GPE Deriv.: Integral Limits & Why Keep Inf. as Lower Limit?

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In gravitational potential energy (GPE) derivation, the lower limit is set at infinity to represent the energy required to bring an object from a point of no gravitational influence to a specific distance r from a mass. This approach reflects the concept that gravitational potential energy is defined relative to an object at rest at infinity, where the potential energy is zero. The integral calculates the work done against gravitational force as the object moves from infinity to the point r. Keeping infinity as the lower limit allows for a consistent reference point in gravitational calculations. Thus, the use of infinity as the lower limit is essential for accurately defining GPE.
Miraj Kayastha
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GPE is the energy needed to bring the object from infinity to r.
 

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