Wednesday, December 21, 2011

The Planetary Parade Continues

News of NASA's Kepler's telescope and its planetary findings continues to fascinate many, as more and more Earth-like planets are reported. Most recently, astronomers have reported for the first time the discovery of two Earth-sized planets, one of which (Kepler 20f) is almost the exact same size as Earth, and the other (Kepler 20e) is about 4/5 its radius. The pair were discovered between three much brighter planets orbiting a star designated as Kepler 20 in a solar system 1,000 light year distant. That means its light has taken 1,000 years to reach us and also when Kepler observes these planets now, or their sun, it is seeing them as they were in our year of 1011, when the Inquisition was barely being planned and no printed books yet existed.

On the downside, both planets appear much too hot to expect the emergence of any Earth-type carbon based life, and they may lack water or a normal atmosphere as well. Kepler 20f 's orbit is so near its star that its year lasts only 19.5 days or 0.053 Earth years. Using Kepler's 3rd law this leads to a distance of only about 0.14 AU or 13 million miles. By comparison with our system, the planet Mercury is about 36 million miles from the Sun and parts of its surface are hot enough to melt lead! Meanwhile, Kepler 20e is so close that its period is only 6.1 days or 0.017 yrs. so its distance works out to slightly over 6 mllion miles. Roast much?

Despite the unearthly conditions, Kepler astronomers are still confident that they will eventually detect one or more worlds that have very nearly Earth-like conditions as well as physical properties. After all, the odds are with them. Kepler is designed (see graphic attached) with ultra-sensitive photometers - to detect and analyze the slightest light variations- to look for any planets around 156,000 stars orbiting within 3,000 light years.

As the graphic shows, the craft can determine a number of key parameters, including:

- Planet size (from how much the light of the star dims when the planet passes in front)

we call this the "light curve" during partial eclipse and use it also for binary stars along with radial velocity curves, see e.g.

- - The size of the planet's orbit - calculated by the interval between dips of light during the "eclipse"

- The planet's temperature, computed from the orbital size (e.g. using semi-major axis a) and the temperature of its star (found from its spectrum)

Say the given planet is found to reflect a certain fraction A of light from its star, and hence must absorb (1- A) and that the "solar constant" of the star (amount of radiation arriving at the planet) is k, then the energy absorbed would be:

E(A) = (1 - A) πR^2 x k/ a^2

where R is the radius and a the mean distance from its star

Setting this equal to the stellar luminosity:

(1 - A) πR^2 x k/ a^2 = 4 π R^2 oT^4

enables one to work out the effective temperature T, where o = 5.67 x 10^-8 Wm^-2 K^-4, the Stefan-Boltzmann constant). Then:

T = {(1 - A) x k/ 4π a^2x o}^¼

- The star's surface temperature, meanwhile, was discussed in a previous blog in conjunction with its luminosity, e.g.

The good news is more than 2,000 so-called exoplanets have been found. The bad news is we are still looking for that specific Earth-type planet that not only possesses similar gravity and size, mass, but also the distance from its star to put it in the 'Goldilocks zone" for life as we know it.

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