# Estimate of the Earth's age

1. Aug 19, 2014

I have been watching Cosmos and it is talking about how we determined the age of the earth from meteors, since it's very difficult finding the oldest pieces of earth otherwise and these are from the creation of the Solar System.

Wikipedia: Estimate of the Earth's Age

I think there is still work to be done on this for 2 reasons:

1. Age of Earth vs. Age of Solar System may vary
2. Time dilation was not taken into consideration (which makes a difference even with GPS satellites)

Any thoughts on this?

2. Aug 19, 2014

### Staff: Mentor

The effects are so ridiculously small that they can be completely ignored. An ultrahigh precision clock put into the same orbit as the GPS satellites would tick faster than its earthbound counterpart by 38 microseconds per day. That's equivalent to 2.3 years over the 4.54 billion year age of the Earth. Clocks well removed from the Sun and planets tick a tiny bit faster than that "fast" GPS clock, about 490 milliseconds per year faster. That's equivalent to about 70 years over the 4.54 billion year age of the Earth.

Compare that with the uncertainty in the 4.54 billion year figure, which is about 50 million years. There's still a lot to do with regard to getting a better picture of how the Earth formed and how old it is, but worrying about relativistic effects isn't one of the things that needs to be done.

3. Aug 19, 2014

Well that's for GPS satellites which are very close to earth, the gravity and velocity of an asteroid in the asteroid belt would be much different. With the difference in gravity and distance from a large source of gravity, time would go much faster when compared to Earth's perceived time.

4. Aug 19, 2014

### Staff: Mentor

Time dilation between the far reaches of the solar system (e.g., the Oort cloud) and the Earth is very, very small, resulting in a 490 milliseconds per year difference. This adds up to 70 years over 4.5 billion, which is still nothing. For stuff in-between the Oort cloud and us, it's less that than minuscule 70 years. Even for Mercury, it's still essentially nothing.

Time dilation is important for GPS because the accuracy requirements are so ridiculously high. Losing 38 microseconds a day would mean the system would be worthless in short order.

5. Aug 19, 2014

Seems kind of strange that time dilation between earth and GPS satellites and the Sun and Asteroid Belt would be the same (actually it'd be impossible). Especially considering things like gravity and velocity are taken into consideration and are much different. Not to mention the distance from the sun (enormous source of gravity) to the asteroid belt is over double the distance from the Sun to Earth.

Can you please show me how you came up with those numbers or show me how to fit these numbers into a time dilation equation? Here are the figures being worked with, I'm having trouble creating the equation though:

EARTH:
Earth’s Gravity = 9.81 m/s2
Earth’s Sun orbit velocity = 18.5169mi/sec
Earth’s rotational velocity = .292044mi/sec

ASTEROID BELT:
Asteroid Gravity = ~0
Asteroid Belt Sun orbit velocity = 15.5343mi/sec
Asteroid Belt Orbital velocity = 11.0740774mi/sec

FROM SUN:
From Sun -> Earth = 92,960,000 miles
From Sun -> Asteroid belt 186 million - 370 million miles

ESTIMATED AGE OF EARTH: 4.54 Billion Years
-time dilation not taken into consideration, nor is the time known when tested asteroid hit Earth.

SOURCES:
http://en.wikipedia.org/wiki/Time_dilation
http://en.wikipedia.org/wiki/Age_of_the_Earth

6. Aug 19, 2014

### Staff: Mentor

The equations for the two different forms of time dilation are fairly straightforward. The velocity time dilation formula is in the wiki link you posted -- see if you can find the right equation, post it, and try to plug in the relevant numbers.

For gravitational time dilation, you'll have to click through to the page with that name, but again, the equation is fairly straightforward.

You'll learn best by doing the math yourself, so we'll just help you through it...

What you will find is:
1. You have to be going really fast for speed based time dilation to have a significant impact. A large fraction of the speed of light. We're not moving anywhere close to the speed of light in our orbit.
2. You have to be really close to a really massive object to experience much gravitational time dilation. Earth isn't that big and we aren't that close to the sun -- and it isn't even all that big compared to what is needed for significant time dilation (close to a black hole, for example). And the further you get away, the smaller the effect gets.

7. Aug 20, 2014

Thanks, I would like to do this equation. I'm having some trouble determining which numbers to plug into the equation and where? On Wikipedia it has odd symbols I'm not familiar with to represent the equation.

I know that c = speed of light, but I have no clue what the "Δt" means? Also, it explains "The separation of the mirrors is "L" and the clock ticks once each time the light pulse hits a given mirror." I am having trouble understanding what this means. Can you please help me understand how to I can put together this equation?

In the meantime I will do some research to check differences is the size of the Sun throughout the course of this period as well as trying to track the progress of the Asteroid Belt forming in case this would make a difference. Although you mention time dilation would not have a major difference but I think this will be a good exercise and help me understand these things better.

I still feel it is wrong to assume the earth is 4.54 billion years old do to the age of an asteroid. It would be more accurate to say that asteroid is believed to be 4.54 billion years old, or a bit less but still more accurate.. The solar system was most likely formed over 4.54 billion years ago. Is there a piece I am missing that would explain why we explain with a certainty that the Earth is 4.54 billion years old?

Thanks for helping me out with this! I appreciate it more than you probably realize. I have a great deal of interest in these kind of things it's common to have trouble verifying and ruling out questions that come up about the subject, due to it's complexity.

8. Aug 20, 2014

### e.bar.goum

Comments about relativity not-withstanding (I agree with Russ_watters and DH - the effect is so negligible as to be not even worth thinking about), we have more than one way of working out the age of the Earth.

Calcium-aluminium-rich inclusions (CAIs) in meteorites give the value of 4.567 billion years for the age of the solar system, which is then an upper limit for the age of the Earth. Then if you worry that through some very strange mechanism the Earth formed after the rest of the solar system (which is what you seem to be getting at?), you can look at the age of the oldest rocks on earth - Zircons from Jack Hill in Western Australia have been dated to 4.04 +/- 0.08 Billion years. http://www.nature.com/nature/journal/v409/n6817/full/409175A0.html This then gives us a lower limit for the age of the Earth.

After you go away from these measurements, you're getting into model dependent values. You need to ask at what point (and where) in the formation of the solar system the CAIs condensed out (fairly early), and then how long after that the Earth took to condense out - models vary between a couple million and a hundred million years. But we're talking about millions in billions - so you can be pretty sure that it's 4.something billion years old.

The other thing that may affect estimates of the age of the Earth and the Solar System is in the re-evaluation of the half-lives of the radioactive isotopes of interest. It's very difficult to measure very long lived isotopes, so these values change occasionally, which feed into the derived ages of CAI's and zircons.

Developing better models of solar system formation is an extremely active area of research. But it's got naught to do with General Relativity.

9. Aug 20, 2014

### davenn

agreed with the others

deadcat, you seem to be wanting a precise date for something that doesn't have a precise date

what are you really trying to achieve out of this that hasn't already been done in scientific circles ?

Dave

10. Aug 20, 2014

### e.bar.goum

In defence of deadcat, working through this sort of thing yourself has teaching value!

11. Aug 20, 2014

The sound of leaving out data doesn't really sit well with me, but I know what you mean if it's only gonna be like 70 years or something out of a few billion. I was not aware they tested rocks in Australia to be over 4 billion years old. I think this makes more sense than testing a meteor because a meteor may have not even originated from our solar system, not to say we shouldn't test them.

I am glad this is still an extremely active area of research, the more concrete information we have the more we have to build on.

12. Aug 20, 2014

Scientific circles? Can you please elaborate? I was trying to determine if time dilation would have enough of an impact to reconsider the estimated age since it was not taken into consideration. The community has helped me understand this better. If everyone thought like you we would never learn anything new, it's somewhat sad to know that many people in the scientific community have this kind of closed minded thinking.

You're not better than everyone so please try to stop acting like your opinions and established opinions are the only ones that matter. Why are you even here? Just to troll people with serious questions?

13. Aug 20, 2014

### e.bar.goum

As in leaving out GR influences? 70 years in 4.54 billion looks like this: 4540000070. Or 0.000001 percent. In science, you can only report significant figures to your level of uncertainty, which in this case is plus or minus 50 million. So even if it was out by hundred thousand years, not 70, it still wouldn't show up in the age of the Earth.

You use meteorites because the Earth is a geological mess, with so much mixing and overturning that your isotopic ratios go out. Meteorites are presumed to be less mixed. In addition, I can't think of a single good solar system model that has the CAI's condense out too much before the Earth.

There is also no evidence for large meteorites originating outside our solar system. You may find very small meteorites (dust, basically) from outside the solar system, but they're also pretty rare, and not the kind of thing you use to date the age of the Earth or the Solar system.

Have you read this yet? http://en.wikipedia.org/wiki/Age_of_the_Earth

ETA: And it's funny to me that you say "still an active area of research". Like we'd ever stop. :P

14. Aug 20, 2014

Dude, I already know all this it's what we've been discussing the whole thread. I'm not the one that said "still an active area of research", you did. Yeah I thought it was kind of stupid too but thought I would be nice.

And thanks for re-posting the link I provided.

Have you read this yet? http://en.wikipedia.org/wiki/Troll_(Internet)

Last edited: Aug 20, 2014
15. Aug 20, 2014

### e.bar.goum

I think you've gotten me confused with someone else, actually I'm the one that said "still an extremely active area of research" and then you said "I am glad this is still an extremely active area of research". I was replying jokingly to that. And I was further talking about why you'd use meteorites not the earth.

The link you provided was not the one I did. Yours was about Clair Cameron Patterson.

And I'm so sorry for spending my time telling you about how the research is currently being done.

16. Aug 20, 2014

Well thanks for trying to help I guess, I've already gotten the answers I need from this thread several posts ago. Actually I provided 3 post and that was one of them.

17. Aug 20, 2014

### e.bar.goum

My apologies, my intent was not to condescend. If you could point out exactly where I was being condescending, I would appreciate it.

18. Aug 20, 2014

### davenn

tisk tisk ... dont be so unkind and nasty .... comments like that to any of us are totally uncalled for and wont encourage people to help you in future is all you do is abuse them!!!

on the contrary I'm very open minded I love learning about new things as we all do here

Dave

19. Aug 20, 2014

Well you're trying to act like I thought 70 years out of 4.54 billion was significant when really I didn't even know 70 was the figure I was comparing, this was the number I was trying to determine. To me my question looked like "x" years out of 4.54 billion. Of course 70 makes no difference, then re-posting my link I provided as to say I didn't read it. Also, sarcasm doesn't come across well in text so that last part came across as to imply I don't know how scientific research is conducted.

Sorry if you were being sincere..

20. Aug 20, 2014