Re: Gravity Paradox

Jeff:



> Would somebody be so kind as to explain to me what would happen if you

> were to travel to the center of the Earth.  Apparently there is some

> kind of a paradox that states that your weight approaches infinity?



I had a problem in one of my graduate physics classes that addressed

this very question!



There is no paradox.



Gravity is a product of mass (though even today, no one is exactly

sure how!).  When you are far out in space, the gravity is weak.

As you approach Earth, the force of gravity becomes stronger until

you reach the surface where it is AT IT'S STRONGEST.  The

gravitational force of the Earth on you is strongest when you are at

the surface because then you have the entire mass of the Earth

beneath you and you are touching it (and can get no closer).



Once you begin your journey beneath the surface of the Earth,

there will be a certain amount of Earth's mass ABOVE you.  At first,

it will be only a litle bit, then, the deeper you go, more and more

mass will be above you.  The force of gravity from all the mass

above you will cancel out an equal amount of force of gravity

from all the mass below you.  The 'net' force on you will be

diminished.



[By calculating the volume and center of mass of the portion of

Earth above you and therefore it's resulting force, and the

likewise force from the mass below you (the actually calculation

isn't as simple as that though!), you can get an estimate

of the net force on your body.  If you travelled to a distance

halfway between the surface and the center of the Earth, your

weight would be about 2/3 of your 'surface' weight!  Some

calculus is required.]



When you finally reach the center, there will be about the same

amount of mass surrounding you in all directions.  Therefore you

will feel weightless!



Now think about this:  If you wanted to live on a planet that was

so much more massive than Earth that the surface gravity would

be uncomfortable, and this planet were completely solid (that is

to say, not molten liquid on the inside), what could you do?

You could live under the surface of the planet at a depth where

the gravity was equal to Earths!



The "paradox" you may be referring to concerns idealized situations

with celestial bodies of "super mass", like black holes.  If you

could crush the mass of ten stars to a singular point, the gravity

might seem like it would become infinite.

But the energy required to crush such mass would also be nearly

infinite, and so the situation would never exist, and neither would

the paradox.



Thanks for your question!