Astronomy Picture Of The Day : A Gravity Map of Earth

NASA ^ | 11.13.01 | Robert Nemiroff (MTU) & Jerry Bonnell (USRA)

[Physicist]

All the mountains surrounding Everest have mass concentrations below the observer atop Everest, in the same general direction as the center of mass of the (assumed spherical) Earth. Imagine, if you will, a sphere with a (small) torus sitting on one side, and a cone extending through the doughnut hole. The C-O'M of that system is still on the axis from the sphere's center to the tip of the cone. It changes the symmetry from spherical to cylindrical.

Right. The point is that the mass of the rest of the Himalayas exerts a net pull downwards, rather than upwards, so it makes you slightly heavier. By how much, I can't say offhand. If you take it to the extreme case, where the Himalayas cover the entire globe, the Earth would be several miles thicker, in which case you'd certainly be heavier (force goes as mass over radius squared, but mass goes as radius cubed).

So there's an interesting homework problem:

A) You're standing on a pole that raises you 10,000 meters above sea level. How much do you weigh, compared to your weight at sea level? B) The diameter of the pole begins to increase, until you are standing on the center of a 10,000 meter high plateau. Assume that the density of the plateau is 4 g/cc. How wide does the plateau have to be before your weight equals what it was at sea level? Assume also that the plateau conforms to the curvature of the Earth, i.e. that its surface is maintained at 10,000 meters. C) Assume that the plateau is replaced by a series of close-packed cones, 10,000 meters high and 10,000 meters wide at the base. Assume you stand atop the central peak. How wide must the mountain range be so that your weight equals what it was at sea level?

[RadioAstronomer]

Bump for reference

[Chemist_Geek]

A) You're standing on a pole that raises you 10,000 meters above sea level. How much do you weigh, compared to your weight at sea level? B) The diameter of the pole begins to increase, until you are standing on the center of a 10,000 meter high plateau. Assume that the density of the plateau is 4 g/cc. How wide does the plateau have to be before your weight equals what it was at sea level? Assume also that the plateau conforms to the curvature of the Earth, i.e. that its surface is maintained at 10,000 meters. C) Assume that the plateau is replaced by a series of close-packed cones, 10,000 meters high and 10,000 meters wide at the base. Assume you stand atop the central peak. How wide must the mountain range be so that your weight equals what it was at sea level?

Show your work for full credit. Do you want that in slugs or Newtons? (grin)

[ssplam]

just to put it on my list.