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(11b)  Alien Planets


9b. The Planets

9c. Copernicus
        to Galileo

10. Kepler's Laws

Kepler's Laws
        (For teachers)

10a. Scale of Solar Sys.

11. Graphs & Ellipses

11a .Ellipses & 1st Law

11b. Alien Planets

12. Second Law

12a. More on 2nd Law

  12b. Orbital Motion

12c. Venus transit (1)

12d. Venus transit (2)

12e. Venus transit (3)

Newtonian Mechanics

13. Free Fall

    Note: This additional web page replaces the end section of (#11a) "Ellipses and Kepler's First Law" on extrasolar planets, written in 2004. Much of the new material is from a colloquium 12-10-2010 by David Charbonneau of Harvard, one of the leaders of the search for new planets.

Refining the First Law

Kepler's first law was:

"The orbit of a planet is an ellipse, with the Sun at one focus"

Actually, this is not 100% accurate. Imagine the planet magically getting heavier and heavier, while the Sun is getting lighter and lighter. At some point both of them would be equally heavy: could we then say which is orbiting around which?

   To be fully accurate, the first law should have placed the focus of the orbital ellipse at the center of gravity of the planet-Sun system. (The center of gravity will be defined later, but intuitively, if the masses are very unequal, as with a planet and the Sun, it lies close to the center of the heavier object.) Because the Sun is so much heavier than the Mars, the effect on the orbit of Mars (which Kepler studied) was too small to be noted by him. Nevertheless, the Sun also moves in response to motions of its planets, and motions of this type have become an important tool in the search for planets outside the solar system.

   An Earth-sized planet orbiting a distant star would be far too dim to be seen with any earthly telescope, especially against the glare of its sun, the star itself. However, as the planet goes around the orbit, its star also moves in a mirror image orbit around the common center of gravity. It is a much smaller orbit and a much slower motion, because the center of gravity is very close to the center of that star (in the Earth-Sun system, it is inside the Sun), but it can still be detected by subtle variations of the starlight.


    Recently a few such planets have been found, but most are Jupiter-sized and none seems suitable for life. The search, however, goes on, and you can find out about its current status (and much more) on the Planet Quest web site of NASA's Jet Propulsion Lab (JPL). One recent discovery (15 April 1999) has been the system of upsilon Andromeda which appears to contain at least 3 planets. For another recent discovery associated with a distant planet, click here.

Planetary Transits         (added December 2010)

    In recent years a second mode of searching for planets has emerged: observing the transit of an "exoplanet" in front of its star, like the observed transit of Venus, and also its passage behind the star. Such events require the Sun-star line to pass close to the orbital plane of the planet, and since orbital planes are randomly oriented, only 1% or fewer were found with this property. When the planet passes in front of the star, the light output dips slightly, and with relatively big planets (or close orbits), this can be observed.

    This method has an important virtue: while the wiggle of an orbit depends on the mass of the planet (relative to that of the orbited star), the dimming depends on the size of the planet, the radius of the dark disk passing in front of the star. If both wiggle and dimming are observed, one can estimate both mass and radius (and hence volume) of the planet, and from those its density.

    That is very important for the search for habitable planets: life based on chemistry similar to life on Earth requires, not only temperature in (or near?) the range of liquid water, it also presumably needs a star with a well-defined surface, solid or maybe watery. Most planets observed so far have masses comparable to those of Jupiter and Saturn, and often are close to their star and too hot. Alien astronomers would have a hard time discovering Earth: because of the one-year orbital period, it would take many years of observation to analyze the orbital wiggle (which would also contain periodicities of other planets) and because Earth is so far from the Sun, the dimming during its transit is very very small.

    However, there also exist "M-class stars", dwarf stars maybe 20% the mass of the Sun and redder. Actually, at least close to us, there exist about 10 times such stars than Sun-size ones. Being smaller and dimmer than the Sun may not bar life - it just means that to be in the temperature range of liquid water, a planet must have a smaller orbit and shorter orbital period, factors which help track the wiggle and increase the chance of an orbit transiting the Sun-star line.

    The "Kepler" spacecraft, a 1-ton instrument sharing the Earth's orbit around the Sun, was launched March 7, 2009 to help detect and observe extra-solar planets, especially those with observable transits. It has a 95-cm telescope and extremely sensitive detectors, which can scan and resolve a section of the color spectrum. By observing the star while the planet passes behind it, one can get the pure spectrum of the star itself, and subtracting that from light with the planet offside gives (within limits) the spectral signature of the planet. The "Eearth" array, a battery of automated telescopes atop Mt.Hopkins, Arizona, scans a selections of M-type stars, searching for transiting planets.

    So far a small number has been found, including a relatively small planet which may be covered by ocean. Stay tuned.

Questions from Users:
***     Search for planets outside our solar system
      ***     SciFi world with short days and long nights
            ***     Life under stronger gravity

Next Stop: #12 Kepler's Second Law

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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   stargaze("at" symbol)phy6.org .

Last updated: 11 December 2010

Above is background material for archival reference only.

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