An Experiment for Viewers of the Feb. 17th Nova Program on PBS
I would like to reference an upcoming program on Nova on PBS, Feb 17th. After the main program on 4 winged dinosaurs, the host, Neil Degrasse Tyson does a segment where he imagines jumping down a tunnel from the surface of the earth, passing through the center of the earth, then re-emerging on the other side. While his cautions about the hazards from this tunnel in the real world are valid, such as the very high temperature with depth and air pressure (building-up with depth as one descended), the central point of the thought experiment is false {although it is the “Standard Book Answer”, as far as almost all textbooks are concerned.}
I would like to propose a simple experiment that your PBS home viewers can safely do in the privacy of their own living rooms (for under $1.00) which will likely suggest that the answer given in that end segment is false, or should at least generate a reasonable and healthy scientific controversy.
The Experiment
Take any reasonable sized ball, and toss it safely into the air, not so hard as to injure anyone, touch the ceiling, or create unsafe conditions for nearby bystanders. Toss the ball high enough that it leaves your hands, and see what happens. Always throw the ball so that you can catch it again. (This is not a necessity for the experiment, but a great convenience for repetition of the experiment, quickly, without chasing the ball over and over again.)
Notice that whenever you (or home viewers) toss the ball up into the air, you are always sending the ball into LESSER gravitational curvature. Notice that, after a brief rise, the ball slows down, and returns back down to (near) the original position, if you were careful with your original toss. Notice that the ball ALWAYS returns back into slightly greater curvature, nearer the surface of the earth. Conclusion : On the surface of the earth, the ball always returns back to greater curvature from lesser curvature. {Please note any exceptions in your home experiments, if any ever occur.}
Viewers at home may remark, that is hardly a new, or remarkable or radical experiment. People have been getting exactly that same result for as far back as we know.
Now, let us consider a different situation, which cannot practically be performed, due to extreme difficulty in re-creating the exact conditions. If one considers the Newtonian equation for gravity = G ( m1 m2 ) / r2, it should be apparent that the value should decrease as the radius decreases, all the way to the center of the earth. This is the standard “book answer”.
In our real world, the true answer is not quite so simple for one simple reason. The density of matter MORE THAN QUADRUPLES with depth, at least until one reaches the core-mantle boundary. After that, the density still increases, but does not quadruple.
If you consult the CRC Manual as a reference book, you can see that gravitational curvature (the strength of gravity) actually INCREASES with depth, ever so slightly, until one gets to about 2,886 Km straight down. Depending upon location at the surface, gravity starts at around 9.81 m/sec2 at the (blue) surface, and increases to 10.69 m/sec2 at 2,886 km below the (light brown) 
surface (the c ore- m antle b oundary) [CMB].
From that maximum area, gravity then decreases to ZERO* at the center of the earth (or more correctly, to it’s minimum value on earth. *The gravitational influence from the moon, other planets, the sun, and other stars and galaxies is still present, so the end value may actually exceed zero.)
Now, if one were to dig a tunnel from this CMB region, through to the center of the earth, gravitational curvature would start-off at MAXIMUM, at the top of that tunnel at the CMB, and decrease steadily until one reached the center of the earth.
If we were to apply our RESULTS of the experiment we just performed above, our conclusion MUST BE exactly the opposite to that of the “world’s greatest experts”, including those results imagined in your program on February 17th, 2009. (I know that broadcast segment has aired before, in previous years. I do know that I sent a brief response before, but I did not include the home experiment with differing results at that time.)
I would challenge you at the Nova staff, if you do not accept the results of the above experiment, that is one thing, but, I would request that you at least offer your home viewers the opportunity to perform the above experiment themselves, and then, decide for themselves whether to accept their own experimental results, or whether to accept the “prevailing opinion of the world’s greatest experts” view(s) as presented and hosted by Mr. Tyson. {A strictly “Newtonian” view, based on the 17th century notion of gravity behaving as-if it emanated from a single-point source at the center.}
You can read more about this at www.cr-theory.org, or The Comedy-Recycling Theory of the Entire Known Universe. I have an edited video of me performing my own experiment above, with my running commentary, on-line. I do have the original high-definition camcorder footage of that same experiment that I could release to support MY conclusions. (Your results WILL be the same, too.)