# Assertion when assuming g = 9.8 or 10

1. Oct 7, 2009

### dE_logics

1) g is not a function of height...or till what hight above the earth's surface can it be considered as...roughly true?

2) aaa....that's about it I guess...but wont it matter with the depth of the sea...I mean we assume pressure as ρgh...but with great depths like of the pacific...it will matter I guess; so the pressure of a the water column equal to the depth of the sea will be less than ρgh (I don't know how does does this formula come actually).

Same can be said about the air column.

2. Oct 8, 2009

### Staff: Mentor

It depends on how much accuracy you need. Calculate

$$g = \frac {GM_{earth}} {r^2} = \frac {GM_{earth}} {(R_{earth} + h)^2}$$

for various values of h to get a feeling for how much g changes with h.

3. Oct 8, 2009

### dE_logics

I was basically asking if I was right about what I said...was I right?

4. Oct 8, 2009

### Pengwuino

The gravitational acceleration, g, does not depend on whether you're in the ocean or on land. It simply is a function of the height approximately.

5. Oct 8, 2009

### D H

Staff Emeritus
That's not the question at hand. The question is how much gravity varies with altitude above land (or water) versus how much gravity varies with depth below water.

To first order, the answer to the first question, gravity as a function of altitude, is given by the free air correction. Gravity decreases about 3.086 µm/s2 for every meter of altitude above the surface, or 0.3086 mGal/m (a galileo (Gal) is 1 cm/s2, so an milligal (mGal) is 10 µm/s2).

The answer to the second question, gravity as a function of depth, is given by the free air correction plus a double Bouguer correction. For sea water, density = 1.03 g/cc, this means gravity increases by 0.2222 mGal for every meter of depth.

All in all, pretty dang small.

6. Oct 8, 2009

### Pengwuino

Ah, ok, I could hardly make heads or tails of the question so I just took a shot in the dark haha

7. Oct 8, 2009

### dE_logics

I was wondering gravity would not be the function of density of the fluid if you're not considering the gravitational field of the fluid itself.