Analogy between satelite orbit and mass oscillating through earth

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The discussion explores the analogy between the period of a satellite orbiting Earth at surface height and a mass oscillating through a hole in the Earth, both described by the formula T=2 π √(R/g). Participants note that this equivalence holds under the assumption of uniform density within the Earth. The gravitational force's proportionality to position in both scenarios allows for the decomposition of circular motion into simple harmonic motion. Some participants express intrigue about the implications of this analogy and the underlying physics. The conversation highlights the importance of assumptions in deriving these relationships.
Ezio3.1415
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The period of a satellite revolving around the Earth earth at surface height is equal to the period of any mass thrown through a hole of the earth(which gains a simple harmonic motion)...

It seemed really interesting to me...

Why both of these periods are same?

T=2 π √(R/g)
 
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Ezio3.1415 said:
Why both of these periods are same?
You can decompose the circular orbit into two simple harmonic motions in two dimensions. The gravitational force component in each dimension is proportional to the position along that dimension. The same proportional relationship exists along a radial line in a uniform mass sphere.
 
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Ezio3.1415 said:
The period of a satellite revolving around the Earth earth at surface height is equal to the period of any mass thrown through a hole of the earth(which gains a simple harmonic motion)...

It seemed really interesting to me...

Why both of these periods are same?

T=2 π √(R/g)

That's only true if you assume the Earth's density is uniform. That's not quite correct.
 
AT Yes,but we are doing another analogy to explain this analogy... I thought of it at first but assumed their could be another approach to explain this incident... It just seems so interesting to me...

Dauto Yes... That's why we have to assume that the Earth is a uniform mass sphere...
 

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