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

Gravitation01:16

Gravitation

8.8K
In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and...
8.8K
Gravitational Potential Energy01:14

Gravitational Potential Energy

26.5K
Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of interaction present in a system, there is a corresponding type of potential energy. The total potential energy of the system is the sum of the potential energies of all the objects. Potential energy can be classified into two major categories: gravitational potential energy and elastic potential energy. The potential energy associated with a...
26.5K
Newton's Law of Gravitation01:15

Newton's Law of Gravitation

17.1K
Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of...
17.1K
Potential Energy due to Gravitation01:27

Potential Energy due to Gravitation

8.6K
Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it resides is independent of the path taken. Thus, similar to the gravitational field, a gravitational potential energy function can be defined, which depends only on spatial coordinates.
Consider a mass gravitationally bound to another object. For example, the Earth is gravitationally bound to the Sun’s gravitational field. The potential...
8.6K
Rocket Propulsion in Gravitational Field - II01:03

Rocket Propulsion in Gravitational Field - II

2.8K
A rocket's velocity in the presence of a gravitational field is decreased by the amount of force exerted by Earth's gravitational field, which opposes the motion of the rocket. If we consider thrust, that is, the force exerted on a rocket by the exhaust gases, then a rocket's thrust is greater in outer space than in the atmosphere or on a launch pad. In fact, gases are easier to expel in a vacuum.
A rocket's acceleration depends on three major factors, consistent with the...
2.8K
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

2.3K
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
2.3K

You might also read

Related Articles

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

Sort by
Same author

What is the effect of measurable respiratory muscle training on respiratory muscle strength in mechanically ventilated adults in intensive care units? A systematic review and meta-analysis.

Australian critical care : official journal of the Confederation of Australian Critical Care Nurses·2025
Same author

The edge-averaging process on graphs with random initial opinions.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Unanticipated demand of Physiotherapist-Deployed Airway Clearance during the COVID-19 Surge 2020 a single centre report.

Physiotherapy·2021
Same author

Communication cost of consensus for nodes with limited memory.

Proceedings of the National Academy of Sciences of the United States of America·2020
Same author

Online learning with an almost perfect expert.

Proceedings of the National Academy of Sciences of the United States of America·2019
Same author

Tractable near-optimal policies for crawling.

Proceedings of the National Academy of Sciences of the United States of America·2018
Same journal

In This Issue.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Long-term cultural continuity across the Neanderthal-modern human sequence at Üçağızlı II Cave, northern Levant.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Dolphins use names to remember whom to avoid.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Retraction for Shaked and Frenkel, Curiouser and curiouser: Meningeal lymphoid structures in the aging brain.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Small but mighty: The outsized role of small water bodies in the global carbon cycle.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Functional traits produce conditional outcomes in different community contexts.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Related Experiment Video

Updated: Feb 5, 2026

Bacterial Cellulose Spheres that Encapsulate Solid Materials
04:42

Bacterial Cellulose Spheres that Encapsulate Solid Materials

Published on: February 26, 2021

5.0K

Gravitational allocation on the sphere.

Nina Holden1, Yuval Peres2, Alex Zhai3

  • 1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.

Proceedings of the National Academy of Sciences of the United States of America
|September 9, 2018
PubMed
Summary
This summary is machine-generated.

Researchers explored fair allocation on spheres using random points. They found the expected distance for a gravitational potential partition is approximately 0.577, proving optimal matching for point collections.

Keywords:
allocationbipartite matchinggravitytransportation

More Related Videos

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
08:52

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

8.7K
Obtaining Cancer Stem Cell Spheres from Gynecological and Breast Cancer Tumors
07:01

Obtaining Cancer Stem Cell Spheres from Gynecological and Breast Cancer Tumors

Published on: March 1, 2020

10.8K

Related Experiment Videos

Last Updated: Feb 5, 2026

Bacterial Cellulose Spheres that Encapsulate Solid Materials
04:42

Bacterial Cellulose Spheres that Encapsulate Solid Materials

Published on: February 26, 2021

5.0K
Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
08:52

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

8.7K
Obtaining Cancer Stem Cell Spheres from Gynecological and Breast Cancer Tumors
07:01

Obtaining Cancer Stem Cell Spheres from Gynecological and Breast Cancer Tumors

Published on: March 1, 2020

10.8K

Area of Science:

  • Computational geometry
  • Probability theory
  • Spherical geometry

Background:

  • Fair allocation problems involve partitioning a space among users.
  • Random point distributions on spheres are fundamental in various scientific fields.
  • Previous work established bounds for optimal matching of points on a sphere.

Purpose of the Study:

  • To analyze the expected distance in a "gravitational" potential-based fair allocation on a sphere.
  • To establish an optimal matching for two collections of random points on a sphere.

Main Methods:

  • Utilizing a "gravitational" potential to define partitions of a sphere.
  • Calculating expected distances for points within allocated spherical regions.
  • Developing a matching algorithm for two sets of uniformly distributed random points on a sphere.

Main Results:

  • The expected distance between a sphere point and its associated point in a fair allocation is approximately 0.577.
  • An optimal matching for two collections of n random points on a sphere was derived.
  • The expected distance for the matched pairs was shown to be approximately 0.577, matching theoretical optima.

Conclusions:

  • The "gravitational" potential method provides a provably optimal fair allocation on a sphere.
  • The derived matching strategy achieves optimal expected distance for random point sets.
  • This work has implications for resource allocation and geometric partitioning problems.