Lost and in Need of Ideas for Finding Inspiration

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Homework Help Overview

The discussion revolves around understanding concepts related to circular motion and kinetic energy, particularly in the context of an object in a circular orbit. Participants express a need for clarification on the principles governing such motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants inquire about calculating kinetic energy in circular orbits and seek explanations for the necessary conditions to maintain such orbits. There are questions regarding the relationship between kinetic energy and total mechanical energy in this context.

Discussion Status

Some participants have offered insights into the formulas related to centripetal force and the nature of energy in circular motion. However, there is ongoing questioning and a lack of explicit consensus on the interpretations of energy components.

Contextual Notes

Participants are navigating through the definitions and relationships between kinetic energy, potential energy, and total mechanical energy, indicating a need for further exploration of these concepts.

fer Mnaj
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Homework Statement
If we have motion in a circular orbit of a body of mass m subject to the gravitational force of the Sun.
Consider the approximation for M >> m in which the Sun is located at the center of mass and μ = m.



How to show that the total mechanical energy associated with the movement of this body fulfills that
##E = −1 / 2U## ?

where U is the gravitational potential energy of m due to M
Relevant Equations
##-∇U= -G Mm/r^2##
Any idea? I am pretty lost
 
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Are you able to calculate the KE of the mass in a circular orbit?
 
Not really, can you explain it?
 
fer Mnaj said:
Not really, can you explain it?
What is needed to keep an object in a circular orbit?
 
fer Mnaj said:
Not really, can you explain it?
If you know that the orbit is circular, you have some formulas that could be used to express the required centripetal force.
 
##m (v^2/r)##
 
By ##E##, I suspect you mean kinetic energy instead of total mechanical energy.
 
why?
 
Because if ##E = U + T##, then for circular motion the following holds at all times: ##E = \frac{1}{2}U = -T##.
 
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