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3-body problem (special case)

According to the Newton's Mechanics:

Let us consider a massMof radiusRo.At a distancehfrom the center of this massM,we place a spherical shell(e.g a spherical elevator)of massm1and radiusR.

Moreover, at the center of the spherical shell we place anotherpointmassm2, (m1 ≠ m2).

Nowt= 0(Phase I), we allow these three masses m1, m2, M to move freely under the influence of the force of universal attraction.

Let us also assume that after a timedt(Phase ΙΙ),υ1, υ2 and Vare respectively the velocities of massesm1, m2 and Μ,relative to aninertial observer Ο.

Note:Massesm1, m2, and Mare considered to be homogeneous and absolutely solid bodies.

In addition, velocitiesυ1, υ2 and Vare considered to be positive numbers (that is, only the meters of their magnitudes are taken into account), while massm2is considered to be found always within the spherical shell(spherical elevator)m1.

The basic question that is being raised is the following:

QUESTION :

At what velocities do massesm1 (spherical elevator) and m2 (point mass)fall in the gravitational field of Mass M once simultaneously dropped in free fall from a height h, namely at the time dt>0 we have V1 = V2 or V1 ≠ V2 ?

I await your anwer.

Thanks,

Tony

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# Galileo's experiment and Equivalence Principle

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