Conceptual problem: Finding gravitational KE

AI Thread Summary
To find the kinetic energy (KE) of an orbiting body, both the formulas 1/2mv^2 and 1/2Gm1m2/r can be used, depending on convenience. In a circular orbit, gravitational force acts as the centripetal force, leading to the relationship mv^2/r = GMm/r^2. This simplifies to 0.5mv^2 = 0.5GMm/r, indicating that kinetic energy can be derived from gravitational potential energy (GPE). The total energy of the orbiting body is expressed as KE + GPE = -0.5GMm/r, highlighting the interplay between these two forms of energy in orbital mechanics. Understanding these relationships is crucial for solving problems related to gravitational systems.
grantP
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Homework Statement



to find KE of an orbiting body, do I use 1/2mv^2 or 1/2Gm1m2/r??

Homework Equations


The Attempt at a Solution

 
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Hi grantP,

grantP said:

Homework Statement



to find KE of an orbiting body, do I use 1/2mv^2 or 1/2Gm1m2/r??

If it's a circular orbit (for example) then it would just depend on which is more convenient for the problem.
 
For an orbiting body, gravitational force provides for the centripetal force:

mv2/r = GMm/r2


0.5mv2 = 0.5GMm/r


Just to digress abit, so the total energy an orbiting body with distance r away from the centre of the planet is:

KE + GPE = 0.5GMm/r + (-GMm/r)

= -0.5GMm/r
 

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