tomlib said:
I would say that the force of the vacuum is greater than the force of gravity.
The two do not have the same units. So neither is greater than the other.
The "force of gravity" is in units of force per unit mass. For example, 9.8 Newtons per kilogram. The "force of vacuum" is in units of force per unit area. For example, 100 kiloNewtons per square meter.
If you want to compare the two to one another, you will have to somehow figure out how many kilograms of atmosphere there is in a square column that is 1 meter on each side and is as tall as the atmosphere.
An overly simplistic calculation would assume an atmosphere which has constant density from top to bottom. Let us attempt such a calculation.
Room temperature air at ordinary atmospheric pressure is about 1.293 kilograms per cubic meter. The atmosphere is, let's say, 100 kilometers in height. Our square tower has a volume of 1x1x100000 = 100000 cubic meters. So that is 129300 kilograms. Multiply by the acceleration of gravity (9.8 Newtons per kilogram) and that's roughly 1.3 million Newtons.
The "force of gravity" on one square meter calculated this way is 1.3 million Newtons.
The "force of vacuum" on one square meter is only about one hundred thousand Newtons.
Calculated this way, the "force of gravity" is way larger than the "force of vacuum". Contrary to your supposition.
But of course, the above calculation is wrong, wrong, wrong. Atmospheric pressure decreases as you go up in elevation.
Wikipedia goes fairly deep into the details. To a decent approximation, there is an exponential decrease in density with altitude. The constant on the exponential is about 8.4 km for a factor of e (Euler's number, base for natural logs, 2.71828...) reduction.
As a rough rule of thumb, this means that the actual amount of atmosphere over any point on the earth is equivalent to a tower of normal pressure air that is 8.4 km in height. Yes, the same 8.4 km as above -- natural logs are nice for this kind of thing.
Let us do that calculation again. 1.293 kg per cubic meter times 8.4 km height times 9.8 N/kg is roughly 101000 N / m^2 for the "force of gravity"
Conclusion: The force of gravity and the force of vacuum are indeed identical. As they must be according to the mainstream understanding of an atmosphere in static equilibrium under gravity.
Edit: Here is the source for the 8.4 km figure:
https://en.wikipedia.org/wiki/Density_of_air#Variation_with_altitude said:
The pressure can be approximated by another exponent:
[...]
[...]
H
p is 8.4 km,
##H_p## is the inverse of the ##\frac{gM}{RT_0}## in the formula above.