# does a minority of all planetary systems show transits?

do most or only a minority of all planetary systems to show transits?

I feel like its minority due to the random orientation of their orbits?

But the thing is I seem to find conflicting information.

Could someone explain which answer is correct because now I am confused?

• What source tells you that the majority of planetary systems exhibit transits? – ProfRob Nov 24 '16 at 7:39
• I just realized that were referring to the fact that the majority of discovered planets were discovered by detecting transits – aa11 Nov 24 '16 at 7:49
• I was going to vote to close but I think there is a useful question in there. Maybe you mean something like "What fraction of planets do our detection methods miss?" I don't know the answer to that it isn't trivial. But you might also mean something simpler like "What fraction of known exoplanets are transiting?" – Warrick Nov 24 '16 at 11:42
• My intended question was What fraction of all exoplanets are transiting from our line of sight? But its clear that it is very very small due to the randomness of the orbits. – aa11 Nov 24 '16 at 14:26

When the radius r of the planet's orbit is such that d/r = sin(a), the planet will just barely touch the limb of the star when it is closest to the Earth. If sin(a) > d/r it will never happen and if sin(a) < d/r there will be a transit of finite length. Since there is no preference for the value of a, we conclude that the probability of the planet transiting must be $$P(sin(a) < d/r) = P{ \left( a < {arcsin \left( { d \over r } \right) } \right) } = { 2 arcsin \left( { d \over r } \right) \over \pi }$$