QUESTION #111

# Do we weigh more at Death Valley than on top of Mount Everest and if we do would it be from gravity or from atmospheric pressure?

Asked by: Larry Knisley

### Answer

Our weight is defined as the force that we exert due to our mass. This force is equal to GMm/r2, where G is a constant, M is the mass of the earth, m is your mass and r is the distance between the center of the earth and you. As you are nearer to the center of the Earth in death valley r will be smaller thus making the force larger, so you would weigh more in Death Valley than on Mount Everest. However the difference is so small that it cannot be measured easily. Atmospheric pressure will not affect your weight. The atmospheric pressure will be greater in Death Valley however, as the air is more dense there than on top of Mount Everest.
Answered by: Sara Al-Assam, Student, Tiffin Girls' School

I agree with the formula above, but there is one dangerous simplification made here.

According to the above statement, the gravity towards the centre of the earth would increase all the way to the very middle of our planet, to reach infinity as r -> 0.

In reality, the gravitational force would instead decrease successively, as more and more of the mass of the earth would be outside a sphere of radius r with its centre at the earth's centre. This mass has a zero contribution to the gravitational force that you are subjected to. At sea level, most of the earth's material is still included in the above mentioned sphere, which means that you weigh more there than on the top of Mount Everest, but as we go down to the centre of the earth, there will be a point where you will weigh exactly as much as on the mountain top. The formula is easily derived by making assumptions about the mass density of the earth.
Answered by: Anders H'gglund, M. Sc. Mechanical Engineering, G'teborg, Sweden