Solve Orbital Velocity Equation: V=sqrt((g*R^2)/r)

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Homework Help Overview

The discussion revolves around the orbital velocity equation v=sqrt((g*R^2)/r) and its derivation. Participants explore the relationships between various gravitational equations and concepts related to circular motion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivation of the orbital velocity equation, referencing related equations such as Vcirc and Vesc. There is exploration of the relationship between acceleration and gravitational force, questioning the components of acceleration in orbital motion.

Discussion Status

The discussion is active, with participants providing insights into the derivation of the equations and questioning the assumptions behind them. Some guidance has been offered regarding the relationships between the equations, but no consensus has been reached on the best approach to the problem.

Contextual Notes

Participants are navigating the complexities of gravitational equations and their applications in orbital mechanics, with some confusion about the appropriate use of different formulas in the context of circular orbits.

chris529911
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I have a homework problem that involves the equation v=sqrt((g*R^2)/r) I am confused as to where this equation comes from. I know that Vcirc = sqrt((GM)/r) and Vesc = sqrt((2GM)/r)
 
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Do you know the formulas a=v^2/r and a=GM/r^2? Equate the two and you get v^2/r=GM/r^2. With a bit of manipulation, you get that equation.
 
a=v^2/r is the equation for the normal component of acceleration

a=GM/r^2 derived from F= GMm/r^2

a satellite orbiting the Earth only has a normal component of acceleration correct ?
 
this is the problem. Why can't you just use v^2=GM/r?
 

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chris529911 said:
a=v^2/r is the equation for the normal component of acceleration

a=GM/r^2 derived from F= GMm/r^2

a satellite orbiting the Earth only has a normal component of acceleration correct ?

For a circular orbit, yes.
 
chris529911 said:
this is the problem. Why can't you just use v^2=GM/r?

You can. That comes from equating v^2/r with GM/r^2.
 

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