The discussion explores the analogy between the period of a satellite in orbit around the Earth and the period of a mass oscillating through a hypothetical hole in the Earth, focusing on the underlying reasons for their similarity in periods.
Participants do not reach a consensus; while some agree on the similarity of the periods under certain assumptions, others challenge the validity of those assumptions, particularly regarding Earth's density.
The discussion highlights the assumption of uniform density for the Earth as a critical factor in the analogy, which remains unresolved. The implications of non-uniform density are not fully explored.
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.Ezio3.1415 said:Why both of these periods are same?
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)