# Drake equeation and planet finding

1. Apr 13, 2006

### DaveC426913

Drake equation and planet finding

I've just finished reading a Discover mag article on the Drake equation. It suggests that - despite the 45 year difference wherein many terms have been changed or anchored with more precision - the final number is about the same as it always was; there should be about 1 intelligent, radio-capable civilisation within 1000ly of us.

The Drake equation:
$$N = R^*f_pn_ef_lf_if_cL$$
where
$$R^*$$ = # of life-friendly stars born each year (~10)
$$f_p$$ = the fraction that have planets (~.9)
$$n_e$$ = the number of habitable planets in the system (~2-3)
$$f_l$$ = the fraction that have life (~.1)
$$f_i$$ = the fraction that have achieved intelligence (~1)
$$f_c$$ = the fraction that have achieved radio (~1)
$$L$$ = the duration of the civilisation (~50,000)

But considering the amount of hype in planet finding going on these days, I think we'd be happy finding any kind of life. That would mean we could ignore terms 5 and 6 and drastically incease term 7.

Well, since terms 5 and 6 are =1 anyway, they have no effect. I guess it simply boils down to term 7 - how long life exists at all on that planet. Here, it existed for what? 3.5Gy? So, that's 70,000 times longer.

I don't know the math they do to get from the final Drake number to a number within 1000ly, but it seems to me that all I have to do is use my multiplying factor.

Which means that, according the the Drake equation, there could/should be about 70,000 planets within 1000ly of us that have with some form of (chemically detectable) life.

And to boot, this number is significantly more accurate than the traditonal Drake equation, since the margin for error dramatically increases as we move to the right of the equation. Eliminating 2/2 and nailing 1/7 of the right-most terms goes a long way to getting a mroe accurate number.

Hm, well, looking even further, it all boils down to term 4: the percent of habitable planets that actually spawn life. That's the big question isn't it? Basically, we can throw the Drake equation away and simply ask what is the likelihood of life on any given habitable planet we find. They say 10%.

Last edited: Apr 13, 2006
2. Apr 13, 2006

### arildno

The Drake equation is, essentially, a worthless collection of symbols.

3. Apr 13, 2006

### JustRobert

How did they come up with that number of 10%? For such an important variable in the Drake equation, it seems a little rounded off and arbitrary.

Besides, everyone knows the home system of the Greys (Zeta Reticuli) is significantly closer to Sol than 1000 lys

Robert

4. Apr 13, 2006

### scott1

Does the Drake equation only repsent carbon-based life/life as we know it?
What do you mean?Do you mean is mathmatically incorrect or is just that you don't belive in exteritally life.

5. Apr 13, 2006

### DaveC426913

It's not that sophisticated. Many of the numbers are pretty much guesswork. eg. What are th chances that a planet friendly to life will actually have life? With a sample size of one, we have no idea. So they guessed - 10%.

Because several terms are complete guesswork, there is no real value in the formula.

6. Apr 14, 2006

### Chronos

The Drake equation is not a bad try, just overly complex. I prefer a simpler approach. Given we evolved in orbit around a G star, let's start with the number of nearby G stars. And there are 10 within 25 parsecs of earth – re: Nearby Stars, Preliminary 3rd Version (Gliese+ 1991). Using this as the average density distribution, there are about 8 million type G stars similarly positioned in our galaxy. Assuming 50% of them are as old, or older than Sol, how many have an earth like planet? I'm guessing one in a thousand. The number of likely candidates is now 4000. The question now becomes how many have evolved intelligence currently able and willing to communicate with us? It is a vanishingly small number, IMO, considering we have only had such capabilities for about 50 years.

7. Apr 14, 2006

### arildno

Well, Dave has basically answered what my objection is to the Drake equation;
personally I prefer the arildno identity:
N=N
where N is the number of civilizations in the universe at the moment.

8. Apr 14, 2006

### Entropy

Not that the Drake Equation by itself isn't ridiculous, but these number in particular are completely ridiculous. Why would every planet that has life, develop intelligent life? For over 99.9% of Earth's history there has not been intelligent life. Shouldn't this number be around 1/1000? And why would intelligent life have to develop radios? It could be argued that whales are intelligent, but they cannot build radios. This also assume that intelligent species automatically persue technology, it could very well be that most intelligent aliens just want to live on their home planet, living simple lives, not caring about the universe around them. We assume that simply because we have an interest in science and technology, other beings must as well.

9. Apr 14, 2006

### Arian

Yeah, the drake equation is essentually crap. There are only five numbers. Yet each of these numbers have minature numbers which have minature numbers. So you got N=d+D+g+f. A much easier way to do it is to look and rather important things likie, the right star, right distance form the star, has carbon, not silicon, has no oxygen to begin with, and so then you get, or at least I did, that out of every 2 Billion Stars, only 12 civilization will rise. Thats not alot...

10. Apr 14, 2006

### arildno

On another note, apart from the guessworking involved,
to see how unbelievably dumb the thinking behind the Drake equation actually is, I'll present the analogous "rabbit equation":

Let R be the number of rabbits in the world.

Let N be the total number of animals in the world.
let [itex]f_{m}[/tex] be the fraction of the total number of animals that are mammals.
Let $$f_{l}$$ be the fraction of mammals living on dry land.
Let $$f_{j}$$ be the fraction of land-based mammals that like to jump around.
Let $$f_{r}$$ be the fraction of land-based jumping mammals that are rabbits.

Thus, we may write:
$$R=N*f_{m}*f_{l}*f_{j}*f_{r}$$
This is the rabbit equation!

The rationale behind the Drake equation is hardly any better.

Last edited: Apr 14, 2006
11. Apr 15, 2006

### Chronos

Not taking the argument seriously is a mistake, IMO.

12. Apr 15, 2006

### arildno

What argument?

That, in principle, the number of civilizations is calculable from other quantities?

Sure I can agree with that, but it's not much of an argument.

13. Apr 15, 2006

### Kurdt

Staff Emeritus
The Drake equation is one of those equations the media publish every so often when a scientist somewhere claims to know the equation of the perfect horror film and so on. While the mathematical arangement of the symbols is entirely correct, the determination of SOME of their values is little more than guess work and thus the equation is redundant.

I rather like arldno's rabbit equation because at least then all of the parameters can be known.

14. Apr 15, 2006

### arildno

Unfortunately, in the case of the Drake equation, we cannot blame dumb journalists for its unwarranted position in the public consciousness.
The Drake equation was made up by the the founder of the SETI project (Drake, the astronomer), and the SETI guys have propagandized their (in my view worthwhile) agenda and their dumb equation to the fullest possible effect. They've even made a golden plaque with the Drake equation inscribed upon it! :yuck:

Thank you!

15. Apr 15, 2006

### SpaceTiger

Staff Emeritus
The idea behind the Drake equation is to divide one question that's not directly answerable into several that might be answerable in the (sort of) near future. We can get an idea of how close we are to answering the big question, the existence of intelligent life in our neighborhood, by looking at which of the terms in this equation we've already measured. Of course, the expansion is not unique, but the individual terms in the equation are interesting in of themselves and are usually presented in the order in which we expect to measure them. There's nothing particularly revolutionary about it -- the same basic process goes on with most OOM estimates in astronomy -- but it is a better way of posing the problem, I think. On the other hand, it's only useful insomuch as the subquestions are easier to answer than the main one.

In the rabbit analogy, to me the expansion is not particularly useful, since I don't have any more intuition for the total number of animals in the world than I do the total number of rabbits (perhaps less). Rather, I might start by estimating how many rabbits I've seen in my life, followed by an estimate of how much land area I can see at a given time, followed by an estimate of how much land area I've covered in my life, etc. Or, if I knew how many rabbits there were in a given area, I might try to extrapolate that based on my knowledge of the relative abundance of rabbits on different continents. Estimates like this are common fare on the general exam (the one taken before we get our Masters degree). The professors want to see if we have a sense for dividing difficult problems into multiple tractable ones.

As for the Drake equation itself, we've got a pretty good hold on the first term, a decent hold on the second, and only a rough idea on the third. Beyond that, it's mostly speculation. If I had to pick terms, I don't think I'd be as optimistic as Dave, but I don't think anyone can really say at this point.

16. Apr 16, 2006

### arildno

No, we don't.
Not even that.
With possible exception of the last factor. We DO have empirical evidence that might give us a better-than-nothing idea about the average lifetime of a civilization, namely HISTORY.

Last edited: Apr 16, 2006
17. Apr 16, 2006

### SpaceTiger

Staff Emeritus
Obviously, I disagree, but feel free to give an actual argument. I think current observations suggest that planets are a common phenomenon. We haven't detected them around every star that we've looked at (~10% of sun-like stars), but we're only sensitive to the most massive planets and then only when they're in close enough orbits. Also, at least half of young stars in the Orion Nebula possess gas disks, which is almost certainly where planets are formed. I would put this parameter in the range 0.5 to 1 without much fear of future contradiction.

On this, we have numbers to approach the problem, though they don't directly answer the question. We have an idea of the eccentricity, semimajor axis, and mass distributions of extrasolar planets in the high-mass regime, so a naive extrapolation gives us something to work with. I won't try to estimate it, but at least we have data for someone who wanted to try.

Evidence that's littered with anthropic bias...

18. Apr 17, 2006

### Chronos

Apologies for the confusion. I'm only considering stars very similar to our sun that harbor planets very similar to earth as candidates. Given our solar system is the only life bearing [I hesitate to say intelligent life], it seems a reasonable approach. My bare assumption is that any very similar planet, as old or older than our own, has a fair probability of being populated by beings similar to ourself. But the timeline may be very narrow, IMO. Given human history, intelligent life forms are vulnerable to self destruction as soon as the prerequisite technology becomes available. Fermi's question might be more ominous than we care to ponder.

19. Apr 17, 2006

### arildno

SpaceTiger:
Are you planning to write a fantasy novel?
Whatever facts supports your assertion that well over 50 percent of stars have planets around them?

Only a minuscule fraction of known stars has been shown to have planets about them; you have balloned that fraction to an extent you haven't got any justification for.

Last edited: Apr 17, 2006
20. Apr 17, 2006

### SpaceTiger

Staff Emeritus
~10%, subject to the constraints I quoted.

The justification is given in my previous post and another argument can be found in more detail here:

Lineweaver & Grether

Note, they haven't detected planets around 50% of stars, they have extrapolated current data based on reasonable assumptions. Thus, this is not the final word, which will come from future observations of exoplanets.