Calculating Gravity at Half Earth's Radius

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Homework Help Overview

The problem involves calculating the distance external to the surface of the Earth where the acceleration due to gravity equals that within the Earth at half its radius, assuming a uniform internal density.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of gravitational forces inside a uniform sphere and question how mass distribution affects gravitational pull. There are attempts to clarify the concept of gravitational effects from mass above versus below a certain point within the Earth.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of gravitational effects and referencing theoretical principles such as Gauss's Law. There is no explicit consensus yet, but hints and clarifications are being provided.

Contextual Notes

Participants express uncertainty regarding the assumptions of uniform density and the implications of gravitational forces within a non-hollow sphere. The discussion includes references to theoretical concepts that may not be universally accepted or understood.

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Homework Statement



Taking the internal density of the Earth to be uniform, calculate, in terms of
the Earth’s radius R, the distance external to the surface of the Earth at which the
acceleration due to gravity is equal to that within the Earth at half the Earth’s radius.

Homework Equations





The Attempt at a Solution



Not sure about this one..Inside the Earth surely the bits of mass further out will pull out on an object.. so how do i work this out?

Thanks!
 
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Hint! It is assumed, and mostly true that inside a hollow sphere of mass the forces acting upon an object cancel each other, wherever it is placed. So something like zero gravity.
 
but the Earth isn't a hollow sphere :(
 
No, but if you hollowed out a small cave and made your measurement in there, you'd be on the right track. Additional hint: the "force of gravity" is zero in the center of the earth.
 
bon said:
but the Earth isn't a hollow sphere :(

yes, but if you are at a certain distance inside the Earth then all that mass above you would not contribute to any gravity felt by you, only the mass below you. ( the sphere with radius= Earth radius-depth, while the hollow shell of depth thickness would not contribute)
 
Lok said:
yes, but if you are at a certain distance inside the Earth then all that mass above you would not contribute to any gravity felt by you, only the mass below you. ( the sphere with radius= Earth radius-depth, while the hollow shell of depth thickness would not contribute)

why would the mass above you not contribute sorry? or is this just a theorem i should accept? :P
 

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