most of those heat maps are result of direct measurements of the local gravitational acceleration, g. this is usually done with something called a Gravimeter. they are basically very high precision accelerometers. there are a number of effects that need to be taken into account when measuring gravity. relative altitude is one factor, because the force due to gravity decreases as 1/r^2, where r is the distance between the masses of interest. because of this we see that the acceleration due to gravity on top of mount Everest is ever so slightly smaller than that measured in death valley. another factor to account for is the fact that the earth rotates, and so every object on the earth carries an angular and linear acceleration. because of this we measure a change in gravitational acceleration as we move from either pole towards the equator. this effect on the acceleration is similar to the changing acceleration on a roller coaster as it goes through a loop. there are other effects as well, but these are the two big ones we can calculate. once these are accounted for, the resulting map is a direct measure of the specific gravity (density) of the material underneath the meter. this allows us to use gravitational measurements to "scan" the earth for resources like oil or rare minerals and elements.

as for your question about the sun, i don't know off the top of my head. i would have to calculate it, but the difference would be A LOT. the important thing to understand is that the "pressure" you are referring to is caused by gravity pulling the mass of the sun towards the center. hydrogen is the lightest of the elements, so to get a large enough pressure at the center to initiate fusion you need a great deal of it.

this question actually gave me pause. i was going to try and quote empirical evidence for the geometry of the universe that did not rely on our current cosmological models, and therefore the speed of light, but i couldn't (at least not off the top of my head)! if we ever gain the ability to travel astronomical distances easily, the measurement of spacial geometry becomes trivial. simply travel vast distances and make three turns. if you are able to return to your initial location by making only 90 degree turns, then the universe is "closed" (spherical. like drawing a large triangle over the surface of the earth). if you can return to your initial position and the angle of the turns add up to less than 180 degrees, then the universe is "open" (saddle shaped, like trying to draw a triangle inside of a large bowl). if you return to your initial position and the angles of your turn add up to exactly 180 degrees, then the universe is "flat" (like drawing a triangle on a piece of paper).

on another note, the speed of light is different in all mediums when compared to a vacuum =D in water it is approximately 33% slower, and we can get this directly from the refractive index, n. the refractive index is defined as the ratio between the speed of light in a vacuum, c, and the speed of light in a material, V. we can measure n from a simple geometric examination of how light bends in a given material, and yes, this is somewhat of a simplification (there are wavelength effects as well) but the point is

matter slows light down.

the universality of c can be seen directly from classical electrodynamics. i think i wrote about this in an earlier post, which was to answer a similar question.

hope this helps!

T.

i've said it before and i'll say it again, you can be as uncomfortable with the scientific results all you want, but that wont change the nature of the universe.

yes, light is self propagating. this comes directly from Maxwell's equations when applying them as a solution to the wave equation. a changing E field can induce a changing B field which can induce a changing E field etc...

the other thing to note that the slowing down of light i am referring to in my previous post is a change in its velocity when it enters a medium, not the continual deceleration of light. we have no evidence to support the latter. light traveling at c enters a medium where the speed of light is 1 m/s, the light will start traveling at 1 m/s and keep traveling at 1 m/s until it is absorbed or it leaves the medium.

as for the spinning toy thing, i've never heard of this. now, it IS true that that space-time curves in the presence of energy densities (and mass carries a great deal of it, hence Newtonian gravitation). we have indeed proved this in the lab and it implies that a compressed spring is ever so slightly "heavier" than an uncompressed spring, but to see this at a macroscopic level, and in a toy non the less, makes me suspicious. do you have a link to this thing? i would love to read about it! =D