Thursday, March 31, 2016

An Earthlike Planet

The press is full of the news that a new Earthlike planet, Kepler 452b, has been discovered by the revived Kepler planet-hunting spacecraft.  The discovery of a planet “much like Earth” garners more attention because the planet orbits in the so-called “Goldilocks zone” around its star, the range of distances within which water can exist as a liquid on its surface rather than only as ice or hot vapor.

Kepler 452b is 60% larger in diameter than Earth and is presumed to have Earthlike composition, although it is important to note that there is as yet no way of measuring its mass.  Nonetheless, the phrase “Earthlike world” has the press reeling, including suggestions that worlds like this are the places radio astronomers should look to find radio signals from intelligent aliens.

OK, let’s play this game and see what Earthlike composition would imply.  A diameter of 1.6 times Earth’s means a surface area of 1.6x1.6, or 2.56 times Earth’s, and a volume of 1.6x2.56, or 4.1 times Earth’s.  Assuming Earthlike material, this planet would have a core/mantle/crust structure very similar to Earth’s, but the internal pressures would of course be significantly higher, and the core and mantle material must be compressed to higher density than Earth’s average of 5.5 grams per cubic centimeter, probably close to 7.5 for the whole planet.  Now, that would generate a planet with 5.6 times Earth’s mass.  This mass and diameter would correspond to a surface gravity that is 5.6/2.56 times Earth, 2.18 times as large, or 21.4 meters/second2. 

“Similar composition” means similar abundances of radioactive elements, which decay inside the planet and eventually lose their heat by radiating heat from the planetary surface into space.  This planet, generating 5.6 times as much heat as Earth, which it radiates into space through a surface with area 2.56 times Earth’s, so the heat flux (Watts per square meter per second) is about 2.2 times Earth’s.  At steady state, with heat loss rate equal to heat production rate, this requires that the temperature gradient in the crust (the rate at which temperature increases with depth) must be 2.2 times as large as on Earth. 

Mountains can build up only to a finite height because the temperature gradient under them leads to softening and melting of the continental rock deep under them.  On Earth the Himalayas rise about 13 kilometers above the abyssal plains of the oceans.  Mars has half the radius of Earth, so its heat flow and temperature gradient should be about half that of Earth, meaning that softening of the rock should occur about twice as deep, and Martian mountains should build to about twice the height as on Earth.  In fact, the highest peak on Mars, Olympus Mons, rises about 26 km above the plains.  Of course, to calculate this precisely we need to account for the slightly lower density of Mars and its slightly lower surface temperature, but we still get a similar answer. 

Now let’s apply that to Kepler 452b.  The topography, Earth’s standard scaled down by a factor of 2.2, would have the highest mountain regions about 6 kilometers above the abyssal plains.  Now let’s think about the oceans on this world.  On Earth, there is enough water to make a layer about 4 km deep covering the entire planet.  Kepler 452b, if it has the same composition as Earth, would contain 5.6 times as much water spread out over a surface area that is 2.56 times as large.  Thus it would contain enough water to make a layer 2.56 times as deep as Earth’s 4 km, or about 10.2 km deep.  Since the highest land would rise about 6 km from the abyssal plains, this means that the tops of the highest mountains would lie roughly 4 km below mean sea level.  Thus Kepler 452b, if truly Earthlike in composition, would be a true water world.

Now consider the conditions on the sea floor.  An ocean 10.2 km deep in a gravity field of 2.2 Earth gravities would exert tremendous pressure at the ocean floor: the weight of the ocean exerts an average pressure of 2240 atmospheres, which is essentially the highest pressure at which pure liquid water can exist, irrespective of temperature.  At approximately this pressure, water freezes to make dense (sinking) ice III rather than familiar (floating) ice I.  Such an ocean could start to freeze from the bottom up.

We’re also told the planet has had liquid water for 6 billion years or more, without mentioning how the luminosity of its parent star (and the surface temperature of the planet) have changed over time.

Of course, with data on the mass of the planet we could see whether it really is a “terrestrial” planet or a sort of warmed-up ice ball: if the latter is the case, then the planet could be much less dense and the ocean much deeper.

So this is “Earth 2.0”? 

If you are interested in the wonderful game of designing planets that accord with the laws of physics, astronomy, and chemistry, you can find a number of examples in my 1998 book Worlds without End, which explores the possibilities for many types of planets allowed by nature, but not present in our Solar System.

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