Why does Proxima Cen b have only a 1.5% chance of transiting Proxima Centauri?

[jordankonisky]

In descriptions of the newly discovered exoplanet, named Proxima Cen b, orbiting Proxima Centuri, it is mentioned that a determination of its size could be established by observing the planet’s transit in front of Proxima centuri, which would reveal the exoplanet’s diameter. It is my understanding that, to date, such projects have failed. I have also read that such projects are “expected” to fail, since geometrically speaking, there is only a 1.5% chance that Proxima Cen b passes across the face of Proxima. Why is is? And how is 1.5% calculated.

 

[mfb]

The planet is far away from the star (compared to the stellar radius). Space is three-dimensional - the orbital plane has to be nearly parallel to our line of sight in order to have the planet in front of the star once per orbit. Where "nearly parallel" is the size of the star divided by the orbital radius of the planet: The closer the planet to the star, the less precise the alignment has to be.

If you do a proper integral over the whole sky, you can calculate that a fraction of (radius of star + radius of planet)/(orbital radius) of the sky can see a transit.

 

[jordankonisky]

Than you so much for responding to my query and providing such a clear answer.

 

[lifeonmercury]

If we sent a probe that way at 10% of the speed of light, by about 2060 we'd have all the answers.

 

[mfb]

Or we wait until E-ELT takes a direct picture in ~2025. The maximal angular separation is 0.04 arcseconds, contrast should be something like 1 in a million. In the range of EPICS, which can resolve 1 in 1 million contrasts down to 0.033 arcseconds, or 0.04 arcsecond separation up to a contrast of 1 in 1 billion.
Source, page 2.

 

[Vanadium 50]

If we sent a probe that way at 10% of the speed of light, by about 2060 we'd have all the answers.

And if he had some ham we'd have ham and eggs, if we had some eggs.

This is 4000x faster than any space probe built.