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It is my impression that most planetary systems have, at most, three to four planets. Is that real? Or is it just that we lack the ability to detect most planets?

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Perhaps the way to answer this is ask - could we detect the planets in our solar system if we were looking at the Sun, using current technology, from distances of many light years?

The short answer is that we could detect Jupiter using the Doppler radial velocity technique, if we observed for more than 10 years (at least one orbit is required). If we were lucky, and the orientation is right, we might then also be able to detect a transit of Venus or the Earth, using a satellite observatory like Kepler. Kepler could detect Earthlike planets by the transit technique, but the solar system is not "flat" enough that you would observe multiple transiting planets.

So the answer is that we would currently have seen Jupiter and maybe one other planet. Therefore we cannot at the moment conclude that 8 planets is an unusually high number; it may be quite typical. Although we do know that solar systems can be much more densely populated with planets (in their "terrestrial planet zones") than our own.

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There are two things to consider when thinking about this.

The first is that by virtue of living within our solar system, we are much closer to our planets, have a much easier time seeing and documenting them. We can point ground based telescopes at them and get reasonably detailed pictures of them. The point is, since we're so close, we're less likely to miss planets; But it should be noted there may still be planets in our Solar System we have not documented

Secondly is that we're really not all that great at identifying extra solar planets. Most techniques for doing this require the exo-planet to be rather large, on the scale or our gas giants.

Because of these two points, it's hard to definitively answer this question. We have identified multiple solar systems containing more than one planet, but that doesn't mean we have identified ALL planets in these systems.

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