How to find out if a planet can have a atmostsphere

[leonne]

Homework Statement

Need to figure out if a planet can have a hydrogen atmosphere

Homework Equations

ves=(2GM/R)^.5

Vrms=(3kt/m)^.5

The Attempt at a Solution

Ok so I would first find the escape velocity of the planet, than find the velocity of the molecule. I am given the mas of planet radius and the temperature.
I would just use ves to find escape velocity, but not sure about the hydrogen particles.
Would i just use Vrms? what would m =? for nitrogen its 28mp mp= mass of proton, but no idea where the 28 comes from.
also in my notes says
Tesc=1/54 (GMm/kR) than they do it for nitrogen on Earth and get 3900k and than does it for the moon and gets 175 k and says this is why Earth has a atmosphere and moon doesn't, but does not really explain wht the numbers mean. I know its temperature but how would i know if there is a atmosphere or not.
thanks

 

[revnaknuma]

I think it does not have such a simple solution.

 

[Claude Bile]

In order for a planet to retain gases, the escape velocity of the planet must exceed the rms velocity of the gas.

Would i just use Vrms? what would m =? for nitrogen its 28mp mp= mass of proton, but no idea where the 28 comes from.

m would be the mass of the particle. The 28 comes from the number of nucleons present in the atom. Thus for a Hydrogen atom, m would be approximately equal to the mass of the proton, since there is only one nucleon present.

Tesc=1/54 (GMm/kR) than they do it for nitrogen on Earth and get 3900k and than does it for the moon and gets 175 k and says this is why Earth has a atmosphere and moon doesn't, but does not really explain wht the numbers mean. I know its temperature but how would i know if there is a atmosphere or not.

I think the point they are getting to is that Earth has an atmosphere, because its escape velocity is larger than that of Nitrogens rms velocity, while the moon does not because its escape velocity is less than Nitrogens rms velocity.

Claude.

 

[leonne]

yeah figured it out thxs

 

[paranormal]

To determine if a planet can have a hydrogen atmosphere, we need to consider several factors such as the planet's mass, radius, temperature, and the properties of hydrogen molecules.

First, we can use the escape velocity equation (ves=(2GM/R)^0.5) to calculate the minimum speed at which a molecule needs to travel in order to escape the planet's gravitational pull. This will give us an idea of the planet's ability to retain an atmosphere. If the escape velocity is too low, the planet may not be able to hold on to gases and therefore may not have an atmosphere.

Next, we need to consider the average velocity of hydrogen molecules in the planet's atmosphere, which can be calculated using the root mean square velocity equation (Vrms=(3kT/m)^0.5). Here, m represents the mass of the hydrogen molecule, which is equal to 2 times the mass of a single proton (mp). This equation will give us an idea of the average speed of hydrogen molecules in the planet's atmosphere.

We can then compare the escape velocity and the average velocity of hydrogen molecules to determine if the planet can retain a hydrogen atmosphere. If the escape velocity is greater than the average velocity of hydrogen molecules, then the planet may be able to hold onto a hydrogen atmosphere. However, if the average velocity of hydrogen molecules is greater than the escape velocity, then the planet may not be able to retain a hydrogen atmosphere.

In addition to these calculations, we also need to consider the temperature of the planet. If the temperature is too high, it may cause hydrogen molecules to move at a higher speed, making it easier for them to escape the planet's gravitational pull. On the other hand, if the temperature is too low, it may cause hydrogen molecules to move at a slower speed, making it easier for the planet to retain a hydrogen atmosphere.

The values of 3900k and 175k that were mentioned in your notes are the temperatures at which the escape velocity and average velocity of nitrogen molecules on Earth and the moon are equal, respectively. This means that at these temperatures, the Earth can retain a nitrogen atmosphere, while the moon cannot. This further emphasizes the importance of considering the temperature when determining if a planet can have an atmosphere.

In conclusion, to determine if a planet can have a hydrogen atmosphere, we need to consider the planet's mass, radius, temperature, and the properties of hydrogen molecules. By comparing the escape velocity and average velocity of hydrogen