What is the Difference Between Escape Velocity and Orbit Velocity?

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SUMMARY

The discussion clarifies the distinction between escape velocity and orbital velocity. Escape velocity is the speed required for an object to break free from a planet's gravitational pull, calculated using the formula \( v = \sqrt{\frac{2GM}{R}} \). In contrast, orbital velocity is the speed necessary for an object to maintain a stable circular orbit around a planet, represented by the formula \( v = \sqrt{\frac{GM}{R}} \). The key takeaway is that orbital velocity is lower than escape velocity, as it only needs to counteract gravitational pull without escaping it.

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  • Knowledge of basic physics formulas involving mass (M), radius (R), and velocity (v)
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Badger01
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"Given a planet has mass M and radius R, find the speed it would have to be launched at. Compare this to the speed required to put the object in the circular orbit."

I understand the first half where Ep=Ek
i.e: GMm/r = 1/2 mv2
rearrange to find v

how ever, I'm unsure of what exactly the 'orbit velocity' is.
is the the value of v in centripetal force, F = mv2/r
is this the same as the speed needed to launch it into orbit or what? i am rather stumped here..
 
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The problem statement is a bit confusing. I suppose it could be asking you to compare the escape velocity for an object leaving the planet's surface (planet radius R) to the velocity of a hypothetical object orbiting the planet at the planet's surface. Obviously one would have to ignore the problem of terrain variations, such as mountains!

To answer your query, yes, the orbital velocity is the speed of the object along its orbital path. So it is indeed the 'v' in mv2/r.
 

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