From the July 2018 issue

How are so many exoplanets detected via transits, while transits of Mercury and Venus are so rare? Do all the chance transit alignments fit statistically?

Kenneth Caine Crafton, Pennsylvania
By | Published: July 26, 2018
Venus crosses the face of the Sun in this ultra-high-definition image taken by NASA’s Solar Dynamics Observatory June 5-6, 2012. Transits of Venus are visible from Earth about twice a century. Similar transits allow astronomers to identify planets in other solar systems by watching for dips in starlight associated with a planet crossing the face of its star.
To answer your first question, let’s start with the transit of Venus, whose orbit is tilted with respect to Earth’s orbit by about 3.4°. This seems like a small amount, but it leads to a maximum separation of 9.6° between the Sun and Venus from our point of view. So Venus typically misses crossing the face of the Sun by a wide margin, making transits rare.

As a result of its orbital tilt, Venus can transit only when it is near one of two points in its orbit where it crosses Earth’s orbital plane. Due to the ratio of Earth’s orbital period compared with Venus’ period, transits come in pairs separated by eight years and then long gaps on the order of 100 years. 

Now, imagine that Earth is stationary where the plane of its orbit intersects with Venus’ orbital plane. We would get a transit once every Venus orbit (225 days). This is essentially the situation we have with exoplanets. We are so far away from those stars that Earth’s orbital motion is insignificant. This means that the only thing controlling whether a transit occurs is the orbital inclination of the transiting system with respect to our line of sight. We assume these orbits are randomly oriented in the sky, and from that, we can statistically derive the number of planets total in a given population of stars, based on the number of transits that we observe. 

We can answer your second question by doing a back-of-the-envelope calculation using planets discovered by a different method called radial velocity (RV, which identifies planets by their gravitational tug on a star), and then asking how many of them transit. About 10 out of 481 RV planets transit, which is in line with what one would expect from random orientations, based on average values for the sizes of stars and the distance of exoplanets from them.

Nathan De Lee 
Assistant Professor, Department of Physics, 
Geology and Engineering Tech, 
Northern Kentucky University, 
Highland Heights, Kentucky