Two particle system - find their angular velocities

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SUMMARY

The discussion centers on solving a problem from "Orbital Mechanics for Engineering Students" by Curtis, 2nd edition, regarding the angular velocity of two particles under gravitational influence. The problem states that two particles of identical mass, m, maintain a constant distance, d, and requires the application of Newton's second law using the center of mass as the inertial frame. The derived formula for angular velocity is ω = √(2Gm/d³), confirming the correct approach to the solution.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with gravitational forces and their equations
  • Knowledge of angular velocity and its calculation
  • Basic concepts of center of mass in physics
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  • Explore advanced topics in orbital mechanics using "Orbital Mechanics for Engineering Students"
  • Learn about the implications of the center of mass in multi-body systems
  • Investigate the applications of Newton's laws in celestial mechanics
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Students of physics, particularly those studying orbital mechanics, as well as educators and professionals seeking to deepen their understanding of gravitational interactions and angular motion in multi-particle systems.

Alexanddros81
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Hi! I want to start solving problems from the text
'Orbital Mechanics for Engineering students' by Curtis 2nd edition.
Is this the right place to post?

Homework Statement


2.1 Two particles of identical mass m are acted on only by the gravitational force
of one upon the other. If the distance d between the particles is constant, what is the
angular velocity of the line joining them?
Use Newton's second law with the center of mass of the system as the origin of
the inertial frame.
{Ans.: ##ω=sqrt{2Gm/d^3}

Homework Equations

The Attempt at a Solution



Orbital Mechanics 2_1.jpg


Is this the right way to solve this problem?
 

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Looks good.
 

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