reply to post by spy66
Spy, you are misunderstanding what a " vacuum" is.
A vacuum is an absence of gaseous phase matter, not an absence of all matter.
Like so many people have said it has no effect on the force of gravity, none what so ever.
And all mass has a gravitational field, very likely down to the quantum level, for those interested look into quantum gravity detection experiment
being put together by Cal State Humbolt, fascinating stuff.
Anyhoo, Spy in your OP, the scenario you have works like this,
Your tunnel is a vacuum, the only effect it will have is an absence of media to provide friction, that's it ,it will not effect gravity at all.
So now , the force of gravity follows an inverse square relationship with distance from the center of mass, that is to say the force falls off at a
rate that is proportional to the square of the distance between the objects.
That's why the acceleration due to gravity , which at the earths surface is 32/sec^2, falls off so quickly.
The weightless of " space" is not a gravityless environment, it is micro gravity environment, as long as there is mass there is gravity.
With all that in mind, if one were to drop your mass down the tunnel from the north to south pole, your mass would start with a specific amount of
gravitation potential energy, it will accelerate at 32 feet/sec^2, to start with. It will change because the of the differing densities of the
materials that make up the earth and their relative masses. But to keep it simple we will say it falls at a 32ft/sec^2. As it falls the gravitational
potential energy is turned into kinetic energy, according to the equation U=mgh, where U is gravitational potential energy
m is mass, g, acceleration due to gravity 32ft/sec^2 and h is height of object or in this case the distance from the theoretical center of gravity.
Now a body in motion will stay in motion a body a rest will stay at rest, that is verbal expression of conservation of momentum. In absence of
external forces acting on a moving body a moving body will stay in motion.
Back to the hole, your mass accelerates toward the centers of gravity, turning gravitational potential energy to kinetic energy. As it it approaches
the center the force of gravity in front of it increases, because of the increasing density, but conversely as you pass through the earth all of the
mass behind the falling mass has a gravitational effect on the motion of the moving mass slightly slowing it down.
This is where I differ from the poster who said, that in a vacuum, it would be a simple oscillation scenario and the mass would oscillate back and
forth forever, it would not. If your are using the.force of gravity as a force in the analysis, you can't also discount it.
Classical newtonian physics treats the earth as a point mass, but if you are looking at the mass of the earth as as a system then you have have to
account for the mass in relationship to the position of the object and differing forces of gravity due to changes in density as it moves through the
gravitational system that is the earth as a whole. It would appear to follow a simple straight line oscillation back and forth losing energy and
eventually settling and coming to rest at the bottom of the gravity well.
No it would follow a extremely eliptic path orbiting the theoretical center of gravity. This orbit would decay over time in to rotational motion of
the original mass at the center of the earth.
So the mass would swing back and forth not going quite as far each trip and it would eventually come to rest at the center of the earth, spinning, at
a very high rate it might add as momentum must be conserved.
All of the momentum of the original mass has to be maintained it is converted from linear momentum to rotational momentum.
This is why stars and planets rotate around thier own axes and why planets and asteroids and comets rotate around stars and why star systems orbit
the center of the galaxy and galaxies orbit even larger groups of each other.