Mapping Gravity

overThruster writes: "No, you don't need to drink the water... Gravity is less strong in India--enough so that you weigh almost 1% less there. See BBC story about NASA's gravity map." Here's another story about the mission, and the GRACE home page (or NASA's less-informative page).

Comments

Re:okaaaaaay

[Anonymous DWord]

No, then it would be cheaper to ship things FROM there, since you get more than a ton per ton. And you could get on the plane with 70 lbs. of stuff, and when you arrive in (wherever) laugh uproariously at the ticket agent, dancing around and saying "ha HA! I have 71 pounds in my bag!"

Well, I already knew this.

[tlipcon]

Hell, in my physics classroom it's about 30% as strong as anywhere else. I proved it myself in a lab last week- it's about 3.2 m/s^2 in our corner of the room!

Strangely enough, it's just about 9.8 up front. I guess the earth is pretty aspherical.

-Toad

And what about...

[rice_burners_suck]

...the fact that moving at speeds approaching the speed of light will cause you to move faster through time, so that if you left Earth, travelled at near light speeds, and then came back shortly afterwards, 100 years might have elapsed on Earth in what you perceived as about 10 minutes.

I think that physical laws like this have a very significant effect on the lumpiness of the Earth, and therefore, on the variations in gravitational pull.

Imagine that you're running down a square field, from one side to the side parallel to it, and it takes you 10 minutes to run across this field. Ok, now imagine that you're running across the same field, but instead of running "straight," you're running at an angle, so that you're not perpendicular to the edges of the field that you're running from and to. It will take you a bit longer to get to the other side of the field, even though you're running at the same speed, because by going at an angle, you've increased the distance you have to go to get from one edge to the other.

Now suppose we call the field a 2-dimensional surface, like a piece of paper. You could say that the first time you ran across the field, you travelled along one axis, or dimension--let's say the X axis. But on the way back, you ran at an angle, which means that you've gone along two axes, the X and Y axes. But you went the same speed. This means that you have split the same speed across two dimensions.

We say that time is a fourth dimension. Now picture this: No matter what's happening, you're ALWAYS moving through the 4 axes (the three "space" dimensions and the one "time" dimension) at exactly the speed of light. It's just that you're splitting that speed (the speed of light) across some combination of the 4 dimensions. You're doing one of the following:

• Standing perfectly still in the 3 space dimensions and moving only through time. (I know that motion is relative, but imagine for a moment that your motion is relative to the universe itself and that you can guarentee that you're really not moving through space at all but only through time). Therefore, you're moving through time at the speed of light.
• You're moving through space and time, which means you're splitting your motion across at least one of the space dimensions and the fourth time dimension, which means that you're moving somewhat more slowly through time. If you're going through space really really fast, whatever speed is left over for time will be much smaller. So if you're moving through space at speeds approaching the speed of light, what might be 10 minutes for you might be a much longer time for everybody else. Because you're moving through time much more slowly, since you're using up all that speed in the other dimensions.
• You're only moving through space itself and are therefore not moving through time at all. Photons, which are light particles, do this. Since they're light, they move through space at the speed of light. (Yeah, that makes sense, right?) This means that there is NO speed left over for moving through time. As a result, if a photon travels in a straight line, it is EVERYWHERE along that line at the same time. We think it takes 8 minutes for a photon leaving the sun to arrive at Earth, because we're the outside world. For the photon, the trip was instantaneous, but for us, it took 8 minutes. Just like if you're travelling through space really really fast (almost the speed of light), you'll think it was 10 minutes but for us it was 100 years.

I think all of these physical laws have a very significant effect on the lumpiness of the Earth, and therefore, on the variations in gravitational pull.

And, of course, the obligatory OH WELL.

Re:And what about...

[dragons_flight]

You make some elementary mistakes, but I'm only going to deal with two of them.

First off relativity has nothing to do with variations in the earth gravitational field. This is entirely related to the fact that the mass density of the materials making up the earth are not uniformly distributed. Some rocks are denser than others, and moisture and magma move around. Relativistic mass scales as 1/Sqrt[1-v^2/c^2], where v is an objects velocity and c is is the speed of light. Thus for a 1% increase in mass you would have to identify objects moving at > 14% of c as measured by a stationary observer on the Earth's surface. Besides which this deals with inertial mass (F=ma), but gravitational fields (F=G*m1*m2/r^2) are more complicated in a relativistic framework.

Standing perfectly still in the 3 space dimensions and moving only through time. (I know that motion is relative, but imagine for a moment that your motion is relative to the universe itself and that you can guarentee that you're really not moving through space at all but only through time). Therefore, you're moving through time at the speed of light.

There is NO UNIVERSAL FRAME OF REFERENCE. When not accelerating everyone experiences time as moving at the same constant rate, and ALL are equally justified in saying they are moving solely in the time direction. One person observering another having a nonzero relatively velocity will interpret their motion as having decreased temporal component and appropriately increased spatial component(s). Sometimes it is useful for someone to interpret their own motion in terms of another person's perspective (such as saying the car is moving along the ground as opposed to saying the ground is moving under me), but this makes no difference to the objective or subjective experience.

Physics of it all

[Simm0]

You probably hear the 9.8 m/s^2 acceleration due to gravity touted but this is just the net affect across the whole of the globe which is actually very inaccurate when used at specific locations.

Did you know that its actually easier to break the force of gravity ontop of mount everest. I'll show it using the formula:

g = G*(m/r^2)
= ((6.67*10^-11)*(5.98*10^24))/(6.389*10^6)
= 9.77 m/s^2

The value of g also can vary locally on the surface because of the presence of irregularities and rocks of different densities. Such variations in g also known as 'gravity anomilies'. Mineral deposits, for example, have a greater density than surrounding material; because of the greater mass in a given volume g can have a greater value on top of such a deposit then at its sides.

Overall altitude, underground minerals and distance from the equator all play apart in changing the acceleration due to gravity across the globe.

Re:This is so COOL!

[ralmeida]

Actually, when you have a slope in the ocean surface the water doesn't run downhill; it runs across the slope. If you have a "seamount", for example, water will circle it clockwise in the northern hemisphere.

Most of the large scale circulation is the result of the subtropical wind circulation, and small anomalies in the geoid will be insignificant. Also, part of the ocean circulation has a thermohaline nature, and is forced by the distribution of salt and temperature across the world.

(Yes, I'm an oceanographer)