Sunday, November 24, 2013

You Do The Math - Life On Other Planets

This is a collage I made many years ago, just before Pluto was voted off the island, and by now we know of many more rocky bodies in our solar system than the 25 or so significantly large bodies depicted here.  Yet, how many have the right ingredients for the kind of life that can give rise to a space faring civilization that can visit us from distant stars?  After all, the furthest stars in our galaxy's habitable zone are 50 thousand light years away, and you have to circumvent a black hole and the radioactive central bulge of our galaxy to get here, which adds another dozen or two dozen light years to the trip.

If you can even travel 1/10th the speed of light, which would be truly amazing, it would still take 620 thousand years to get here.  By that time, the travelers wold have evolved into other beings, beings that loved space, and wouldn't possibly want to colonize the Earth.  Hence, flying saucers with space aliens do not seem likely.  Unless they just want to make a photo bomb.  After all, a sense of humor is definitely required to travel the galaxy in a titanium can.

UFO photo bombs unsuspecting couple

The closest stars are much closer, but no Earth-like planets have been found yet.  They are mostly gas giants orbiting closer than Venus and Mercury orbit our Sun.  The closest star, Proxima Centauri, and its 2 star partners, are 4 light years away.  However, those 3 orbit each other.   Stable planetary orbits on the order of the billions of years required to create an environment that can give rise to intelligent civilizations doesn't seem likely.


How can I possibly make that claim?   Look at the above collage.  Earth is about 7930 miles across, while our ocean averages 1 mile in depth.  Using a dozen sources from the experts across the globe, they all tend to agree that the total amount of water on Earth, in the atmosphere and most importantly, under the ground where half our water resides, add up to a sphere between 750 and 800 miles in diameter:

In terms of volume, the Earth is about 1/1000th water, a scant, frightening and miniscule 0.1 percent:

Volume = radius cubed times 4/3rds Pi

Ratio of radii:

7928 / 775 = 10.23
7930 / 775 = 10.23

7930 / 750 = 10.5
7930 / 800 = 9.9

Since Earth's average density is 5.5 times that of water, then measured by mass, water would be around 1/5500th of the earth, or about 0.018 percent.  But, let's stick with 1/1000th the volume, it's a lot easier to think about.

Experts say if the Earth had twice as much water (1/500th water), the ocean would be another 2 miles deeper, and the only land jutting above sea level would be mountain tops.  Denver would be a mile BELOW sea level, not above.  There would be no continents for civilizations to mine platinum and gold and titanium for space travel.  Heck, forget mining copper for the bronze age, iron for the iron age, and aluminum for the airplane age, which were prerequisites of thousands of years before rocketry was invented.  And what about all the metals that created our ancient bronze alloys, like tin and zinc?  What about the metals required to make our jet age alloys, like magnesium and titanium?  Forget about it.

From props to jets, planes are made of aluminum/copper alloy.

What if the Earth had half as much water?  It would almost all be under ground, and all we would have is the occasional Yosemite National Park with poisonous, boiling, hot springs entertaining extremophiles.  When's the last time one of them made a space ship?  Never, bee-atch.

So, how many rocky bodies in our solar system have oceans and continents?  None.  But, that's because they are all frozen.  What is their actual water content?  Are any like the Earth at 1/000th water by volume?

Europa is famous for being covered in ice and a liquid ocean about 60 miles thick, and compared to a 1900 mile diameter (Wikipedia), this comes to 17.8% water by volume.  That's closer to 1/5th than 1/1000th.  Way too much.  However, doing more research, I see people should be making a bigger deal about Ganymede, which is almost 50% water by mass.  It's ice mantle is approximately 900 km of its 2634 km radius, giving it 71.5% water by volume.  Give me a few !!! please.

Enceladus is an ice-covered water world with water volcanoes.

Let's compare the planets and their water content. (data from Wikipedia)

planet             mean            ice/water         water
                    radius (km)    mantle (km)    by volume
Mercury        2,439.7              0                   0%
Venus           6,051.8               0                  0%
Earth            6,371.0             6.4                  0.1%
Moon           1,737.1              0                    0%
Mars             3,386.2           0.011               0%
Ceres                    (50% water by mass)     25%
Callisto          2,410.3            300               33%
Ganymede     2,634.1             900              71%

Io                  1,821.3               0                  0%
Europa           1,560.8            100              18%

Titan               2,576               876              71%
Triton                       30%-45% water by mass
Rhea                             75% water by mass
Iapetus                          80% water by mass

Dione                            54% water by mass
Tethys                           94% water by mass
Titania               788.4          268.4              71%
Enceladus               est. 48% water by mass
Pluto                      est. 40% water by mass
Charon                   est. 45% water by mass

Saturn has Titan, which has extremely large lakes made of hydro-carbons, such as methane and ethane.  It's atmosphere is mostly nitrogen, and has rain in the form of liquid methane and ethane.   It is also about 50% water by mass, similar to most other cold, distant satellites.  It may indeed have a layer of water under it's icy crust, because the crust was seen to shift 30 kilometers in a few years.

Cassini satellite has strong evidence for Enceladus' liquid ocean.

Enceladus is a satellite of Saturn that is like Europa, covered in ice, with evidence of a liquid ocean underneath (  But, it's not big enough to be in the next 6 smaller satellites after Europa.  At 300 miles across, it is smaller than the 3 largest asteroids.

Tethys is 94% water at least.

Tethys is at least 94% ice, because it's average density is less than that of water.  On the other end of the spectrum Io is about 0% water, but no planetoid seems to have anywhere near the Earth's 0.1 percent.  Seems that when it comes to water content, it's either feast or famine, flood or drought.


Most of these satellites are smaller than our Moon, so gravity is too weak for an atmosphere.  If they were in the habitable zone, the gasses and water would literally boil away, making them like our Moon.  Titan is a bit larger than Mercury, but about 1000 miles smaller than Mars.  It would loose most, if not all, of it's atmosphere.

The same is true for all the rocky bodies other than Venus and the Earth,  Comets have a large percentage of ice, like Europa.  So large that they boil away when nearing the Sun.  But, they are all too small for an atmosphere.  Some are so small they have been seen breaking apart, turning into interplanetary dust and vapor.   (Appropriately, just after I finished this blog, comet ISON was recorded going around the sun and being vaporized:

Comet McNaught evaporates ice into a great tail.

Which planets have enough mass to maintain an atmosphere?  Only Venus and the Earth, 2 out of the 25 or so.  Unfortunately, Venus is too close to the Sun, and has run away global warming.  The water evaporates, is destroyed by solar radiation, and the the hydrogen escapes, leaving only oxygen and carbon.  It's atmosphere is mostly carbon dioxide, with acids thrown in to completely sterilize the environment.  The surface of the planet is about 850 degrees Fahrenheit, hot enough to melt lead and turn humans into sticks of black, crumbly carbon and calcium.

Mars is only half the diameter of the Earth, and has 38% of the gravity.  It's atmosphere has 166 times less pressure than Earth's average, so it's about 50 times less pressure than the top of Mt. Everest.  It is said that if you were lifted to the top of Mount Everest (or your jet airliner had an air leak, same thing), a height of 29,029 feet above seal level, you would pass out in 3 seconds and be brain dead in 3 minutes.  Even those who spend several weeks acclimatizing only have enough red blood cells to survive 24 hours, before permanent damage occurs.  Besides, Mars' atmosphere is almost entirely carbon dioxide, so it's a moot point.

Pluto and Charon both orbit the center of mass.


Mathematically speaking (and math is king) the best theory for our Moon's creation is that 4.5 billion years ago a young Earth was struck by a Mars-sized planet named Theia.  This strike was perfectly aligned, and had the perfect amount of kinetic energy, to blast a large amount of material into orbit to create the Moon.  The Moon is 3.67 times smaller than the Earth, has about 49 times less volume, and 81 times less mass.  Only Pluto has a planetary partner anywhere close to this ratio.  (In fact, it's satellite Charon is a mere 8.6 times less massive.)  Mars' satellites are the size of cities, merely captured asteroids.

The gas giants Jupiter, Saturn and Neptune have large satellites, but Uranus does not.  Uranus is also the only gas giant to be tilted on its axis.  Coincidence?  Scientists say no.

Uranus poles point towards the Sun, unlike planets with large satellites.
Planet    mass (kg)    Satellites     mass (kg)   ratio planet/satellite mass
Earth     5.98E24      Moon        7.36E22     81
Mars     6.34E23      Phobos      2.72E16     21,862,069
                                Deimos      1.8E15
Jupiter   1.90E27      Io              7.87E22     5,367
                                Europa       4.78E22
                                Ganymede  1.54E23
                                Callisto       7.35E22
Saturn   5.68E26      Titan           1.2E23      4,577
                                Iapetus        2.3E21
                                Rhea           1.8E21
Uranus  8.68E25      Titania         2.1E21      22,604
                                Oberon       1.1E21
                                Ariel           5.0E20
                                Umbriel      1.4E20
Neptune 1.03E26     Triton         1.46E23    705
                                Nereid        5E19
Pluto       1.3E22      Charon       1.52E21    8.6

(data from Physics, Richard T. Weidner, 1985, except Pluto/Charon data from Wikipedia )


Earth's early Moon was only 15,000 miles away, and tides were miles high, not a few feet.  Modern life would have been impossible.  Complex life would have been impossible, except for ocean life prior to the age of amphibians.  Basically, only fish, shellfish, jellyfish, crustaceans, worms, etc.  This 15,000 miles is closer than today's geosynchronous satellites that lie 22,000 miles from the surface, and orbit in exactly 24 hours. So the Moon orbited in how many hours?
You have to use four basic equations.

F = GMm/r^2

You set the first two equations equal to each other, thus arriving at the centripetal acceleration of the Moon as it orbits the Earth.  The third equation uses this acceleration to calculate the orbital velocity.  Divide circumference by speed and you get the time it takes to complete one orbit.

Long story short, I get about 16 hours for a lunar orbit (assuming 15,000 miles was the distance from the surface of the Earth to the surface of the Moon).  If the Earth had a 6 hour day as they say, then the highest tide would occur about every 9.6 hours, when the Moon is overhead.

The interesting thing is the speed.  Currently, the equator is about 25,000 miles around and a day is about 24 hours, so the tide moves about 1,000 miles per hour (have to subtract a bit for the Moon's speed).  But, since the tide is several thousand miles wide, it takes several hours to rise and fall.  You don't notice the 1,000 mph speed.

The same might not have been true back then.   With a 6 hour day, a spot on the equator would be moving 4 times faster, about 4000 mph.  With the Moon orbiting in 16 hours, it's shadow on the Earth's surface (a stationary Earth) would be moving about 1,500 mph.  Subtract 1,500 from 4,000 and we get 2,500 mph, the speed of the tidal bulge.

If the tidal bulge (of land AND water) was miles high, then it would be probably a lot wider than today's tidal bulge.  Perhaps half the planet.  This friction would create a LOT of heat, not unlike Jupiter's Moon's that have hot interiors due to tidal forces. But, back to speed.

If the bulge was 12,000 miles across, and 4 miles high, and came around at 2,500 mph, then to calculate it's rising rate, simply take half of that 12,000 miles, and divide by the speed of the bulge to get the time it takes to rise.

6,000 miles / 2,500 mph = 2.4 hours

Since the total height is 4 miles, then the speed of the surface of the water upards is 4/2.4, or a scant 1.67 mph. Doesn't sound too dangerous.  Of course, after an hour your beach house would be 1.67 miles under water!  Even worse, if this tide is rushing onto a continent, then it would be pouring in very fast.

Because 1.67 mph is equal to 2.4 feet per second, then you can well imagine a 24 foot tall house being swamped in 10 seconds, and the horizontal flow must be hundreds of miles per hour, if not the half of that 2,500 miles per hour.

What's my point?  For human civilization to be possible 4.5 billion years after the Earth-Theia collision, then the Moon must start out this close, and complex life on Earth would be impossible for millions of years.  Heck, even continents themselves would be a washed away before they got a chance to form. Basically, it has to start out rough to finish smooth.


The Earth had been hit at just the right angle and velocity to spin it up so fast that one day was only 6 hours.  The strike was counter-clockwise, as is all daily and yearly rotation in the solar system, when looking down from the North Pole.  This kept the Earth spinning in the correct direction. 

It is theorized that Venus and Mercury were hit by large bodies at the wrong angle, or from the wrong direction, thus slowing their daily rotation down to a large fraction of their year.  In fact, all planets form with multitudes of collisions of smaller bodies.  What are the odds that all these collisions will result in a rocky planet spinning the correct way?  In our solar system, those odds are 2 out of 4 inner planets.  That's as good as flipping a coin.

A huge day length creates really hot days and really cold nights and immense winds that erode everything, including mountains.  Forget civilization, it would be difficult for bacteria to live above ground.  Evolution?  Forget it.

Theia impacts early Earth, vaporizing solid rock.

Earth's early Moon was extremely close, and tides were unbelievably high.  If the Moon had formed any closer, the tides would have ripped it apart and it would fall back to Earth in small pieces.  The Moon could not form any closer than a mathematical limit called the Roche limit, or Roche radius.  The Earth's Roche radius is 14,000 miles.  Luckily, the Moon was thought to have started out approximately 15,000 miles from the Earth.

But physics makes the Moon move away from the Earth, provided it's also going counter-clockwise.  The tidal bulge of the oceans and the planet's crust create a torque on the Moon that increases its velocity, and sends it further away.  But the Moon also slows down, cool huh?  This bulge on the Earth is pulled backwards by the Moon, and slows down the Earth's daily rotation.  After 4.5 billion years, the Earth day is perfect for a stable climate and the evolution of animals that appreciate an 8 hour work day, and evolved to sleep through the night to recharge our complex brains, a requirement for intelligence.

If the pole points to the sun, you get ice on one side, hot sand on the other.

The Moon's distance now, and half a billion years ago when fishes evolved into amphibians, is perfect for small tides and tidal pools, perfect for many forms of life and keeping the food chain strong.  It is also said that Human's long lost ancestor, tiktaalik, a walking fish, evolved that way thanks to either one of two things: tidal pools or shallow seas and swamps.  Since mammals evolved from reptiles, which evolved from amphibians, human life is probably dependent on a large satellite that makes tides.  If Earth's Moon had been in a retrograde orbit, like one of Mars' satellites, the tidal bulge would have pulled in the wrong direction, slowed it down, decreased it's orbit, and quickly crashed it back into the Earth, annihilating all life.

But it doesn't end there.  The main advantage of a large satellite is that it stabilizes the Earth's axis of rotation.  Physics shows that an Earth without a large moon will wobble on its axis, like a top falling down.  At many points in Earth's history the north pole would point toward the Sun for a few months becoming boiling hot, and away from the Sun for a few months, dropping temperatures way below zero.  This scenario would last as long as, for example, the evolution of a land creature into a whale, millions of years.  But said evolution would not happen.

Theia blows away much of Earth's crust, ocean and atmosphere.

Living on the equator would give a nice average temperature, but the winds would be a thousand miles per hour.  Continents would erode away and wash into the ocean.  Good bye all forms of life that came after the fishes: amphibians, reptiles, dinosaurs, birds and mammals.  No space faring civilization will come from the octopus, crab or shark.

But it doesn't end there!  The impact with Theia has been credited with blowing away half of our ocean.   Remember how important it is to have an ocean 1/1000th the volume of the Earth?  Well, Theia apparently blew away just the right amount.  And the Earth started with that much extra water.  What are the odds of that?

But, it doesn't end there.  Theia has been credited with blowing away much of our atmosphere.  Scientists think that life couldn't have evolved in a thick atmosphere that the Earth would have been formed with naturally.  Life needed a "reducing atmosphere", aka thin air.  And Theia came along just in time to blow away all the extra air that the Earth had.  What are the odds of that?

But, it doesn't end there.  In computer simulations Theia's core merges with Earth's core, and the Moon ends up being made mostly of Earth's crust material.   This was also proven by the rocks retrieved by the Apollo misisons.  The Earth's core got a huge growth spurt from Theia, and we'll see below why this is very important to life on Earth.

The perfect impact between Earth and Theia.


Well, there's only one rocky body in the habitable zone.  Venus is obviously too hot, as discussed.  Mars' atmosphere is cold enough to make dry ice, frozen carbon dioxide, at the poles during the Winter.  Basically, there is probably only one planet per star that lies in the habitable zone.


Seems that carbon dioxide is the norm, since Venus and Mars both have atmospheres of nearly 100% CO2.  (Mars has a small amount of nitrogen.)  Geologists have determined that Earth's early atmosphere was also greatly CO2.  Since the Sun grows 10% hotter every billion years, the Earth absolutely needed all that greenhouse gas 4.5 billion years ago to maintain a liquid ocean.

And this warm atmosphere creates a humid atmosphere.  Humidity is also a greenhouse gas, and helps regulate daily temperature swings, stabilizing the climate.

Humid conditions plus low pressure make fog, as do F-14 Tomcats.

Geologists have also determined Earth's temperature has been maintained nearly perfectly for 4.5 billion years to have liquid water covering most of its surface.  As the Sun grows hotter, the CO2 level drops, thanks to cyanobacteria that remove carbon from the air, leaving oxygen.

Since our atmosphere is 78% nitrogen, but Venus and Mars have little, I'm guessing that is a key ingredient.  However, the correct amount is determined by the warmth of the star, and the distance the planet is from the star, and the gravity of the planet, which makes a denser atmosphere, thus changing climate and its stability.  A hotter planet would also make a denser atmosphere.  Just look at Venus!  The thickness is so great a jet airliner could fly at 5 mph.  (But it would need to be made of titanium, because at 850 degrees aluminum would melt and steel would be like rubber.)

Which rocky bodies in the solar system have significant nitrogen?  Titan has a mostly nitrogen atmosphere, and Triton is so cold  it's surface is dusted with frozen nitrogen.  Of the other hundred or two hundred rocky bodies... too small and too cold to matter.

In the habitable zone, heat can make rocks out-gas, especially volcanic heat, which makes rocks explode thanks to their dissolved gasses CO2 and sulfur dioxide.  Conservatives actually blame volcanoes for CO2 levels in the air (see one of my other blogs for math that disproves that idea).  Rocks also absorb atmospheric CO2, which is delivered by rain when it absorbs it from the sky.  Chemical reactions are endlessly varied, and the rate of these reactions depends on temperature.  Therefore, the chemical makeup of the planet's rocks is critical.

Besides heat that breaks down chemical bonds, there is also radioactivity.  Earth's rocks have so much radioactive potassium in them that our atmosphere is nearly 1% argon, thanks to the fact that radioactive potassium degrades into argon.  Imagine what other strange rocks could exist on other rocky bodies.  The possibilities are endless, seeing as how the periodic table of the elements is so vast.

periodic table of the elements


A planet needs a daily rotation to avoid long, hot days, long cold nights, and mountain-eroding winds on the terminator line.  Earth and Mars have a 24 hour day, but that's it.  Mercury and Venus have days that are huge fractions of their year.

Earth's magnetosphere and the Sun's radiation


A planet also needs a magnetic field to protect it's atmosphere from the solar wind, which strips away enough of it so that after billions of years of evolution there isn't enough to live on.  As mentioned earlier, Venus' water was destroyed by solar radiation, the hydrogen escaped the planet's gravity, as it would on Earth.   Mars' atmosphere was stripped away, as mentioned earlier, it's 10 times thinner than the top of Mount Everest.

Mars' surface rocks have weak magnetic fields, indicating that Mars had a hot core and planet-sized magnetic field at one point in time.  However, it has since cooled.  Ganymede is the only satellite in the solar system with a magnetic field, attributed to an iron and silicate based core that is kept hot by tidal forces from Io, Europa and Jupiter.  Triton orbits Neptune, and has a surface that indicates interior heating.  This heat is assumed to come from radioactive rocks in it's core.

Earth's magnetic field is thought to be thanks to a core with plenty of uranium and other radioactive elements, plus a lot of mass in the form of nickel and iron to reduce cooling and increase heat capacity.  Thanks to Theia's sacrifice, the Eath's core is plenty big and hot.  These theories make sense, because Earth's density is so great that it has 5% more mass than Venus, Mercury and Mars combined, despite the fact that Venus is only 87 miles smaller than the Earth.  What are the odds that the Earth ended up with all that uranium and mass, but the other rocky bodies did not?  Looking at a statistical bell curve, our inner solar system probably lies near one end (but not AT the end).  We're talking 5% to 10% odds just for the mass alone, not the uranium.

Planet      Mass (kg)  Satellite     Mass (kg)
Mercury  3.28E23         --             --
Venus     4.82E24          --             --
Earth       5.98E24     Moon        7.36E22
Mars       6.34E23     Phobos      2.72E16
                                 Deimos      1.8E15   
(Earth+Moon) / (Mercury+Venus+Mars+Phobos+Deimos) = 1.05

Instruments show that there is a stream of particles being blown away from Venus.  Earth just so happens to be in the firing line, and picks up any debris in it's path, including water and several tons of meteors a year.  It is possible that Venus was one day covered in enough water for life.  However, it may have been blown to Earth by the solar wind.  Therefore, the Earth cannot have been formed with the perfect amount of water, an 800 mile diameter ball.  It would have needed less, perhaps a 700 mile ball.  And this means that a 100 mile shell-of-a-ball-of-water would have to be the exact amount captured by the Earth after it was blown off of Venus for billions of years.

A star is born inside nebula LDN43, a blob of ice, dust and gas.


Mercury's early atmosphere would also have been blown to the Earth, and even more of it to Venus.  Why would Mercury have had an atmosphere, being too small to have enough gravity, and too hot due to it's vicinity to the Sun?

Actual image of a protoplanetary disc with planets clearing their orbits of debris.
Proof that planets form before the star ignites.

Because the Kepler mission is finding many exoplanets orbiting other stars.  These are almost entirely huge gas giants orbiting closer than Earth's orbit, and many closer than Mars' orbit.  Because all star systems that Kepler has looked at are this way, it stands to reason that our solar system started out the same way.  The solar wind and heat blow away all this gas, leaving rocky bodies with a small amount of gasses and liquids, an amount dependent on their distance from the star, the heat retained, their gravity, and the strength of their magnetic field.  This may explain all the icy bodies further out from Mars' orbit, including the asteroid belt.  Water is blown outward, then freezes.

This also explains why there is still so much interstellar hydrogen 13.7 trillion years after the Big Bang.  Every newborn star destroys all the water molecules in the primordial dust cloud surrounding it, sending the hydrogen away.

Artist's rendering of a protplanetary disc where the star ignites before the planets form.


The combination of qualities of the Earth is not the only coincidental thing.  The combination of qualities of the other planets also matter, from nearby gas giants evaporated by their star, to a Theia sized planet giving rise to a large Moon.  And the planet's qualities must match the star's output, such as Earth's nitrogen/CO2 atmosphere matching the Sun's heat and the Earth's orbital radius in the habitable zone.

The habitable zone of a star is not the only necessity.  The galaxy also has a habitable zone.  Who's to say that a region of the Milky Way has had enough super novae to have created an abundance of uranium in a small enough area, to create a large enough concentration, to create one planet out of dozens with a hot core?  

I say the odds of many of these qualities is on the order of 1 in a trillion.  That's a 1 followed by 12 zeros.  Multiply that by the next quality.  A trillion times a trillion.   That's 24 zeros.  Why multiply them?  Because the odds of rolling a 7 on a die is 1 out of 6.  But the odds of rolling two 7's with two dice is 1 out of 36.

The odds of rolling three 5's is 1/6th cubed, which equals 1 of 216 rolls.

I believe the odds of Theia being right, uranium being right, and nitrogen/CO2/rocks/orbit being right are each 1 in a trillion.  Multiply them and you get 36 zeros.  These three alone create long odds of 1 in an eleven-zillion, formally known as undecillion.
one trillion = 1,000,000,000,000

one trillion cubed = 1,000,000,000,000,000,000,000,000,000,000,000,000
= 1 undecillion

Seeing as how there are only 200 billion stars in an average galaxy, and only 200 billion known galaxies, that's a total of 40 sextillion stars.  And one undecillion divided by 40 sextillion is 25 trillion.

200 billion squared = 40 sextillion
200,000,000,000 x 200,000,000,000
= 40,000,000,000,000,000,000,000

1 undecillion / 40 septillion = 25,000,000,000,000

The Universe is shy by a factor of 25 trillion.  In other words, if there were 25 trillion universes, there would be only 2 Earths.  I can honestly stop donating money to SETI, the Search for Extra-Terrestrial Intelligence.

This means we all have to get along, because we are all we got.  We also need to develop our own science to travel the stars.  ET is not coming to help.   (As if!)


. said...

Very good math, kind of answers the Fermi paradox :)

What would help confirm this all is if we had actual data on the amount of water on planets orbiting a nearby star.

WoodHugger said...

I look forward to finding out what the exo-planets are made of. Maybe one or two telescope generations away.