# Is it possible to calculate earth's massiveness

Hi everybody ,

This is the first time i am posting on this forum.

A couple of days back i was having a conversation with a religious person who went on telling that the position of earth and gravity is so perfect that it was at right distance from sun and earth is massive enough that oxygen is present as gas in the atmosphere ... so i wondered how massive the earth should be that the atmosphere, under the influence of gravity compresses itself under its own weight such that oxygen is present as a liquid .... by calculating this we would know how much variation in earths mass is required for this to happen and hence determine whether this is divine plan or not.

Regards
Pankaj D

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Ummm. Your post is confusing. You should proofread what you write before posting. At least I am having a very hard time understanding what you are saying.
First, of course the earth is massive enough to have oxygen as a gas in the atmosphere, its what you are breathing.
I think you were asking how massive a planet must be to create liquid oxygen on the surface right?
Also i don't see what this has to do with God.

Ummm. Your post is confusing. You should proofread what you write before posting. At least I am having a very hard time understanding what you are saying.
First, of course the earth is massive enough to have oxygen as a gas in the atmosphere, its what you are breathing.
I think you were asking how massive a planet must be to create liquid oxygen on the surface right?
Also i don't see what this has to do with God.

Sorry for my style of delivery ... yes it was even confusing to me ... i guess what i was asking is how can we calculate .... the massiveness (the mass) of a planet so that ... it creates liquid oxygen on the surface.

It is related to a question that a religious person posed infront of me, he said that the gravity of earth is so right that we have gaseous oxygen in the atmosphere. other wise if it were little less earth would be incapable of holding the atmosphere and if it were to much, there would be no gaseous oxygen ... in his view it is gods divine plan ... so i thought about calculating how much variation in earths mass would create liquid oxygen ... to know how precise is the gods plan anyways. I hope u understand. Staff Emeritus
2021 Award
Whether oxygen liquifies is not so much a function of a planet's mass as its temperature.

So liquifiability of a gas is more relevant to temperature than pressure ... ?

If that is so do we have to consider distance of earth from sun to calculate the temperature variation that would be needed to account for oxygen's availability as a atmospheric gas ..?

Whether oxygen liquifies is not so much a function of a planet's mass as its temperature.

So liquifiability of a gas is more relevant to temperature than pressure ... ?

If that is so do we have to consider distance of earth from sun to calculate the temperature variation that would be needed to account for oxygen's availability as a atmospheric gas ..?

Ah ok I understand now. Thank you for clarifying. This is a very interesting problem.

I've been trying to find a phase diagram that shows what pressure would be required to liquify water at room temperature,but to no avail. I don't understand the way different phases work above the critical point enough.

However This I think is unnecessary. First, the boiling point of water is 90K at 1 Atmosphere of pressure. Seeing how we live at around 300-400K we can assume that the pressure would have to be a great deal of a lot more to liquify the water at these temperatures. I have found something that gives a more quantitative argument of this.

If you look at the diagram on the first page of this document,
http://iweb.tntech.edu/albu/teaching/CHEM3520-S04/HW06S.pdf

You can see that there is a crude phase space diagram made for oxygen. The point on the liquid gas line is the 90K boiling point. if we look at around 150K(around the critical point) the pressure required to keep the oxygen a liquid is approximately e^10 torr, or about 30 atmospheres. This means at about -130 degrees Celcius. there would have to be 30 times as much pressure as normal to liquify water. At higher temperatures i would imagine that this would become exponentially greater.

As i said before though my knowledge of materials above the critical point is minimal. I still feel my argument is valid to say that a quite a bit of extra mass on the earth would definitely not liquify oxygen.

As for the calculation of the mass required to do this, we would first need to find the pressure at room temperature where water liquefies.

the lower pressure of a smaller earth not being able to hold oxygen is a less extreme assumption than the liquid water thing. but i think it is definitely safe to say that the earth would have to lose quite a bit of mass before life was not possible. however if there were less oxygen, then life would have just evolved to deal with it (to a certain extreme of course).

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Your deduction is very thoughtful and interesting , from what i understand is that u are trying to say That at about 90K almost 30 times pressure would be required to keep oxygen as liquid. What i see form this link here http://hypertextbook.com/facts/2005/JudyTang.shtml is that average temperature of earth is 15 degree Celsius. At thermodynamic equilibrium it would be -18 celsius , so would it be safe to assume that even if earth was 30 times as massive, still it would be very tough to produce liquid oxygen on the surface untill the distance of earth from sun is so far (atleast 10 times farther) so that surface temperature of earth drops to around -130 celcius …only then can we expect oxygen on the surface ….?

To convert oxygen into water at atmospheric temperature 300 K, pressure required is 5 GPa or 5000 MPa. See link http://en.citizendium.org/images/thumb/b/bc/Oxygen_phase_diagram.png/250px-Oxygen_phase_diagram.png
Atmospheric pressure is 0.1 MPa. So, 50,000 times more pressure is required to convert oxygen into liquid. So it is required to increase the weight of vertical air column by 50,000 times. To increase the weight of air column, acceleration of gravity is required to increase 50,000 times more so, it is 9.81 * 50,000. To increase gravity acceleration g= G * M/R. G= universal gravity const. M & R are mass & radius of earth. Here we assume that as mass of earth increases there is no increase is radius, only increase in density of earth. So, mass of earth required 50,000 times more than exist now.
After this also only lower layer of air undergo this much higher pressure & so oxygen is converted into liquid. Above this layer weight of air column is decreases & so air pressure is also decreases so oxygen on layer above not converted into liquid.
Here we take only atmospheric pressure is equal to oxygen pressure but it is required to take partial pressure of oxygen into consideration. Oxygen present into air is 21% say fifth part of all gases. So partial pressure of oxygen is fifth part of 0.1 MPa. So, to convert it into liquid five times more pressure & so five time more gravity acceleration & so mass required. So, mass of earth required 50,000 * 5=2,50,000 times more.
If, we take earth of only mass of 50,000 times more, than also if liquid oxygen put in open atmosphere, it is not converted into gas immediately, because only top layer of liquid oxygen undergo partial pressure of oxygen (Fifth time of atmosphere) & so start converted into gas. But the layer below this undergo pressure of oxygen is equal to atmosphere pressure because it is surrounded by liquid oxygen, so it remain liquid.

To convert oxygen into water at atmospheric temperature 300 K, pressure required is 5 GPa or 5000 MPa. See link http://en.citizendium.org/images/thumb/b/bc/Oxygen_phase_diagram.png/250px-Oxygen_phase_diagram.png
Atmospheric pressure is 0.1 MPa.

Here Oxygen conversion takes place at 300K which is roughly 30 degree Celsius or room temperature. The answer is complete, except i have one doubt that we dont take temperature into consideration.

The earth is able to hold heat in the atmosphere due to green house effect .... what would happen if we were so far away from sun that the average temperature drops .

Now lets assume that if earth were not 50000*5 times massive and let alone temperature play the equation would it be possible to achieve liquid oxygen on the surface by only decreasing the temperature and not changing the pressure at all, because as you observed that partial pressure of liquid oxygen below the top layer in liquid oxygen is equal to atmospheric pressure or 5 times partial pressure.

And If so .. how far fro sun do we have to be observe this phenomenon.

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It's a combination of different factors, gravity/mass, distance from sun/temperature, atmosphere, external gravitational forces etc.

Your friend has probably half understood some version of the 'goldilocks' theory where hundreds of coincidences make our existance possible, everything is 'just right' exactly.

An argument against that is that there are countless billions of solar systems, and the one we are part of is by definition the one able to support life.

There is a deeper argument on the nature of quantum physics, on the nature of consciousness, on the nature of the big bang, and on the magic of the symetry of equations.

Your friend means well, he is trying to bring you closer to heaven, but his science is poor.

I'm gonna feed this debate, and maybe provide a stronger argument to counter your religious acquaintance.

Consider the moon of Saturn, Enceladus (don't know it-- Wikipedia it. It was in a recent Scientific American). It is clearly very far from the sun. It is much smaller than the earth.

And it has water.

How? It's made out of the right material, and a tidal force caused by the eccentricity of its orbit makes it generate heat. There are clearly many circumstances in which water can arise.

Granted, Enceladus' situation is rather unique--one of Saturn's other moons is "pulling it along" in their synchronized orbits. Still, my point stands, that there are many situations in which we can have liquid water, and so to think that the only variables involved are mass and distance from a star, is narrow-minded. Plaster is absolutely right: there are many other variables involved, and the earth, while albeit it is still unique to our knowledge, our discoveries are making it seem less and less unique every day.

--Jake

DaveC426913
Gold Member
If Earth were too distant and cold for God to put people on it, he'd have just put them on Venus instead, where it's warmer.

Just like if Mars were too distant and cold for God to put people on it, he'd have just put them on Earth instead... oh wait, he did.

Here Oxygen conversion takes place at 300K which is roughly 30 degree Celsius or room temperature. The answer is complete, except i have one doubt that we dont take temperature into consideration.

The earth is able to hold heat in the atmosphere due to green house effect .... what would happen if we were so far away from sun that the average temperature drops .

Now lets assume that if earth were not 50000*5 times massive and let alone temperature play the equation would it be possible to achieve liquid oxygen on the surface by only decreasing the temperature and not changing the pressure at all, because as you observed that partial pressure of liquid oxygen below the top layer in liquid oxygen is equal to atmospheric pressure or 5 times partial pressure.

And If so .. how far fro sun do we have to be observe this phenomenon.

if we were so far away from sun that the average earth temperature drops & as it attain 90 K, oxygen start to liquefy, as 90 K is boiling temp. of oxygen at atm. Pressure.
To calculate distance so many assumptions are required.
Take only sun as a source of energy for earth, no other source. Take earth has constant specific heat.
Average temperature of empty space is 3 K. May be average temperature of empty space in the galaxy may by different & higher than 3 K. So If sun is not exist the temp. of earth comes down to 3 K But for simplicity take it as 0 K.
Average temp. of earth is 13 C, 286 K.
Sun gives some energy Q & increase temp. of earth 286 K. To increase temp. of earth to temp. 90 K only (90/286) * Q energy is required. It is required energy from sun to earth decreases to (286/90)=3.1777th part.
If distance increased to double, radiation energy decreased to fourth part (Inverse square law).
So, If we want to decrease sun energy to 3.1777th part, the distance required to increase by
sqrt. of 3.1777=1.7824.
So, minimum earth distance required from sun to attain temp. below 90 K is
149 million km * 1.7824= 265 million km

if we were so far away from sun that the average earth temperature drop…….
sqrt. of 3.1777=1.7824.
So, minimum earth distance required from sun to attain temp. below 90 K is
149 million km * 1.7824= 265 million km

Thanks Suhag u are amazing …..

I'm gonna feed this debate, and maybe provide a stronger argument to counter your religious acquaintance.

Consider the moon of Saturn, Enceladus (don't know it-- Wikipedia it. It was in a recent Scientific American). It is clearly very far from the sun. It is much smaller than the earth.

And it has water.

How? It's made out of the right material, and a tidal force caused by the eccentricity of its orbit makes it generate heat. There are clearly many circumstances in which water can arise.

Granted, Enceladus' situation is rather unique--one of Saturn's other moons is "pulling it along" in their synchronized orbits. Still, my point stands, that there are many situations in which we can have liquid water, and so to think that the only variables involved are mass and distance from a star, is narrow-minded. Plaster is absolutely right: there are many other variables involved, and the earth, while albeit it is still unique to our knowledge, our discoveries are making it seem less and less unique every day.

--Jake

Thanks Mazerkham got some ore material to counter the religious fanatic ….