|
|
| | | | | | | | |
A Hole through the Earth Theory
1. The Newton's Law of Gravitation.
γ: The Universal Gravitational Constant = 6.67428 · 10-11 Nm2/kg2
M1: The mass of the part of the earth inside the sphere with center at the center of earth and radius equal the distance from the earth center to the particle.
m : The mass of the particle.
x : The distance from the center of the earth to the particle.
2. The mass M1 eqaul to the mass density ρ multiplied by the corresponding volume of V1.
3. The volume V1 equal to the volume of a shpere with radius x.
4. The mass density ρ equal the the mass M of the earth divided by the volume of the earth.
5. Simplification of the expression in 4.
6. Newton's Second Law of the particle with mass m.
7. Insertion of Newton's Second Law in 6 to the expression in 5.
8. In a differential equation ax + bx = 0 the angular velocity ω
is equal to the square root of b/a.
9. In a periodic motion (SMM) as in equation 7, the period is equal to 2π/ω.
|
