Owen217a

2007-Nov-05, 07:50 AM

FREE FALL OF BODIES

3-body problem (special case)

According to the Newton's Mechanics:

Let us consider a mass M of radius Ro. At a distance h from the center of this mass M, we place a spherical shell (e.g a spherical elevator) of mass m1 and radius R.

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

Now t= 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 time dt (Phase ΙΙ), υ1, υ2 and V are respectively the velocities of masses m1, m2 and Μ, relative to an inertial observer Ο.

Note:Masses m1, m2, and M are considered to be homogeneous and absolutely solid bodies.

In addition, velocities υ1, υ2 and V are considered to be positive numbers (that is, only the meters of their magnitudes are taken into account), while mass m2 is 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 masses m1 (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 u1 = u2 or u1 ≠ u2 ?

I await your anwer.

Thanks,

Tony

3-body problem (special case)

According to the Newton's Mechanics:

Let us consider a mass M of radius Ro. At a distance h from the center of this mass M, we place a spherical shell (e.g a spherical elevator) of mass m1 and radius R.

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

Now t= 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 time dt (Phase ΙΙ), υ1, υ2 and V are respectively the velocities of masses m1, m2 and Μ, relative to an inertial observer Ο.

Note:Masses m1, m2, and M are considered to be homogeneous and absolutely solid bodies.

In addition, velocities υ1, υ2 and V are considered to be positive numbers (that is, only the meters of their magnitudes are taken into account), while mass m2 is 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 masses m1 (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 u1 = u2 or u1 ≠ u2 ?

I await your anwer.

Thanks,

Tony