Earth orbit -- geosynchronous orbit calculation

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Homework Help Overview

The discussion revolves around calculating parameters related to a geosynchronous orbit, specifically focusing on the relationship between speed, radius, and gravitational forces in circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of angular velocity and centripetal acceleration in the context of circular orbits. There are attempts to derive relationships using Newton's laws and gravitational forces, with some questioning the need for integration and others clarifying the definitions of acceleration in this scenario.

Discussion Status

The discussion is active, with participants providing guidance on the correct application of Newton's laws and the definitions of centripetal acceleration. Multiple interpretations of the problem are being explored, particularly regarding the relationships between force, mass, and acceleration.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding the fundamental principles rather than arriving at a final solution.

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Homework Statement


upload_2016-9-21_22-36-1.png


Homework Equations



ε= r_max - r_min / r_max + r_min
= r*v2 / gRE

The Attempt at a Solution


I first find that 1 revolution is 2π rad , the angular velocity ω = 2π rad / 24h = π/43200 rad /s
so v = rω where r is the unknown
ε = 0 (circular orbit)

r*(rω)2 / g RE = 0Correct route?
 
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Your approach is incorrect. You need to use Newton's 2nd law to find a relation between speed and radius in a circular orbit.
 
st
kuruman said:
Your approach is incorrect. You need to use Newton's 2nd law to find a relation between speed and radius in a circular orbit.
start with F= ma, then integrate?
 
No need for integration. Remember that the acceleration here is centripetal. What is an expression for F?
 
F=ma then a is gravity?
 
No, a is the centripetal acceleration. What is an expression for it? F is the force of gravitational attraction between two masses according to Newton's law of gravitational attraction.
 
GmM/ r2
 
That's F. What about a on the other side of the equation?
 
m (r'' + rω) because it is the angular movement ?
 
  • #10
Centripetal acceleration is ω2r, not ωr. Also, what is r'' for a satellite in a circular orbit?
 

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