Earth - What is the real age?

[John Cuthber]

"If we do it correctly, we will be able to extract the real cooling time!"

May be, maybe not.

How do you plan to account for the heat produced by radioactive decay?

In particular, how do you plan to estimat , for example, the mass of uranium in the earth's core?

It's not as if anyone has been there to check.

[swansont]

 

So, let's go back to Radiative Cooling Time:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html#c1

P = dE/dt = ε·σ·A·(T(hot)⁴ –T(ambient)⁴)

Here P is the power emitted from the area, and E is the energy contained by the object.

However, we must add to this formula the contribution of the Sun radiation as well as the effect of real surface.

Therefore:

E(updated total energy) = E(energy contained by the object) + E(energy from the sun)

Hence:

P(updated) = dE(updated total energy)/dt =dE(energy contained by the object)/dt + dE(energy from the sun)/dt

If we do it correctly, we will be able to extract the real cooling time!

 

Run the numbers. How much power do we get from the sun vs the radiated power at, say, 1000K?

[David Levy]

 

Run the numbers. How much power do we get from the sun vs the radiated power at, say, 1000K?

 

Well it's not straight forward.

Hence, let me explain how we should solve this issue:

 

-Earth phases: Verify the four main phases of the planet.

-Emissivity: Verify emissivity at each phase.

-Solar Radiation: Verify the sun radiation at each phase

-Formula: Use the correct formulas for each phase as needed.

-Cooling time: Extract the requested cooling time for each phase of the Earth.

 

Earth phases

Phase one – Full melting Planet, from its first day till setting the crust all over the surface. During this phase, the Expected temperature on the surface should decrease from about 6,000K (or above) to about 1,000K (lava curst temp)

Phase two – Hot Planet, from getting the crust till sustaining the first drop of water. During this phase, the Expected temperature on the surface should decrease from about 1,000K to about 373K (100 c)

Phase three – Wet Planet, from getting the first drop of water till having the first sign of life. During this phase, the expected temperature should decrease from 373K to 318K (45 c)

Phase four – Habitable Planet, from having the first sign of life till today.

 

Emissivity

The thermal emissivity range of an object is (0 ≤ ϵ ≤ 1 ). A theoretical blackbody has ϵ = 1.0. However, due to the greenhouse effect the Earth is considered as a gray body.

We need to verify the emissivity of Earth for each phase.

Solar Radiation

http://nptel.ac.in/courses/112108149/pdf/M9/Student_Slides_M9.pdf

"The magnitude of the energy leaving the Sun varies with time and is closely associated with such factors as solar flares and sunspots. Nevertheless, we often choose to work with an average value. The energy leaving the sun is emitted outward in all directions so that at any particular distance from the Sun we may imagine the energy being dispersed over an imaginary spherical area. Because this area increases with the distance squared, the solar flux also decreases with the distance squared. At the average distance between Earth and Sun this heat flux is 1353 W/m2."

However, we need to verify the emissivity effect "A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity ϵ <1".

Therefore, it is needed to verify the real impact of this sun radiation on Earth. We also need to take in account that the sun is drifting outwards from the Earth (by about 1.5 cm per year). Hence, it could potentially increase the impact on Earth as we go back on time.

More to come.

Edited April 4, 2015 by David Levy

[swansont]

Well it's not straight forward.

The question I asked is.

[David Levy]

O.K.

Let's start by extracting the emissivity during the habitable planet phase of time. This value should cover the effects of the solar radiation and atmosphere factors.

During this phase of time the planet had been cooled down to the current temperature – 300K.

It is known that life on Earth had started about 3.5 By ago. Unfortunately, there is no clear evidence about the temperature on Earth at that time. Therefore, let's assume that in the worst case scenario the temperature at that time was 318K (which is 45 c).

Hence: t(cooling) = 3.5 By, T(final) = 300K, T(hot) = 318

Based on that info, we will use Stefan-Boltzmann law to extract the Emissivity of the Earth (for a gray body).

The t(cooling) time formula is as follow:

t(cooling) = Nk · (1/T(final)³ – 1/T(hot)³)/(2·ε·σ·A)

Hence:

t(cooling) · ε = Nk·(1/T(final)³ – 1/T(hot)³)/(2·σ·A)

We also know that for black body (ε=1) at T(final) of 300K the t(cooling) is 30 My.

Therefore, by the following extrapolation we can find the emissivity for the habitable planet phase.

So,

3.5 By · ε = 30 My · 300³ · (1/300³ – 1/318³)

3.5 · 10⁹ · ε = 30 · 10⁶ · 27 · 10⁶ · 5.94· 10^-9

3.5 · 10⁹ · ε = 4,811 · 10³ = 4.811 · 10⁶

ε = 4.811 · 10⁶ · / (3.5 · 10⁹) = 1.375 · 10^-3

Let's assume that this emissivity is applicable also for the wet planet phase.

In this phase of time the planet had been cooled down from 373K to 318K.

t(cooling) · ε = 30 My · 300³ · (1/318³ – 1/373³)

t(cooling) = 30 My · 27 · 10⁶ · 1.1827 · 10^-8 / ε

t(cooling) = 30 My · 27 · 10⁶ · 1.1827 · 10^-8 / (1.375 · 10^-3)

t(cooling) = 6.967 By

Hence, base on our worst case scenario the minimum requested cooling time for the wet planet phase time is 6.967 By.

Therefore, the total cooling time from 373K (100 c) to current time is:

t(cooling from 100 c till today) = t(cooling from 100 c till 45 c) + t(cooling from 45 c till today)

t(cooling from 100 c till today) = 3.5 + 6.967 = 10.467 By.

Please be aware that if 3.5 By ago, the temperature was lower than 45 c then it should decrease the value of the emissivity and therefore it could increase the requested time for the wet planet phase.

Let's set a brief calculation for 308K, which is 35 c

3.5 By · ε = 30 My · 300³ · (1/300³ – 1/308³)

3.5 · 10⁹ · ε = 30 · 10⁶ · 27 · 10⁶ · 2.812 · 10^-9

3.5 · 10⁹ · ε = 2.812 · 10⁶

ε = 2.812 · 10^-6 · 10^-9 / 3.5 = 0.803 · 10^-3

t(cooling) · ε = 30 My · 300³ · (1/308³ – 1/373³)

t(cooling) = 30 My · 27 · 10⁶ · 1.495 · 10^-8 / ε

t(cooling) = 30 My · 27 · 10⁶ · 1.1827 · 10^-8 / (0.803 · 10^-3)

t(cooling) = 11.930 Gy

Therefore, in this scenario, the total cooling time from 373K (100 c) to current time is:

3.5 + 11.93 By = 15.43 By.

Now we need to add the requested cooling time for phase one and two.

Edited April 4, 2015 by David Levy

[imatfaal]

David - your 'T's and 't's are getting mixed up. And surely Stefan Boltzman is based upon watts, Kelvin and metres; so wouldn't your answer be in seconds? But rechecking the way you are doing the sums it doesn't really matter - you have (inadvertently?) taken the conversion into your epsilon.

 

Are you going to continue to ignore all the people who are trying to help you? It's simple - you either start listening to arguments and actually taking notice or we decide this is soap-boxing rather than a discussion. By the way in your use of the cooling during the period of life on earth to calculate the emissivity where have you taken account of the Big Yellow Star in the Sky?

[David Levy]

David - your 'T's and 't's are getting mixed up. And surely Stefan Boltzman is based upon watts, Kelvin and metres; so wouldn't your answer be in seconds? But rechecking the way you are doing the sums it doesn't really matter - you have (inadvertently?) taken the conversion into your epsilon.

 

Are you going to continue to ignore all the people who are trying to help you? It's simple - you either start listening to arguments and actually taking notice or we decide this is soap-boxing rather than a discussion. By the way in your use of the cooling during the period of life on earth to calculate the emissivity where have you taken account of the Big Yellow Star in the Sky?

 

Thanks for the remarks about the T and t. I have fixed it.

I'm using Stefan-Boltzmann law correctly. There is no error in my calculation. Stefan-Boltzmann can be proud of using their formula as it should be. If there is any error in this calculation, please do not hesitate to inform. Stefan-Boltzmann law specifically covers a gray body star. Unfortunately, the science had decided to ignore completely that yellow star in the sky. Therefore, the emissivity had been set to one. That is the biggest mistake of the modern science. As I have already stated, a black body planet means – that the planet had been set outside the solar system, in full darkness, without any green house effect or atmosphere protection. This is a great mistake. There is no possibility to assume that in the first 30 My of the Earth life, it had been set at this unrealistic conditions – black body. But just after cooling down to the current temperature, the Earth had been set back to the solar system and starts to work as gray body.

Please look again at this calculation. You also should be proud of it.

This discovery is a breakthrough. The science should consider a Novel price. Not for me, but for this forum and all the members that participated in this thread.

Edited April 4, 2015 by David Levy

[imatfaal]

 

Thanks for the remarks about the T and t. I have fixed it.

I'm using Stefan-Boltzmann law correctly. There is no error in my calculation. Stefan-Boltzmann can be proud of using their formula as it should be. If you think that there is any error in this calculation, please do not hesitate to inform. Stefan-Boltzmann law specifically covers a gray body star. Unfortunately, the science had decided to ignore completely that yellow star in the sky. Therefore, the emissivity had been set to one. That is the biggest mistake of the modern science. As I have already stated, a black body planet means – that the planet had been set outside the solar system, in full darkness, without any green house effect or atmosphere protection. This is a great mistake. There is no possibility to assume that in the first 30 My of the Earth life, it had been set at this unrealistic conditions – black body. But just after cooling down to the current temperature, the Earth had been set back to the solar system and starts to work as gray body.

Please look again at this calculation. You also should be proud of it.

This discovery is a breakthrough. The science should consider a Novel price. Not for me, but for this forum and all the members that participated in this thread.

 

No no no.

 

Take some time to read this thread through - your answers are all in here. You are talking complete and utter nonsense.

 

For starters take a read of ophiolite's post with good empirical evidence - even well balanced theory does not counter evidence let alone half-baked. You didn't even know about radiative power loss a few posts ago and now you have the cheek to proclaim a great scientific error.

[swansont]

There is no error in my calculation

 

It doesn't matter. Your calculation is nonsense. You have already been told why.

 

Are you going to answer my last question or not? (How much power do we get from the sun vs the radiated power at, say, 1000K?)

[Robittybob1]

 

It doesn't matter. Your calculation is nonsense. You have already been told why.

 

Are you going to answer my last question or not? (How much power do we get from the sun vs the radiated power at, say, 1000K?)

David - That would depend on the qualities of the atmosphere surely. Early atmosphere had methane and CO2 at high levels and both are greenhouse gases so it could even be balanced if the blanket of thick dense atmosphere absorbed as much heat as it allowed out.

Taking that to mean the surface was 1000 degrees. Venus has got a situation approaching this even today.

Edited April 5, 2015 by Robittybob1

[swansont]

David - That would depend on the qualities of the atmosphere surely. Early atmosphere had methane and CO2 at high levels and both are greenhouse gases so it could even be balanced if the blanket of thick dense atmosphere absorbed as much heat as it allowed out.

Taking that to mean the surface was 1000 degrees. Venus has got a situation approaching this even today.

 

Why are you quoting me but addressing David?

[Robittybob1]

 

Why are you quoting me but addressing David?

Giving him clues as to what to argue. That is allowed isn't it?

[David Levy]

 

It doesn't matter. Your calculation is nonsense. You have already been told why.

My calculation is 100% correct. I have already explained that it was a severe mistake to assume that the Earth is a black body. In all the articles it is stated that the Earth is a gray body due to the solar radiation and greenhouse effect. Therefore, it was great mistake to assume that in the first 30 My the Earth will be considered as black body while in the rest of 4.4 By it will become a gray body. So, there is no error in Stefan-boltzmann law. There is also no error in the formulas which the science is using. All of them are 100% correct. The error was in the assumption that the thermal emissivity for the earth could be same as for a theoretical blackbody ϵ = 1.0. The Earth was never ever a blackbody! I have just used the Stefan-Boltzmann formula correctly. The science must verify this critical issue. It is expected to forward this breakthrough discovery to all the relevant scientists. I'm quite sure that they will confirm it. We all must be proud of this discovery and in this forum.

 

 

Are you going to answer my last question or not? (How much power do we get from the sun vs the radiated power at, say, 1000K?)

 

Well, the title of this tread is: "Earth - What is the real age?". I have proved that by using correctly the formulas we can get the real answer, without digging in solar radiation and find its impact on the Earth at any specific temperature. However, if you wish, I will try to help with your request, although - it might take me some time to set it.

Edited April 5, 2015 by David Levy

[pavelcherepan]

Well, the title of this tread is: "Earth - What is the real age?". I have proved that by using correctly the formulas we can get the real answer, without digging in solar radiation and find its impact on the Earth at any specific temperature. However, if you wish, I will try to help with your request, although - it might take me some time to set it.

 

David, your "real answer" disagrees with geological evidence. Please explain how you plan to account for that?

[David Levy]

 

David, your "real answer" disagrees with geological evidence. Please explain how you plan to account for that?

 

There is no contradiction between this discovery and the geological evidences. Those evidences give us the min age of the Earth. There is good chance that in the future we will discover new evidence which will confirms that the age of the earth is significantly higher than our current expectation.

Don't forget that in the past people believed that the age of the Earth was only 5,000 years

Edited April 5, 2015 by David Levy

[pavelcherepan]

There is no contradiction between this discovery and the geological evidences. Those evidences give us the min age of the Earth. There is good chance that in the future we will discover new evidence which will confirms that the age of the earth is significantly higher than our current expectation.

 

What about meteorite dating? Those contradict with your calculations too.

[Mordred]

The Earth isn't older than the other bodies in our solar system. This includes the evidence gathered from the meteorites. I posted a paper on that subject a while back.

 

You've been given 9 pages worth of details.

 

Science doesn't base its answers solely on formulas. Though it is a major player. In this case we have means such as carbon dating etc.

 

The one link I provided constrains the age within 160,000 years. How did you miss that?

http://www.google.ca/url?sa=t&source=web&cd=4&ved=0CC0QFjAD&url=http%3A%2F%2Fwww.psrd.hawaii.edu%2FNov12%2FPSRD-ages-CAIs-chondrules.pdf&rct=j&q=The%20Absolute%20Chronology%20and%20Thermal%20Processing%20of%20Solids%20in%20the%20Solar%20Protoplanetary%20Disk&ei=k9kUVYWqDoS1ggTNv4HwDg&usg=AFQjCNG34qgwTUEwgU2wqhg6dHxg7LOkOQ&sig2=XKbP_XRYdR0sGjSxiIsLMw

[Robittybob1]

 

What about meteorite dating? Those contradict with your calculations too.

 

 

There is no contradiction between this discovery and the geological evidences. Those evidences give us the min age of the Earth. There is good chance that in the future we will discover new evidence which will confirms that the age of the earth is significantly higher than our current expectation.

Don't forget that in the past people believed that the age of the Earth was only 5,000 years

Out by how much?

[David Levy]

 

What about meteorite dating? Those contradict with your calculations too.

 

Meteorites are not part of the Earth itself. There is no need to explain the current dating of those Meteorites. In the future, we might find older dating meteorites. So what?

 

The Earth isn't older than the other bodies in our solar system. This includes the evidence gathered from the meteorites. I posted a paper on that subject a while back.

 

You've been given 9 pages worth of details.

 

Science doesn't base its answers solely on formulas. Though it is a major player. In this case we have means such as carbon dating etc.

 

 

The assumption that the Earth could be considered as a blackbody is a severe mistake.

However, the willing of the science to fit each evidence to the current concept is a fatal error.

Therefore, we all must verify every observation and get a conclusion of what we see.

Just after getting all the real evidences/observations/calculations we can set down and figure out the source of the Universe enigma.

 

 

 

We have to ask ourselves the following questions –

Do we agree that Stefan-Boltzmann law is correct formula?

Do we agree that the Earth is a graybody, and it should never ever consider as blackbody?

If the answer for both questions is yes, then there is no need for further evidences.

Edited April 5, 2015 by David Levy

[pavelcherepan]

 

Meteorites are not part of the Earth itself. There is no need to explain the current dating of those Meteorites. In the future, we might find older dating meteorites. So what?

 

 

 

The assumption that the Earth could be considered as a blackbody is a severe mistake.

However, the willing of the science to fit each evidence to the current concept is a fatal error.

Therefore, we all must verify every observation and get a conclusion of what we see.

Just after getting all the real evidences/observations/calculations we can set down and figure out the source of the Universe enigma.

 

Your attention to details and disregard of contradicting evidence is baffling.

 

Meteorites formed from the same nebula that formed the Earth and around the same time and also due to smaller size of meteorites and asteroids they were never largely molten and so give us a better understanding of the time of formation of Solar System.

 

<Age of meteorites and Earth>

 

 

 

Within experimental error all meteorites have one age as determined by three independent radiometric methods. The most accurate method ( ²⁰⁷Pb/²⁰⁶Pb) gives an age of 4.55+-0.07*10⁹ yr.

Edited April 5, 2015 by pavelcherepan

[David Levy]

 

Your attention to details and disregard of contradicting evidence is baffling.

 

Meteorites formed from the same nebula that formed the Earth and around the same time and also due to smaller size of meteorites and asteroids they were never largely molten and so give us a better understanding of the time of formation of Solar System.

 

 

 

Our current assumption about the Nebula couldn't consider as an evidence! It is a theory.

Please read again my following reply:

The assumption that the Earth could be considered as a blackbody is a severe mistake.

However, the willing of the science to fit each evidence to the current concept is a fatal error.

Therefore, we all must verify every observation and get a conclusion of what we see.

Just after getting all the real evidences/observations/calculations we can set down and figure out the source of the Universe enigma.

I have a simple questions:

Do you agree with my calculation based on Stefan-Boltzmann law?

Do you agree that the Earth is a graybody, and it should never ever consider as blackbody?

Edited April 5, 2015 by David Levy

[pavelcherepan]

 

 

Our current assumption about the Nebula couldn't consider as an evidence! It is a theory.

Please read again my following reply:

The assumption that the Earth could be considered as a blackbody is a severe mistake.

However, the willing of the science to fit each evidence to the current concept is a fatal error.

Therefore, we all must verify every observation and get a conclusion of what we see.

Just after getting all the real evidences/observations/calculations we can set down and figure out the source of the Universe enigma.

I have a simple questions:

Do you agree with my calculation based on Stefan-Boltzmann law?

Do you agree that the Earth is a graybody, and it should never ever consider as blackbody?

 

I'm not going to argue Stefan-Boltzman law with you. I'm not qualified enough for that and there are plenty of physicists about who can do it better, but what I am qualified to argue about is geological evidence and you can't just go and disregard it because that way your (apparently incorrect) calculations work better.

[Mordred]

There is also the age of our sun.

 

Try not to ignore science simply because it doesn't agree with your perception. That's a fatal and all too common a mistake. Thousands of scientists far more capable of the majority on this forum, over the past century of research, both mathematical and measurement went into determining the age of the Earth.

 

Do you honestly believe your going to discover something, without full understanding?

 

You base your calculations upon approximation formulas. Did you not consider different elements, and composite particles cool at different rates?

 

Different materials have different heat conductivity, some make better conductors, others better insulators.

 

This is why we look for the age of formation of known minerals. We can measure the properties of those in terms of dating with high accuracy.

 

The Earth formed from the protoplasmic disk. Same with every planet. How did we tell the moon formed at a different time, involves sampling. No one was around to witness, so how did they determine a collision?

 

It's great that your studying, but you cannot ignore disagreeable research. You have to consider and account for it

 

 

Here is one thing to consider about formulas. They work great modelling a system they are intended to model.

 

Add an influence, you must adapt.

[swansont]

Giving him clues as to what to argue. That is allowed isn't it?

 

OK, then. You are massively overthinking the problem I posed. All one needs to do is compare the incoming solar radiation with the radiated power of a blackbody at 1000 K. The context here was whether we could ignore solar radiation.

 

A concept that has been inexplicably missing one one side of this discussion is when terms in equations are important or not.

 

Since I'm getting frustrated that the reticence to do fairly simple analysis, I'll show the numbers myself. We receive about 1.3 kW/m2 from the sun if it's directly overhead, so the average of that over the earth is about 325 W/m2. A blackbody at 1000 K will be radiating 56.7 kW/m2.

 

That's a pretty straightforward calculation. It should not be melting anyone's brain who is interested in discussing science.

 

It's been pointed out that the earth is not a blackbody, so that reduces the emitted radiation, but it also reduces the amount of incoming radiation that's absorbed. So any way you want to slice it, you can ignore the effect of the sun while the earth is very hot. The solar radiation begins to be important at about 500 K (that's when incoming solar is several percent of the radiated power)

 

Remember, in the big picture of this thread, the original scenario was 6000 K, and the question was whether cooling to the point that we could form oceans could occur in around 100 my. Solar radiation was negligible for the initial rapid cooling of such a molten proto-earth. Emissivity is not the problem that it's being portrayed as. Half of a really big number is still a really big number.

My calculation is 100% correct.

 

…

 

Well, the title of this tread is: "Earth - What is the real age?". I have proved that by using correctly the formulas we can get the real answer, without digging in solar radiation and find its impact on the Earth at any specific temperature. However, if you wish, I will try to help with your request, although - it might take me some time to set it.

 

It doesn't matter if the calculation is "correct" (i.e. did the math right) if the overall analysis is flawed. A proper analysis needs to account for all sources of heating and cooling and all forms of heat transfer. You originally asked a very general question — how the earth could cool in 100 my — and were given a conceptual answer. Over the course of this very long thread you have been given various explanations by a number of people of other details that would have to go into a more detailed analysis, most of which are missing from your "correct" calculation.

[David Levy]

Dear Mordred

You are a best teacher. I consider you as my partner. You have significant part of this discovery. I have learned many aspects of modern science from you. Therefore, I have some sort of disappointment from your feedback. I would expect that you would verify the calculation, look at the formulas and ask me about blackbody or graybody.

Instead, it seems that you are unhappy as this discovery contradicts some of the current unproved theories.

So let's try to distinguish between theory, reality and none relevant issue:

 

 

There is also the age of our sun.

The Earth formed from the protoplasmic disk. Same with every planet. How did we tell the moon formed at a different time, involves sampling. No one was around to witness, so how did they determine a collision?

 

Theories

 

Try not to ignore science simply because it doesn't agree with your perception.

You base your calculations upon approximation formulas. Did you not consider different elements, and composite particles cool at different rates?

 

It isn't preception.It isn't approximation. It is a real verification.

Please read Stefan-Boltzmann Law.

I have used the formula exactly as it should be!

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2

 

Different materials have different heat conductivity, some make better conductors, others better insulators.

 

Let's assume that you have some zircon and we estimate that the age is 4.5 My. What does it mean? It just give us an indication for the min age. We have no guarantee that the minerals that we have are the oldest ever made on earth or in the universe.

 

Thousands of scientists far more capable of the majority on this forum, over the past century of research, both mathematical and measurement went into determining the age of the Earth.

 

I have High appriciation for all the scientists. But in this case, it is expected to verify the formula and the calculation. .

Edited April 5, 2015 by David Levy