniformly accelerated detector” Sov. Phys. Usp. 30 1073–1095 (1987)
  11. Yu.I. Hovsepyan “Some notes on the relativistic Doppler effect” Phys. Usp. 41 941–944 (1998)
  12. S.I. Blinnikov, L.B. Okun, M.I. Vysotskii “Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity” Phys. Usp. 46 1099–1103 (2003)
  13. A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects” Phys. Usp. 47 797–820 (2004)
  14. V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field” Phys. Usp. 52 937–943 (2009)
  15. V.L. Ginzburg, Yu.N. Eroshenko “Once again about the equivalence principle” Phys. Usp. 38 195–201 (1995)
  16. G.B. Malykin “The relation of Thomas precession to Ishlinskii’s theorem as applied to the rotating image of a relativistically moving body” Phys. Usp. 42 505–509 (1999)
  17. V.I. Ritus “On the difference between Wigner’s and Møller’s approaches to the description of Thomas precession” Phys. Usp. 50 95–101 (2007)
  18. V.A. Aleshkevich “On special relativity teaching using modern experimental data” Phys. Usp. 55 1214–1231 (2012)
  19. Gaite José “The relativistic virial theorem and scale invariance” Phys. Usp. 56 919–931 (2013)
  20. B.M. Bolotovskii, A.V. Serov “Details of the motion of charged nonrelativistic particles in a variable field” Phys. Usp. 37 515–516 (1994)

The list is formed automatically.
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions