How to Find Exoplanets
Exoplanets are to see because the star they orbit can be millions of times brighter than the planet itself. A good example is to imagine a firefly flitting around a spotlight.
Exoplanets, What can We really See?
5 Methods:
Direct Observation: 
Direct Imaging - See this Actual Video from Keck Observatory!
The direct imaging observation is very difficult with current technology because of the brightness of the host star. This difficulty has led to only 82 exoplanets being imaged through this method from the Keck Observatory in Hawaii. The JWST (James Webb Space Telescope) has been able to capture one exoplanet with direct imaging using its cameras that take advanage of different wave lengths.. There are several ways that the exoplanets have been imaged. One technique is to use coronography in which the host star and its corona are hidden, leading to a coronograph. Here is an example of a coronograph of a host star with four planets orbiting it. Host star coronograph and four orbiting exoplanets.
The star's diameter is the small 'star' image in the center of the disc that hides the star's corona. Time-lapse information was collected for twelve years on this HR 7899 star system.
JWST Image: 
Cameras onboard JWST respond to different wavelengths for imaging the exoplanet. It is anticipated that this type of direct imaging will lead to divulging many characteristics of exoplanets.
Resource for Direct Imaging Exoplanets
Radial Velocity:
High Accuracy Radial velocity
Planet Searcher (HARPS) in Chile is used here. The key is looking at the
spectrum of the star. As the star moves towards us, its light is compressed,
and the spectrum shifts to red. As the star moves away, its light is stretched,
and the spectra shifts to blue. The star’s spectrum is slightly affected by the
planet's motion. (Credit: Inverse.com)
Gravity Microlensing Effect:
The planet’s gravity adds an
additional lensing event to the star’s light, brightening the image of the
background star and allowing astronomers to learn a lot about that planet,
including its mass and orbital period despite the fleeting nature of the event.
Here are two four minute video on Gravity Micrograitational lensing Effect:
Microlensing Effect from NASA.gov
Tutorial with Fraser Cain: Gravitation microlensing effect
30 second Walt Feimer (NASA Site) Animation of lensing of star around a planet:
lensing of star around exoplanet
Schematic animation of gravitational microlensing;
Astrometry:
Astrometry locates planets by directly detecting the position of the host star perturbed ('wobbling') by the planet’s gravitational force, so it can get the planet’s mass and orbital inclination. The paper below explains the mathematical derivation used to determine the astrometric detection of exoplanets.
Perturbation is the deviation in the motion of a celestial object caused either by the gravitational force of a passing object or by a collision with it.
The Transit Method:
Put in transit method albedo from AIAA ppt here, then explain.
In this simulation, an exoplanet is orbitting its star while a ligth curve is recording the light that is reflected and absorbed in reference to the time elapse of the orbit. Notice there is an increase in the curve just before the 'planet' slides behind the 'star,' then a slight dip as the 'planet' is fully behind the star. This change demonstrates the planet adding to the stars albedo and then the cumulatve albedo affect of the planet and its star dipping when the albedo of the planet is hidden behind the star.
Astronomy Stack Exchange
Take a look at the 5 detection methods from Journal of Physics Article
Inverse.com, a magazine that gives smart, in-depth coverage of the latest discoveries and research in science, from evolution to space exploration has the following article on the 5 detection methods. Methods for exoplanet detection
https://iopscience.iop.org/article/10.1088/1742-6596/2012/1/012135/pdf
Comparison of TRAPPIST 1 System to Solar System - March 22, 20177
The entire TRAPPIST 2 system would fit in the orbit of Mercury around the sun!
Statistics Data on TRAPPIST 1
Habitable zone planets in TRAPPIST 1 System
Video of the TRAPPIST 1 Systems:
Spitzer - Launched 2003, deactivated 2020
with transit spectroscopy of relatively short period planets and coronagraphic
imaging of ones with wide separations from their host stars.
Neptunian worlds, similar
to Uranus or Neptune in our solar
system. with high density are a current type. They are also know as the Ice Giants.’’
with the top shelf removed usually has the supports that can be used to anchor your 'planet.'
planet’s potential for habitability, its weather patterns, and even its formation history. Here are some key points about exoplanet atmospheres:
