“No pessimist ever discovered the secret of the stars, or sailed to an uncharted land, or opened a new doorway for the human spirit.” –Helen Keller
If you’ve been paying attention, you heard that the Kepler mission, earlier this week, announced the discovery of 706 candidate planets orbiting stars in its field of view.
And while most of the planets it found were Neptune-sized or smaller, they were still mostly gas giants, and still mostly closer than Mercury to their parent stars. Kepler’s looking at 100,000 stars, and while finding 706 planets is certainly not bad for just over a month’s work, there’s a big question to be asked.
Where are the planetary systems like ours?
To answer that, I’ll run through a little hypothetical analysis with you. What if one of the stars Kepler was looking at was just like ours? What if an identical copy our Solar System was sitting out there, 10 parsecs (or so) away, and Kepler had the good fortune to be looking at it? What are the chances we would find something interesting?
Would it even be lined up correctly? If the planets are misaligned with respect to us (like Saturn’s rings sometimes are with respect to Cassini),
they’ll never block any of the Sun’s light! Unless the planet sometimes sweeps directly in front of the star, blocking the light during a transit,
we’ve got no chance of seeing anything. Well, how accurate would this alignment need to be to see the different planets? And what are the chances of that happening, considering that orientations of solar systems appear to be completely random?
Let’s investigate, for each planet, how good the alignment would have to be for Kepler to see something:
|Planet||Degree Range (out of 180)||% chance of good alignment|
|Mercury||1.37 degrees||0.76% chance|
|Venus||0.738 degrees||0.41% chance|
|Earth||0.533 degrees||0.30% chance|
|Mars||0.320 degrees||0.18% chance|
|Jupiter||0.101 degrees||0.056% chance|
|Saturn||0.0556 degrees||0.031% chance|
|Uranus||0.0277 degrees||0.015% chance|
|Neptune||0.0177 degrees||0.0098% chance|
But there’s even more to the story. Even if we were lined up perfectly, we might not have seen something yet. Remember, Kepler has to observe for long enough to observe the planet both begin and end the transit — and for confirmation, repeat itself — before we have a good planetary candidate.
Assuming we did have a good alignment, how long would it take each planet to transit the Sun? And how long does the planet take to make an entire orbit? And what’s the percent chance that Kepler would have seen it yet, after 33.5 days?
|Planet||Transit time||Orbit time||% chance after 33.5 days|
|Mercury||8.07 hours||88 days||38.1% chance|
|Venus||11.0 hours||225 days||14.9% chance|
|Earth||13.0 hours||365 days||9.17% chance|
|Mars||16.1 hours||687 days||4.88% chance|
|Jupiter||29.6 hours||4332 days||0.773% chance|
|Saturn||39.9 hours||10759 days||0.311% chance|
|Uranus||56.7 hours||30799 days||0.109% chance|
|Neptune||71.2 hours||60190 days||0.056% chance|
What does this mean, overall? That if every one of the 100,000 stars Kepler is looking at had a solar system just like ours, then by this point, we would have expected Kepler to have found 391 planets. Their actual findings so far? 706 planetary candidates. I’m just saying here, we’ve got every reason in the world to be optimistic! We’ll know more when they release more data in February of 2011!