The discussion centers on the analogy between the period of a satellite orbiting Earth at surface height and the period of a mass oscillating through a hole in the Earth, both described by the formula T=2 π √(R/g). Participants highlight that this equivalence holds under the assumption of uniform Earth density, which simplifies the gravitational force analysis. The conversation emphasizes the decomposition of circular motion into simple harmonic motion, illustrating the underlying physics principles governing these phenomena.
PREREQUISITESPhysics students, educators, and anyone interested in orbital mechanics and harmonic motion will benefit from this discussion.
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)