Re: Kepler and the plane of orbits


"McSwell" <maxwell@xxxxxxxxxxxxxx> wrote in message
news:1a7658c9-6ad7-4349-9f87-6a42dc429a51@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I have been looking for some discussion of the proportion of planets
that Kepler could detect, based on the plane of their orbits. I'm
sure this is discussed somewhere, but I can't find it.

If I'm understanding correctly, it's looking for what amounts to an
eclipse. The eclipse will always be partial (or more correctly,
annular). But it seems to me that the chance of seeing such an
eclipse at all will be very slim, because we will be out of the plane
of the planet's orbit in all but a small minority of cases. If I'm
thinking about this correctly, then an eclipse by the planet will only
happen if, from the planet's point of view, the Earth would be covered
up by the planet's star at a point in its orbit (the opposite point
from where the planet would eclipse its star). So if the planet is at
a distance from its star such that the star was one degree across
(i.e. twice the apparent size of the Sun from Earth), then the chance
that the star would eclipse the Earth at some point in the orbit is
1/180.

The number will vary, of course, with the distance of the planet from
its star, and the size of that star. That size and distance will be
within some limited range for a habitable planet (Kepler is designed,
of course, to see any planet with the right alignment, not just
habitable ones). But it seems that for planets in habitable zones,
the chance of us seeing the planet eclipse its star (or equivalently,
the planet seeing its star eclipse the Earth) is on the order of one
in a hundred, perhaps less. Meaning that Kepler could only detect
something like 1% of terrestrial-like planets that are out there.

Am I misunderstanding? Can someone point me to a discussion of this
issue?

Mike Maxwell

Transits by terrestrial planets produce a small change in a star's
brightness of about 1/10,000 (100 parts per million, ppm), lasting for 2 to
16 hours. This change must be absolutely periodic if it is caused by a
planet.
The Kepler Mission Design
For a planet to transit, as seen from our solar system, the orbit must be
lined up edgewise to us. The probability for an orbit to be properly aligned
is equal to the diameter of the star divided by the diameter of the orbit.
This is 0.5% for a planet in an Earth-like orbit about a solar-like star.
(For the giant planets discovered in four-day orbits, the alignment
probability is more like 10%.) In order to detect many planets one can not
just look at a few stars for transits or even a few hundred. One must look
at thousands of stars, even if Earth-like planets are common. If they are
rare, then one needs to look at many thousands to find even a few. Kepler
looks at 100,000 stars so that if Earths are rare, a null or near null
result would still be significant. If Earth-size planets are common then
Kepler should detect hundreds of them.

http://kepler.nasa.gov/about/

If you want a discussion, start here:
http://www.androcles01.pwp.blueyonder.co.uk/Algol/Algol.htm


.

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