Escape velocity question - constant is wrong....

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SUMMARY

This discussion clarifies a common misconception regarding escape velocity in orbital mechanics. The original poster mistakenly categorized a problem as an escape velocity question, but it was determined that escape velocity is not necessary for maintaining an orbit at a fixed radius. The arithmetic error identified was a factor of √2, which contributed to the confusion. Ultimately, the conclusion is that understanding the distinction between escape velocity and orbital velocity is crucial.

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  • Basic understanding of orbital mechanics
  • Familiarity with the concept of escape velocity
  • Knowledge of fixed radius orbits
  • Ability to perform arithmetic operations involving square roots
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  • Study the differences between escape velocity and orbital velocity
  • Learn about the physics of circular orbits
  • Explore the mathematical derivation of escape velocity
  • Investigate common arithmetic errors in physics problems
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maxelcat
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Homework Statement
A planet of mass M and radius R rotates so quickly that material at its equator only just remains on its surface.
What is the period of rotation of the planet?

This is a multiple choice question. I must be doing something wrong.9
Relevant Equations
V=-GMm/R=0.5mv^2
This is a multiple choice question. I assumed that this is an escape velocity question. I have been going round and round...
Here's what I have done:
1663239000057.png
 
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It is not an escape velocity question. You do not require escape velocity to just orbit at a fixed radius.
 
Also you made an arithmetic error. Your answer should be wrong by √2
 
yes - found that.
 
and yes, it is not an escape velocity question. D'oh - I see that now.

Thanks
 
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