In principle, if the transit can be followed carefully enough, we could
observe the shadowing of the exoplanet as it crosses the limb of the star.
And as the light passes through the atmosphere of the exoplanet,
we can get a sense of what kind of atmosphere it has.
So the depth and shape of the transiting light curve can give information on
the atmosphere of the exoplanet.
In fact, there are two kinds of eclipses.
There are primary eclipses, when the exoplanet passes in front of its star,
that gives us the size of the exoplanet, and
if light filters through the atmosphere of the exoplanet,
we can in principle learn what the atmosphere is made of.
But when the exoplanet passes behind its star, if we look in the infrared,
we can get a measure of its temperature, because the thermal emission from
the exoplanet will disappear momentarily as it passes behind the star.
Both types of information are useful in characterizing exoplanets.
A final, niche way of detecting exoplanets is microlensing.
It's an elegant technique but
has only been used to detect of order a dozen exoplanets.
It's importance comes from the fact that in principle,
it can detect extremely low mass objects, perhaps even down to the moon's mass.
In microlensing, a nearby star passes almost
directly in front of a more distance star.
General relativity says that the light will be bent around the nearby star and
cause lensing.
This is called microlensing because the lensing effect of a star and
another star induces an angle of deflection of only 1,000 or
a million of an arcsecond, not detectable from the ground.
The image splitting in distortion is not detectable, but
the momentary magnification caused by the lensing event is.
Microlensing has been observed dozens of times with one star passing in front of
another star.
The use of this method for
detecting exoplanets depends on tracking the brightening caused by the lensing of
the foreground star from the background star.
And then looking for a secondary spike on the light curve caused by the fact that
the foreground star has an exoplanet which causes a little extra bit of brightening.
The limitation of microlensing as a method is that it's statistically rare, and
the worst limitation is the fact that the foreground star continues its
passage across the sky, and so the event is not repeatable.
Detailed gravitation and radiation physics gives us the detection sensitivity of
the various techniques, microlensing, direct imaging, the Doppler method, and
transits for any particular exoplanet of a given size and mass.
Each of the techniques has its own merits and deficits.
There are trade-offs and selection effects for
each one, and all have been useful in characterizing the exoplanet population.
Transits or eclipses are a very effective way of detecting exoplanets and
determining their size.
Mass does not come from this measurement.
That requires the Doppler method.
Exoplanet transits are also only possible when the orbit of the star and
the planet are such that the planet passes directly in front of the star,
as seen from our perspective.
And that only occurs for a small fraction of the situations.
So transit surveys have to observe thousands, or tens, or
hundreds of thousands of stars to detect the rare transits.
Nonetheless, this method is very sensitive and
has been used to detect Earth-sized planets or even smaller.