IAL 18: Exoplanets & General Planetary Systems

Don't Panic

Sections

1. Worlds Without End
2. Life
3. History
4. Discovery
5. Statistics
6. The Kepler Spacecraft (2009--2018)
7. The Habitable Zone
8. A Few Classes of Planets
9. Exomoons
10. Future
11. Amazing Stories

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Worlds Without End

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Planets outside of the Solar System are called exoplanets, or more longwindedly, extrasolar planets.

We often just call them planets when we know what we are talking about---and to include Solar System planets too---they are all in the same category nowadays.

There is short introduction to planet types in the figure below (local link / general link: planet_types.html).

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Not so long ago---before 1992, in fact---there were NO known exoplanets.

There are now thousands of known planetary systems exoplanets: see The Extrasolar Planets Encyclopaedia: Interactive Extra-solar Planets Catalog, for the current discovery statistics and see the first video in Exoplanet videos below (local link / general link: exoplanet_videos.html).

The number of known planetary systems and exoplanets keeps growing.

EOF

Our statistics show that exoplanets are to order of magnitude as common as stars (e.g., Dressing & Charboneau 2013)---and this is everywhere in the observable universe.

True, we have only sampled a tiny fraction of Milky Way so far, but the homogeneity of the observable universe implies worlds without end.

For amazing worlds, see the figure below (local link / general link: amazing_stories_super_scifi_1957.html).

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In fact, we---we in a vague sense---always suspected "worlds without end" since the 18th century, even 16th century by a few---and so the universality of planets---the plurality of worlds---is no surprise.

However, we were NOT able predict the range of types of planets and planetary systems.

We tended to think of the Solar System as typical or average for planetary systems even though we knew this It Ain't Necessarily So.

Well the Solar System is typical in some respects---planets tend to orbit in a plane, planets formed out of protoplanetary disks---and NOT in others---gas giants in very small orbits close to their host stars and planets with very eccentric orbits, and super-Earths and ...

Partially, our imagination was NOT stimulated without data----now it is stimulated.

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Life

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Of course, planets are just the leftover slop from star formation.

The total mass in planets and smaller planetary system bodies (e.g., planetesimals, moons, meteoroids, etc.) must be tiny.

In the Solar System---the prototype planetary system---the total mass NOT in the Sun is calculated to be 0.0014 (i.e., 0.14 %) solar masses (see Wikipedia: Solar System).

This factoid is graphically illustrated in the figure below (local link / general link: planet_sun.html) where the gas giant planets are compared to the Sun.

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Of course in the observable universe, the fraction of non-star mass in planetary systems probably varies wildly from planetary system to planetary system, but it is likely to be usually much less than 1 %.

In the evolution of the bulk universe, the role of planetary systems is minute.

About all that planetary systems do in the evolution of the bulk universe is that in every generation of stars some matter must get quasi-permanently locked up into planets and smaller planetary system bodies. This matter is thus removed permanently from cycle of star formation, star life, and star death.

But far more matter gets locked up quasi-permanently into compact remnants: white dwarfs, neutron stars, and black holes.

Of course, some planetary system bodies get evaporated by their host stars when their host stars expand in their red giant phase or asymptotic red giant phase.

We use the word "quasi-permanently" above because extrapolating to the far future it is possible that protons and black holes will both vanish (see Wikipedia: Graphical timeline from Big Bang to Heat Death). Currently, the observable universe is at cosmic time 13.8 Gyr = 13.8*10**9 years after the Big Bang. At of order cosmic time 10**(10**160) years protons hypothetically will have decayed (see Wikipedia: Proton decay) and the only non-particle objects left in the universe will be black holes. At of order cosmic time 10**(10**200) years even the most massive black holes hypothetically will have evaporated due to Hawking radiation. Then only particles will be left: photons, electrons, positrons, neutrinos, and exotic dark matter particles. This is the hypothetical dark era which may be the last phase of the heat death of the universe.

This scenario of the far future is highly speculative. Our cosmological theories are uncertain.

The upshot of the cosmological insignificance of planets is that if planets did NOT exist, cosmologists would NOT have to invent them.

So why do we care about planets?

Well, we live on one.

But why about other planets?

Cosmological importance is NOT everything.

Complexity counts with us---we are fascinated with our own complexity.

Note that stars and galaxies are actually rather simple by comparison say to a unicellular organism. See the figure below (local link / general link: prokaryote_cell.html).

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Life counts with us---consciousness counts with us.

One can say that consciousness likes consciousness---and that aphorism may be a key component in the meaning of everything and the basis of ethics---but yours truly wouldn't know.

Let's NOT get into what consciousness really is---or free will.

But what of the dog in your brain. See the figure below (local link / general link: neural_consciousness.html).

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Perhaps just because of the limits of our intelligence, we CANNOT understand how life can exist---or at least come into existence---that is very different from Earth life.

What is most basic for life as we know it?

1. There have to be Molecules:

   There have to be molecules.

   Life as we know it is complex by its nature.

   We might even say that nothing simple can be life by any definition we could accept.

   But molecules do NOT form unless the temperature is low enough and the density high enough.

   If the temperature is too high chemical bonds do NOT form.

   Many stars are too hot throughout for molecules.

   Some are cool enough on the surface to have simple molecules, but NOT the complex molecules of life.

   The complex molecules are organic molecules (see below subsection There Must Carbon).

   If density is too low, the equilibrium state even of cold matter does NOT allow molecules.

   There regions of interstellar medium (ISM), where the density is high enough for organic molecules and many kinds of organic molecule do exist there. These are regions molecular clouds in which star formation occurs (see IAL 21: Star Formation).

   People have speculated that some kind of life may be possible in those dense interstellar medium (ISM).

   One was the important astrophysicist Fred Hoyle (1915--2000) in his scifi book The Black Cloud (1957).

   But liquid water is missing---and that seems a necessity (see below subsection There Has to Be Liquid Water).

2. There Must Carbon:

   There must carbon.

   Organic molecules are molecules that contain carbon by definition whether they are biotic or NOT.

   But biotic molecules must be based on carbon to our understanding because carbon is the only atom out of the whole periodic table (see figure below: local link / general link: periodic_table.html) that forms complex molecules (see example DNA molecule in the second figure below: local link / general link: dna_rotating.html) which are essential for life as we know it.

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3. There Has to Be Liquid Water:

   There has to be liquid water.

   Life as we know it requires liquid water.

   Links:

   1. Water drop animation
   2. Hopetoun Falls image
   3. Ein Gedi oasis image
   4. Amoeba image
   5. The Blue Marble: See the figure below (local link / general link: earth_blue_marble.html).

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   It is the substance in which all basic life processes happen.

   Liquid water is a remarkable substance in many ways and some of those ways are clearly necessary for life as we know it:

   1. It is liquid, and so it allows free motion with low viscosity (i.e., fluid friction).

      The molecules necessary for life have to be moved around.

   2. It is NOT a gas, and so it doesn't change size much with compression (i.e., nearly incompressible) and it doesn't undergo free expansion.

      For life would be tricky if the smallest leak and it deflated.

   3. It is a remarkable solvent that dissolves many chemicals, and so premits them to mingle and interact with each other and many molecules.???

   And by mass, life as we know it is mostly liquid water. Human body water is typically about 60 % of human body mass.

   Life simply took the ocean when it evolved to live outside of a liquid water environment.

   "You can take the buoy out of the ocean, but you can't take the ocean out of the boy."

   But liquid water exists only in a very narrow range of thermodynamic conditions as illustrated in the figure below (local link / general link: phase_diagram_water.html).

   So life as we know it can only exist in a very narrow range of thermodynamic conditions. The defined habitable zone seems most likely place for those conditions as we discuss below in section The Habitable Zone.

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History

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See the imaginative portrait of Democritus (c.460--c.370 BCE) in the figure below (local link / general link: democritus.html).

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For the atomist cosmology, see the figure below (local link / general link: cosmology_atomist.html).

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With advent of Copernicanism, the idea of cosmic pluralism (AKA plurality of worlds) soon occurred to people like Thomas Digges (1546--1595) and Giordano Bruno (1548--1600). See Digges conception of the observable universe in the figure below (local link / general link: copernican_cosmos_digges.html).

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For Giordano Bruno (1548--1600), see the figure below (local link / general link: giordano_bruno.html).

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Discovery

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There are many methods of detecting exoplanets.

Some of them are only methods in principle since these ones have NOT detected a planet yet.

Several methods have detected planets---some lots of planets, some only a few planets.

The most straightforward method is direct imaging.

But planets are small and dim compared to host stars, and so this method NOT easy.

It has only 19 discoveries of planetary systems circa 2018. This only ∼ 0.7 % of all confirmed planetary systems discovered circa 2013.

Although the number of discoveries by direct imaging will increase with time, the faction of discoveries by direct imaging is always likely to remain tiny.

Of course, direct imaging is important since it gives information other methods do NOT.

But we won't consider direct imaging further here---we can't do everything.

We will discuss the two main methods of detecting exoplanets: Doppler spectroscopy and the transit method.

1. Doppler Spectroscopy:

   Doppler spectroscopy (AkA the radial velocity method or the wobble method) is the same method used for discovering spectroscopic binary star systems and other multiple star systems.

   The time-varying and periodic Doppler shift of the spectral lines in a stellar spectrum proves that there are two or more stars---after you have ruled out other causes of Doppler shifts such as stellar pulsations.

   But discovering planets is harder than discovering that a star-like source in a spectroscopic binary.

   First of all, almost always no light is observable from the planet, and so almost always there is no detected planet spectrum.

   The planet is just far too faint in most cases.

   So you usually only see the host star's spectrum Doppler shifting.

   Second of all, the Doppler shift of the host star is tiny for planet companions---as we will now explain.

   Two astro-bodies orbiting each other both actually orbit their common center of mass which is their mass-weighted mean position.

   If the astro-bodies are equal in mass, they both move the same amount. See the figure below (local link / general link: orbit_elliptical_equal_mass.html).

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   But if one increases the mass difference from zero, the more massive astro-body moves relatively less. See the figure below (local link / general link: orbit_circular_large_mass_difference.html).

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   Binar stars will typically have Doppler shifts resulting from velocities of order tens of KILOMETERS per second.

   These are large Doppler shifts that are easy to measure.

   Host stars of planets will typically have Doppler shifts resulting from velocities of order METERS per second executed by the host stars.

   These are minute Doppler shifts.

   The techniques needed to measure accurately such minute Doppler shifts have only been developed since circa 1990.

   The first definitive discovery of an exoplanet by Doppler spectroscopy was 51 Pegasi b in 1995 by Michel Mayor (1942--) and Didier Queloz (1966--).

   The first definitive discovery of exoplanets was of two pulsar planets (exoplanets that orbit a pulsar) in 1992 by the pulsar timing method.

   Pulsar planets probably form from a protoplanetary disk of debris from the core collapse supernova that left the pulsar (a rapidly rotating neutron star that emits strong, very regularly periodic radio pulses) as a compact remnant.

   Pulsar planets are very unlikely to have life as we know it.

   The Doppler spectroscopy method. is illustrated in the figure below (local link / general link: doppler_spectroscopy_method.html).

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   For an exoplanet from Doppler spectroscopy, one can in the best cases determine a lower limit on mass and two orbital elements semi-major axis (AKA mean orbital radius) and eccentricity.

   Re mass, what is directly measured is M_limit=M*sin(θ), where M is the exoplanet mass itself and θ inclination of the orbital axis to the line of sight to Earth.

   Now M_limit ≤ M since sin(θ) ≤ 1 always.

   But θ is usually unknown.

   Thus, one usually can find the lower limit on mass M_limit, but NOT mass M itself.

   The lower limit goes to 0 when θ goes to 0°---which is a rather useless lower limit.

   This is because Doppler shifts are only caused by the radial velocity (i.e., velocity component along the line of sight) and NOT the velocity component perpendicular to the line of sight.

   So Doppler spectroscopy fails for θ=0°, is viable for θ > 0°, improves as θ increases all other things being equal (since the host star along the line of sight increases all other things being equal), and best for θ=90° all other things being equal.

   In the case of θ ≅ 90°, the transit method (the other one of the two main methods of detecting exoplanets) becomes viable.

   Being able to detect the planet by both main methods is a very good case since then we get complementary information and improved accuracy.

   Say we had that very good case.

   The transit method provides the radius of the exoplanet which Doppler spectroscopy does NOT.

   It shows that the inclination is nearly 90°, thus that M_limit ≅ M.

   It also allows improvement in the determination of the orbital elements and in some cases permits absorption spectroscopy which gives some information about the exoplanet atmosphere composition (see Wikipedia: Exoplanet: Atmosphere).

   There are three detection biases for Doppler spectroscopy:

   1. The Doppler shift increases (and therefore detection and analysis improve) inclination increases from 0° to 90° all other things being equal as discussed above. So planetary system observed nearer to edge-on are favored over planetary system observed nearer to face-on.

   2. The more massive the exoplanet, the greater orbital velocity of the host star all other things being equal. The greater orbital velocity, the greater the Doppler shift and the better detection and analysis. So massive exoplanets are favored over less massive exoplanets.

   3. The smaller the mean orbital radius of the planet, the shorter the orbital period all other things being equal in obedience to Kepler's 3rd law. This make the periodic Doppler shift is to detect---it is easier to notice a period Doppler shift with a period of days than one with a period of years.

   The last to two biases strongly favor the detection of massive planets close to their host stars.

   As we will see below, the transit method has similar same biases as Doppler spectroscopy.

   So both main methods of detecting exoplanets end up being biased toward massive planets close to their host stars.

   So the distribution of detected planets is biased toward massive planets close to their host stars.

   Corrections with some uncertainty must be made to attempt to find the real distribution of planets in the universe.

   Making corrections is ongoing work in which we can expect only gradual improvement.

2. The Transit Method:

   The transit method is ????

   The first exoplanet (called HD 209458 b) discovered by the transit method was in 1999 by two independent teams.

   One team was led by Greg Henry of Tennessee State University in Nashville.

   As it happens, I'd met Greg Henry before 1999 when I was Vanderbilt University in Nashville.

   And in 1999, I was just down road in Murfreesboro, Tennessee working at Middle Tennesse State University.

   So I invited Greg down to give a talk on his discovery---in those good old days, if you discovered a planet, the world would beat a path to your door---NOT like now when new planets are dime a dozen.

   The transit method is explicated in the figure below (local link / general link: transit_method.html).

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   The transits of Venus are explicated in the figure below.

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   Caption: "Diagram showing how transits of Venus occur and why they don't occur frequently."

   We will now explicate the caption.

   In order for any astronomical transit to be observed, the orbit has to be nearly edge-on to the observer's line of sight.

   In other words, its inclination relative to the line of sight must be nearly 90°.

   In general, inclination is the angle between the axis perpendicular to an orbit and a reference axis.

   For Solar System orbits, the reference axis is conventionally the ecliptic axis.

   For orbits outside of the Solar System (e.g., exoplanets and multiple-star systems), the reference axis is conventionally the line of sight from the Earth to the system of the orbit.

   How close to 90° does the inclination have to be?

   This depends on the sizes of the transited object and transiting object relative to the distance between them.

   A little trigonometry shows that that for a remote observer (one to whom rays from the two ojects are approximately parallel), shows for even a marginal transit (i.e., one where the limbs of objects just touch) that

        sin(90-θ) ≤  (r_1+r_2)/R  ,
   
          where θ is inclination,
            r_1 is the radius of the transited object,
            r_2 is the radius of the transiting object,
            and R is the their center-to-center distance.
                

   For a full transit (i.e, one where the transiting object is seen completely circumscribed by transited object),

        sin(90-θ) ≤  (r_1+r_2)/R  ,
   
          where θ is inclination,
            r_1 is the radius of the transited object,
            r_2 is the radius of the transiting object,
            and R is the their center-to-center distance.  

   For a full transit (i.e, one where the transiting object is seen completely circumscribed by transited object),

     sin(90-θ) ≤  (r_1-r_2)/R  ,
   
       where we have assumed that r_2 ≤ r_1.  

   If one assumes, (r_1+r_2)/R << 1, then the two formulae above reduce respectively to

     90-θ ≤  [(r_1+r_2)/R]*(180/π)  and  90-θ ≤  [(r_1-r_2)/R]*(180/π) ,
   
       where the factor (180/π) is needed to convert radians
          to degrees.  

   For transits of Venus observed from the Earth, our formulae to NOT apply since the Sun and Venus are NOT sufficiently remote for rays from them to be regarded as approximately parallel.

   But say an observer is located on ecliptic plane in the outer Solar System well beyond the orbit of Jupiter. There, we could regard the rays as approximately parallel.

   Now for the Sun and Venus,

   
     [(r_1+r_2)/R]*(180/π) = 0.37192° and [(r_1-r_2)/R]*(180/π) = 0.36551°  .  

   These angles are much smaller than Venus orbital axis's inclination to the ecliptic axis.

   This means---if you are still following---that transits of Venus can only occur when Venus simultaneously is very near the ecliptic plane and nearly on the line of sight to the observer.

   The transit-of-Venus situation happens rarely for remote observer.

   Our quantitative analysis does NOT apply for an observer on Earth, but the qualitative conclusion is the same: transits of Venus will rarely be observed from Earth.

   To make a long story short is the point of the image, in fact.

   Transits of Venus (as observed from the Earth) occur in pairs separated by about 8 years with the midpoint times of the pairs being separated by about 121.5 years.

   Why this peculiar cycle?

   To be vague, pretty much all Solar System patterns for the larger astro-bodies approximately repeat in some more or less complicated cycle.

   The cycles are actually all approximate because the Solar System is slowly evolving in a chaotic fashion.

   The last pair were the Transit of Venus, 2004 and Transit of Venus, 2012. Sorry you missed them.

   The next pair occur in 2117 and 2125. Sorry you will miss them.

   Credit/Permission: © User:Theresa Knott, 2004 (uploaded to Wikipedia by Kjetil Ree (AKA User:Kjetil_r), 2007 / Creative Commons CC BY-SA 2.5.
   Image link: Wikipedia: File:Transit diagram angles.png.
   

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   The transit method applied to close binary star systems is easy. See the animation in the figure below (local link / general link: star_binary_eclipsing.html).

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Group Activity:

Form groups of 2 or 3---NOT more---and tackle Homework 16 problems 11--14 on target Earth.

OR

Form groups of 2 or 3---NOT more---and tackle Homework 31 problems 15--20 on cosmology, the Λ-CDM model, Big Bang cosmology, and inflation cosmology.

Discuss each problem and come to a group answer.

Let's work for 5 or so minutes.

The winners get chocolates.

See Solutions 16 or Solutions 31.

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Statistics

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"There are lies, there are darned lies, and then there are statistics."
---attributed to Benjamin Disraeli (1804--1881) by Mark Twain (1835--1910) (see Wikipedia: Lies, darned lies, and statistics) and quoted here from Pollyanna (1913). Yours truly always thought the quote was from Winston Churchill (1874--1965) who is remotely related to Caryl Churchill (1938--).

Some of the statistics for confirmed exoplanets are given in the figure below (local link / general link: planet_statistics.html).

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Group Activity:

Form groups of 2 or 3---NOT more---and tackle Homework 16 problems 11--14 on target Earth.

OR

Form groups of 2 or 3---NOT more---and tackle Homework 31 problems 15--20 on cosmology, the Λ-CDM model, Big Bang cosmology, and inflation cosmology.

Discuss each problem and come to a group answer.

Let's work for 5 or so minutes.

The winners get chocolates.

See Solutions 16 or Solutions 31.

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The Kepler Spacecraft (2009--2018)

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The Kepler spacecraft (2009--2018) is a NASA spacecraft (with an optical telescope) in orbit around the Sun launched 2009 Mar07---on an extended-to-2018 mission to search out strange new worlds.

The failure of reaction wheel on 2013 May15 ended Kepler's main mission. The reaction wheels help point Kepler.

However, the NASA folks found a a workaround and Kepler is now in a second mission called K2, Second Light with interesting results.

Kepler is named in honor of Johannes Kepler (1571--1630), famous for his 3 laws of planetary motion and other works. See Johannes Kepler (1571--1630) in the figure below (local link / general link: kepler_portrait.html).

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Kepler uses the transit method. For explication, see subsection The Transit Method.

Kepler (i.e., the spacecraft) has been a revolution---yes another one---in the discovery of exoplanets, enormously increasing the number of them, confirmed and candidate, since 2009. See the Kepler spacecraft (2009--2018) in artist's conception in the figure below (local link / general link: kepler_spacecraft.html).

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The Kepler mission basic specifications are:

1. Mission period: main mission: 2009 Mar07--2013; K2, Second Light 2013--present
2. Orbital period 372.5 days.
3. Mean orbital radius 1.013 astronomical units (AU). Its orbit is a circular orbit or nearly that.
4. Mass 1039 kg.
5. Length? Seems about 4.5 m.
6. Aperture 0.95 m. This is the real light-gathering power diameter.
7. Primary mirror 1.4 m. At time of launch (2009), this was the largest primary mirror on a space observatory NOT in a geocentric orbit.
8. Field of view (FOV) area 115 square degrees which corresponds a mean FOV diameter (115)**(1/2) degrees ≅ 10° ≅ 1 fist at arm's length.
9. FOV center in Cygnus constellation which is roughly in the Sun direction of motion in the Milky Way. This means the Kepler target stars are at nearly the same Galactic radius at the Sun. This might be an advantage for planetary habitability---we're there after all---the good old anthropic principle at work (see IAL 0: A Philosophical and Historical Introduction to Astronomy: The Anthropic Principle). Also the radial velocity of the Kepler target stars is very small---they are moving at close to the same velocity as the Sun. This may reduce complications in doing Doppler spectroscopy: the mean Doppler shifts will be close to zero.
10. Wavelength range 400--865 nm = 0.400--0.856 μm. The range nearly covers visible band (roughly 0.380--0.750 μm) and extends a little way into the near infrared (roughly 0.75--1.4 μm).

Why is Kepler NOT in a geocentric orbit?

To avoid occultation by Earth and Moon.

Why does Kepler point just one way in the sky?

Cheapness. Kepler was designed to do just one mission and do it well for low cost. So no complicated slewing processes.

Links:

1. Kepler Interior
2. Kepler orbit
3. Milky Way map
4. Kepler's target region in the Milky Way
5. Orion Arm Our neighborhood
6. Kepler Field of View
7. Kepler Field of View close up

The main science goals of Kepler were:

1. To find lots of exoplanets. Of order a few thousands.
2. To find planet orbital elements: mean orbital radius, orbital period, and eccentricity (if possible).
3. To determine the exoplanet radii.
4. To characterize planetary systems insofar as possible.
5. To help determine distribution of the planetary systems by various characteristics.
6. To find planets in the habitable zone---Goldilocks planets which could potentially host life as we know it.
7. To find exomoons if it gets lucky.
8. To find targets for future research. Everything is grist for the mill of future research, of course.

We have to use past-tense for Kepler since it had a mechanical that ended its main mission in 2013.

Kepler has been given an new mission called K2 which it can carry out in its disabled state. It still hunts for exoplanets.

The main mission results of Kepler:

Links:

1. Confirmed Planets 1031, Planet Candidates 4696, small habitable zone planets confirmed 12 (see Kepler main page middle right). Recall Kepler observed than 14500 stars, but only a small fraction of those stars have planetary systems with orbital axes sufficiently perpendicular to the line of sight (or orbital plane sufficiently edge-on) to exhibit transits. So one expected thousands, but NOT tens of thousands of exoplanet discoveries.
2. Candidate planet radius versus orbital period: Mostly big planets, of course.
3. Candidate planet frequency versus radius
4. Candidate planet size and temperature: Dead link.
5. Exoplanet populatiions for various compositions
6. Light curves for transits of multiple planets: Dead link.
7. Kepler habitable zoneplanets
8. Kelper 62 system with habitable zone Dead link.
9. Kelper 186 system with habitable zone
10. Moon size planet, Moon-like artist's conception: Dead link.
11. Artist's conception: Double-sun planet
12. artist's conception: A view from a habitable exomoon: Dead link. The gas giant will always have the same position in the sky from the location of the scene since the exomoon will be tidally locked to it. There will be day and night, of course.
13. Kepler Gallery

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The Habitable Zone

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The habitable zone and planetary habitability. See the figure below.

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Caption: A diagram illustrating how the center of the habitable zone varies with host star luminosity.

The diagram is NOT to scale.

Host star luminosity is given on the vertical axis in units of solar luminosity. The radius coordinate from Host star is given on the horizontal axis in astronomical units (AU).

The habitable zone center is indicated by patches with the radius from the host star inscribed in them in AU.

The Solar System is schematically illustrated for a host star of solar luminosity: i.e., of luminosity 1 L_☉ = 3.828*10**26 W.

We can derive an approximate formula for calculating the habitable zone center radius.

The radiative flux (power per unit area or energy per unit area per unit time) from the star is given by the formula

  F = L/(4π r**2)  ,

       where L is luminosity
       and r is distance from the star.  

Now based on anthropic principle (AKA humankind chauvinism; see IAL 0: A Philosophical and Historical Introduction to Astronomy: The Anthropic Principle), we can estimate that for life as we know it F must be approximately the solar constant F_☉.

We will take solar luminosity L_☉ and solar constant F_☉ as fiducial values.

We find the center of the habitable zone should be given by approximately

    r_habitable zone
         ≅ [L/(4π F)]**(1/2)
         = 1.000 AU * (L/L_☉)**(1/2)/[(F/F_☉)**(1/2)]  ,

           which based on the anthropic principle
           that F/F_☉ ≅ 1 is about right.  

So the habitable zone center radius should scale as L**(1/2).

The habitable zone covers a range in radius because a habitable planet could have a "stellar constant" a bit different from our solar constant, because of the varying size the greenhouse effect, and because of other subtle factors.

The habitable zone limits are defined the range of conditions that allow liquid water.

There are arguments that suggest that habitable zone defined this way is too restrictive.

There might be exoplanet or exomoon conditions that allow life as we know it well outside of the defined habitable zone.

Credit/Permission: © User:Chewie, 2009 (uploaded to Wikipedia by Ignacio Javier Rodriguez (AKA User:User:Ignacio Javier Igjav(, 2009) / Creative Commons CC BY-SA 3.0.
Image link: Wikipedia: File:Habitable zone - HZ.png.


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Links:

1. Solar habitable zone
2. Life may need a magnetosphere
3. Habitable zone chart for M<M_☉
4. Life beyond the habitable zone: Titan: Titan's atmosphere is 98.4 % nitrogen (N_2), 1.4 % methane (CH_4), 0.1--0.2 % molecular hydrogen (H_2), and traces of other gases. Titan has lakes with a composition mainly of ethane (C_2H_6) with some methane (CH_4), and other organic molecule fluids. It probably rains methane (CH_4) on Titan (see Wikipedia: Titan: Climate). There is speculation of non-water-based life on Titan. Wikipedia: Titan: Atmosphere
5. Life beyond the habitable zone: Europa
6. Rare Earth hypothesis

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A Few Classes of Planets

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Planet types: See the figure below (local link / general link: exoplanet_populations.html).

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Exomoons

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moon habitability

For an artist's conception of a habitable exomoon, see the figure below (local link / general link: exomoon_habitable.html).

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Future

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More exoplanets.

Wikipedia: List of exoplanet search projects

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Amazing Stories

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Amazing Stories: See the insert below (local link / general link: amazing_stories_zartlich_twelver.html).

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