Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

1.0K
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
1.0K
Schwarzschild Radius and Event Horizon01:21

Schwarzschild Radius and Event Horizon

2.3K
No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape...
2.3K
Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

1.6K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
1.6K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

8.2K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
8.2K
Newton's Law of Gravitational Attraction01:24

Newton's Law of Gravitational Attraction

1.0K
Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
Newton's law of gravitational attraction is a fundamental law of physics that governs the attraction between objects. It states that the magnitude of the gravitational force between any two objects is proportional to their masses and inversely...
1.0K
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

3.3K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
3.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Damping Versus Oscillations for a Gravitational Vlasov-Poisson System.

Archive for rational mechanics and analysis·2025
Same author

On Self-Similar Converging Shock Waves.

Archive for rational mechanics and analysis·2025
Same author

Naked Singularities in the Einstein-Euler System.

Annals of PDE·2023
Same author

[Effects of twirling-rotating reinforcing and reducing technique for left ventricular morphology, concentration of ET-1 and expression of type I, III collagen mRNA in spontaneous hypertensive rats].

Zhongguo zhen jiu = Chinese acupuncture & moxibustion·2014
Same author

Detection of internal exon deletion with exon Del.

BMC bioinformatics·2014
Same author

Illumina human exome genotyping array clustering and quality control.

Nature protocols·2014
Same journal

On Point Spectrum of Jacobi Matrices Generated by Iterations of Quadratic Polynomials.

Communications in mathematical physics·2026
Same journal

A Mathematical Analysis of IPT-DMFT.

Communications in mathematical physics·2026
Same journal

Asymptotics of Symmetric Polynomials: A Dynamical Point of View.

Communications in mathematical physics·2026
Same journal

Commuting Quantum Operations Factorise.

Communications in mathematical physics·2026
Same journal

On the Open TS/ST Correspondence.

Communications in mathematical physics·2026
Same journal

A Superintegrable Quantum Field Theory.

Communications in mathematical physics·2026
See all related articles

Related Experiment Video

Updated: Oct 15, 2025

Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
09:44

Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System

Published on: June 5, 2014

13.0K

Larson-Penston Self-similar Gravitational Collapse.

Yan Guo1, Mahir Hadžić2, Juhi Jang3,4

  • 1Division of Applied Mathematics, Brown University, Providence, RI 02912 USA.

Communications in Mathematical Physics
|November 1, 2021
PubMed
Summary
This summary is machine-generated.

Researchers rigorously proved the existence of the Larson-Penston solution, a self-similar model for collapsing self-gravitating fluids under Newtonian gravity with an isothermal equation of state.

More Related Videos

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K
Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.7K

Related Experiment Videos

Last Updated: Oct 15, 2025

Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
09:44

Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System

Published on: June 5, 2014

13.0K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K
Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

9.7K

Area of Science:

  • Astrophysics
  • Fluid dynamics
  • Mathematical physics

Background:

  • The Larson-Penston solution, discovered in 1969, describes the gravitational collapse of fluids.
  • This solution is based on an isothermal equation of state and Newtonian gravity.
  • Previous work relied on numerical integration to find this self-similar solution.

Purpose of the Study:

  • To rigorously prove the existence of the Larson-Penston self-similar solution.
  • To provide a formal mathematical foundation for the previously discovered collapse model.

Main Methods:

  • The study employs rigorous mathematical analysis.
  • Numerical integration methods were used in prior work, but this study focuses on analytical proof.

Main Results:

  • The existence of the Larson-Penston solution is rigorously proven.
  • This confirms the validity of the self-similar model for collapsing self-gravitating fluids.

Conclusions:

  • The mathematical existence of the Larson-Penston solution is established.
  • This rigorous proof supports further theoretical and observational studies of gravitational collapse.