# As you move higher on earth do you weigh more?

• Peter Pan

#### Peter Pan

My question is this…

As you move higher on Earth do you weigh more? I thought of this floating in a pool. The pressure around by body caused by the water allowed me to float? Air pressure is high at low altitudes and decreases as you go up.

So, do you weigh more standing on a mountain than at sea level?

Thank you
Pan

Last edited by a moderator:

## Answers and Replies

Just the opposite, you weigh less at higher elevations. You are further from the Earth's center thus the laws of gravity come into effect. Any bouyancy effect due to the atmosphere is also reduced due to the thinner atmosphere, your body maintains the same volumn but at higer elevation, due to the reduced density of the air you displace less air, thus once angain weigh a bit more then at the bottom of the atmosphere.

Both of these effects are so small that it is nearly impossible to measure them, unless you are in orbit.

so, gravity being less, causing you to weigh less and a lower air pressure causing you to weigh more cancel each other out

Air is about 1/1000 the density of the human body. So the buoyant force on a person is about 1/1000 their weight, or just a few ounces.

If you go to the altitude where a jet flies (10,000m), the air is half as dense, so you lose half the buoyant force, which means you gain 1/2000 of your weight.

The Earth's radius is 6400km, so the loss in weight due to gravity change at 10km alt. is 2*10/6400 (the 2 comes from the fact that r comes into the force formula as a square).

This is 1/320, or 6 times more than the weight gain from loss of buoyancy. So Integral is right: the dominant effect is the gravitation dependence on distance from Earth's centre.

Can you post the bouyancy equations that you are referring to? It may be just a difference in the defination of "weight" but I've always thought of weight as mass*gravity. The other bouyancy forces would just be external forces and not truly affect the "weight"

Yes there are differing definitions of weight and I was sloppy: I simply used Peter Pan's definition, which appears to be the net downward force (gravity minus buoyancy). To be more precise, let weight be defined as the gravitational part alone. Then

Net force = Weight - Buoyant force = m g - m_air g

where m_air is the mass of the air displaced by the body. And of course g varies with distance h above the earth:

g = MG/(r+h)^2

HTH

I know that the topic isn't the definition of weight, but I believe it is mass*gravity. By peter Pan's definition(not saying he didn't know the right deffinition), Buoyant forces are included in the measurement of weight. This is certaintly true in practical measures of weight like scales, but buoyant forces are not really completely defineable, since it is hard to distinguish between say movement caused by buoyancy and movement caused by a sudden gust of wind. For instance, what if you jumped? would your weight momentarily be negative for some time? Although this is not bouyant forces acting, how can you distinguish between the two?

Although peter pan's definition could be true when applied to somthing like "the force towards an astronomic object with atmosphere"

Doh! appears Krab already clarified this[/edit]

Last edited: