# Question 2f088

Dec 1, 2017

Gravity is actually equally effective on ALL masses. It is the relatively low mass of gases compared to liquids and solids that makes the effect seem less.

#### Explanation:

Remember, ALL of the planets and stars were condensed ultimately from the gravitational attraction of GASEOUS molecules!

The maintenance of the atmosphere (though it is thin in comparison to other geological features) necessary for life on earth is the result of the gravitational effect on gases.

The "gas giant" planets are much larger than the earth, yet are primarily (totally?) big balls of GAS! And they exert their own considerable gravitational effect in the solar system.

Dec 1, 2017

But it's NOT negligible! (see explanation)

#### Explanation:

...gravity keeps our atmosphere bound to the earth. All those smaller bodies in our solar system with no atmosphere, such as our own moon? Their gravity was not enough to restrain gas molecules from escaping to space.

...gravity explains hot air balloons, zeppelins, and the flames and rising smoke from fire. Heavier gasses tend to be pulled downwards, displacing lighter gases and forcing them upwards.

Now, truly enough, the force of gravity acting on individual molecules is very slight. Not exactly negligible, but slight.

Aggregate enough of them, though, and the total force acting on the aggregate is quite considerable.

From Wikipedia: "...On average, a column of air one square centimetre [cm2] (0.16 sq in) in cross-section, measured from sea level to the top of the Earth's atmosphere, has a mass of about 1.03 kilograms (2.3 lb) and weight of about 10.1 newtons (2.3 lbf)."

...the mass of this column of air is an intrinsic property, but the weight is an effect caused solely by gravity.

GOOD LUCK!

Dec 1, 2017

It is NOT! Gravity is the reason why atmospheric gases have not escaped to outer space. Earth's atmosphere is nothing but gases that are gravitationally bound to Earth's surface. What we feel as atmospheric pressure is the weight of the gas column.

#### Explanation:

I can understand why someone could think gases are not affected by gravity, the way solids/liquids are. We see rain drops falling but have not experience "gas rains".

That is because solids and liquids are more dense and so are more strongly influenced by gravity than gases. If you are inside water, you may see (some) solids drop, influenced by gravity, while the water itself seem "unaffected" by gravity. But it is not that water is unaffected by gravity. It is less affected compared to a sinking solid. If you release a air bubble inside water it appears to ascend by the action of a buoyant force. But that buoyant force is nothing but gravity induced pressure difference in water. The buoyant force is more of water trying to occupy the space of that air bubble, to minimise the gravitational potential energy of the system.

If we consider same volume of solid/liquid and gas, gas has lower gravitational potential energy than solid/gas. So solid/gas appear to "fall down". This is true even for gases. If you drop a blob of denser gas in air, you will see it "falling down". This stratification (gas-liquid-solid) based on density is pure gravity induced fluid-statics.

Dec 1, 2017

Let us put some numbers to see why gases are strongly influenced by gravity.

#### Explanation:

Gravity is considered to have negligible influence on an object only if its gravitational potential energy is minuscule compared to its kinetic energy due to other forces acting it.

Let us take Nitrogen molecules (${N}_{2}$), the most abundant atmospheric gas, as an example and calculate its gravitational potential energy (${U}_{g}$) and thermal kinetic energy (${E}_{k}$) at ${27}^{0} C$ and compare.

|U_g| = 2.91\times10^{-15} J; \qquad E_k = 9.42\times10^{-21} J;

$\frac{| {U}_{g} |}{E} _ k \setminus \approx 3.0 \setminus \times {10}^{5}$

These values show that the gravitational potential energy of gas molecules are at least 5 orders of magnitude (100, 000 times) higher than the thermal kinetic energies. That is the reason why they are bound to Earth. If not, they would have escaped to space long ago.

NOTE: Potential Energy and Kinetic Energy Calculation details are given below -

Gravitational Potential Energy: The gravitational potential energy of a Nitrogen molecule in atmosphere is given by -

$| {U}_{g} | = \frac{G {M}_{\setminus \oplus} {m}_{{N}_{2}}}{R} _ \left\{\setminus \oplus\right\}$, where ${M}_{\setminus \oplus}$ and ${R}_{\setminus \oplus}$ are the mass and radius of the Earth and ${m}_{{N}_{2}}$ is the mass of a nitrogen molecule.

$| {U}_{g} | = 2.91 \setminus \times {10}^{- 15} J$

G = 6.67408\times10^{-11}\quad (N.m^2)/(kg^{2});
${m}_{{N}_{2}} = {M}_{{N}_{2}} / {N}_{A} = 4.65 \setminus \times {10}^{- 26} k g$
M_{\oplus} = 5.972\times10^{24} kg; \qquad R_{\oplus} = 6.371\times10^{3} m;
M_{N_2} = 28.02\times10^{-3}\quad (kg)/(mol);\qquad N_A = 6.023\times10^{23}\quad (mol)^{-1},
where ${M}_{{N}_{2}}$ is the molar mass of ${N}_{2}$ molecules and ${N}_{A}$ is the Avagadro Number.

Thermal Kinetic Energy: The thermal kinetic energies of diatomic molecules like Nitrogen is ${E}_{k} = \frac{5}{2} {k}_{B} T$.

k_B = 1.3806\times10^{-23}\quad J.K^{-1}; \qquad T = 300K#

At a temperature of ${27}^{0} C = 300 K$, this gives a kinetic energy of $4.14 \setminus \times {10}^{- 21} \setminus \quad J$.