There is no atmosphere on the surface of the moon because
Escape velocity of gas molecules is less than rms velocity
The Moon’s escape velocity is smaller than the typical speed of gas molecules, so any atmosphere leaks away — option 2.
The two speeds that decide the matter.
| Quantity | Formula | Depends on |
|---|---|---|
| Escape velocity | \(v_{e}=\sqrt{\dfrac{2GM}{R}}\) | The body’s mass and radius |
| Root-mean-square molecular speed | \(v_{rms}=\sqrt{\dfrac{3RT}{M}}\) | Temperature and molecular mass |
A body retains a gas only if its escape velocity is comfortably greater than the molecular speeds — in practice several times greater, because the Maxwell distribution always has a fast tail, and over billions of years even a small leak empties the atmosphere.
The numbers.
| Body | Escape velocity | Atmosphere ? |
|---|---|---|
| Earth | 11·2 km/s | Yes — retains nitrogen and oxygen, but has lost most of its hydrogen and helium, the lightest and fastest molecules |
| Moon | About 2·4 km/s | No — only a trace exosphere |
| Jupiter | About 60 km/s | Yes — retains even hydrogen and helium |
Why the Moon fails the test. Its mass is about one-eightieth of the Earth’s, so its gravity is weak; and with no atmosphere to moderate it, the surface reaches roughly 120 °C in sunlight, which raises molecular speeds further. Weak gravity and high daytime temperature together mean that gas molecules routinely exceed 2·4 km/s and are lost.
Why the other options fail. Distance from the Earth, option 1, is irrelevant — Titan is far further from the Sun than the Moon and, being cold, holds a dense nitrogen atmosphere despite modest gravity. Revolving around a planet does not strip a gas envelope; again Titan is the counter-example. And receiving sunlight is true of every body in the solar system.
The consequences on the Moon : no sound, no weather, no scattering of light, so the sky is black even in daylight; extreme temperature swings between day and night; and no protection from micrometeorites or cosmic radiation.
Hence, the answer is escape velocity of gas molecules is less than rms velocity.
Important Questions from Gravity
Which of the following statement is correct?
I. Gravitation is a weak force unless large masses are involved.
II. The weight is equal to the product of mass and acceleration due to gravity.
What is the reason that the value of g (acceleration due to gravity) becomes greater at the poles than at the equator?
If the acceleration due to gravity on the surface of earth is g, then the acceleration due to gravity on the surface of a planet whose mass is same as that of earth and radius is twice as that of earth is ___________.
A man's mass is 72 kg on the earth. His mass on the moon will be:
At which of the following place, weight of an object is maximum?
