1. May 12, 2004

Terminus

can someone tell me how i can calculate what the weight of a 100lb man (on the surface of the Earth) would be on different parts of the Earth: the core and at all the layers of the atmosphere

thanks

2. May 12, 2004

ZapperZ

Staff Emeritus
Use the Gauss's law equivalent for gravity, find "g", and use the person's mass to find his weight.

http://scienceworld.wolfram.com/physics/GausssLaw.html

[Since you didn't describe what level you're at, I have no idea if you can do this or not]

What I am more curious about is, why are you asking for help from "Meteorologists" in particular?

Zz.

3. May 12, 2004

Gokul43201

Staff Emeritus
I'm not a meteorologist, but I'm sure most of them would not try to answer this question, though they might tell you the thicknesses of various layers of the atmosphere off the top of their heads.

Anyway, the weight of an object varies linearly (this is an approximation assuming the density of the Earth is the same everywhere) with its distance from the center of the Earth. This is valid anywhere inside the Earth. So, if you are halfway to the core, your weight would be about half your surface weight. When you've gone 90% of the way down, your weight is only 10% of its surface value. And at the core, you have no weight, because you are being pulled equally in all directions, and these forces cancel each other out.

The measured weight of an object in general is the difference between its gravitational weight and its buoyant force. For most objects that are solid or liquid, the buoyant force is smaller than 0.5% of the gravitational weight, so it is neglected. This buoyant force decreases as you climb up through the atmosphere, but like I explained, it hardly affects the weight, so we'll not worry about it. Above the surface, the gravitational force is inversely proportional to the square of the distance from the Earth's center. A good formula for the weight as a function of height (above the Earth's surface) is :

W(at some height, h) = W(surface)/[1 + (2h/R)], where R is the radius of the Earth.
Also, a slightly rougher version is W(h) = W(surface) * [1 - (2h/R)]
Both these formulas work only fairly close to the Earth's surface. If you fly far into outer space, they become inaccurate. Then you'll need to use
W(at distance r from Earth's center) = W(surface)*SQR(R/r).
This last formula is valid everywhere, so long as you don't go really far away, like to the moon. For the atmosphere calculations, the first 2 formulas are fairly accurate.

At the top of the troposphere (10mi), your weight has decreased by only 0.5%, so it's 99.5lb.
At the top of the stratosphere (30mi), near the ozone layer, your weight is about 98.5lb.
At the top of the mesosphere (55mi), it's about 97lb.
At the top of the ionosphere (400mi, this is above the auroras) it's about 82.5lb.
And at the outer edge of the exosphere (800mi, you'll notice the temperature rising during this last part of your journey) it is about 70lb.