Analysis and Comparison for Scenarios of Detection Exoplanets
Zicheng Chen
Olive Tree International Academy, Hangzhou, China
Keywords: Exoplanet, Radial Velocity, Transit, Astrometry.
Abstract: As a matter of fact, detections of exoplanets are always important for cosmology observation. With this in
mind, this study focuses on the introduction of different exoplanets detection method and comparison between
these methods. To be specific, three scenarios, i.e., radial velocity method, transit and astrometry method, are
introduced. In fact, radial velocity method makes use of the redshift of absorption lines. At the same time,
transit detects the periodic variation of intensity of host stars. Differently, astrometry focuses on the slight
change in position of host star in the sky. Based on the evaluations, Radial velocity method has high accuracy
but large scaled equipment. According to the analysis, transit is the most popular method and astrometry is
least welcomed due high precision needed. Overall, these results provide a guideline for researchers to choose
appropriate exoplanet detection method as well as shed light on guiding further exploration of exoplanet
searching.
1 INTRODUCTION
Exoplanet is an old and popular topic in the history.
It was first suggested ancient Greek people. In
modern history of astronomy and physics, Giordano
Bruno was the first person to declaring this concept,
in his book called “De L’Infinito, Universo E Mondi”.
Isaak Newton also mentioned this concept in the book
“Philosophiae Naturalis Principia Mathematica”.
Exoplanet region is very popular that occupying 3 to
4 percent of all papers in astronomy (Parthasarathy,
et al., 2025). Meanwhile, large amounts of missions
and projects are related to exoplanet area such as
TESS. This popularity is not surprising due to the
meaning and purpose of doing research on exoplanet.
The first aim is to find aliens or creatures away from
earth (Lee, et al., 2012). On the ground of current
studies, lives similar to human beings are more likely
to live in planets rather than stars. Secondly, finding
exoplanet helps to find the possible destination for
human’s space travel. It is essential for human to find
an exoplanet with similar condition to earth allowing
human to live without large adjustment. Thirdly,
learning exoplanet can improve the knowledge to
solar system. Evaluating different star system can
provide a better vision and model of principles of star
system. This enables further prediction the solar
system.
Different method was applied to determine
exoplanets in the history. In reinvent years, satellite
provide a huge improvement on finding exoplanets,
because they can provide full-frame image with
higher precision and clarity (Ricker, et al., 2015).
This is because they are not affected by the
atmosphere. Kepler mission and Transiting Exoplanet
Survey Satellite (TESS) provide a lot more raw data
and identify a large number of exoplanets. They
found these stars by mostly transit and radial velocity
methods. Kepler and TESS also reveal more theory
behind exoplanets based on their observational results.
This includes astrochemistry, other features of the
planet (e.g., radius, age and mass). For instance, the
composition of star was widely learned and
researched in recent papers. Astrogeodetic
measurements are also implemented in newer
researches. This astrogeodetic analysis helps
researcher to build a more precise astrometry model.
Meanwhile, new and upcoming missions like PLATO
are likely to provide a more precise and scoped vision
to exoplanets (Deeg, 2024).
This research aims to provide a clear introduction
to current methods on detecting exoplanets and make
comparison between these methods to figure out the
limitations and advantages of each method (Sekhar,
et al., 2025). The first chapter will give an overview
of common methods in determining exoplanets. The
second chapter will about the radial velocity method.
664
Chen, Z.
Analysis and Comparison for Scenarios of Detection Exoplanets.
DOI: 10.5220/0013864000004708
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy (IAMPA 2025), pages 664-668
ISBN: 978-989-758-774-0
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.
This chapter will focus on the principle, the main
equipment of this method and the observational
outcomes by this method. The third part will
introduce the second method which is transit. This
Section will follow the same structure as the second
section. Thus, the third chapter will cover principles,
equipment and observation too. The fourth section is
going to be about astrometry. This method is
relatively not that popular and have less results due to
the lack of precision of detection. The first
determined planet was just found in 2013. However,
as the development of scientific equipment and
methodology, astrometry becomes increasingly
welcomed by astronomers. In this paper, fourth
chapter will have the same structure as previous two.
The fifth chapter is about the comparison between
these three methods and prospects. Lastly, the sixth
chapter is conclusion.
2 DESCRIPTIONS
Radial velocity method is a common method in
detecting exoplanets. It detects the redshifts of planets
and calculate the radial velocity by Doppler effects.
Through this analysis, the presence, the orbit and the
mass of exoplanets can be determined. Transit is
another method of detecting exoplanets. This method
traces the intensity of host stars. If there is a periodic
decrease in intensity, this indicates the presence of a
planets which will transmit the star. By analysing the
length of decreased intensity, the size and the orbit of
the exoplanets can be measured. Astrometry uses
precise comparison of position to detect the presence
of exoplanets. The host star will have slight
movement in the sky by measuring the distance
between other stars, the position can be measured to
see whether a change in position occur. The orbit and
the mass of the planets can also be calculated by the
amount of position change of the host stars. Direct
imaging is a straight forward method of determining
an exoplanet. A single pixel of the image may be
considered as a noise, but a continuous images of an
orbiting light spot can illustrate the presence of an
exoplanet. Thus this needs continued observation and
only work for large planets which emits noticeable
light and far enough from the host stars. Gravitational
microlensing has a relative complicating mechanism.
Due to relativity, the planets will bend the space
around it, this causes the light travelled passed by or
near this planet to bend into a different direction,
scientists can determine this bend and figure out the
presence of exoplanets. In other words, the image
seen from human vision varies from the actual
location of stars in 3 dimensions.
3 RADIAL VELOCITY
This method is based on the principle of Doppler’s
effect. Doppler effect is a traditional principle in
classical physics. It claims that the wavelength
observed by the observer depends on the relative
speed between the source and the object and the
original wavelength. The formula is shown bellowed.
(1)
However, in astronomy, scientists more often to
obtain the observed wavelength and the origin
wavelength, thus they want to figure out the radial
velocity of this object. This is because astronomers
use Doppler’s effect in the context of spectroscopy.
In spectroscopy, the redshifts are measured on these
absorption or emission lines rather than a pure light.
Therefore, it is easy to figure out the original
wavelength where scientists can obtain this
wavelength from the laboratory. As a result, the
formula will vary in the from as shown followed:
(2)
Besides the theory part, the reality shows far more
complexity. This mainly includes two stages, light
obtains and fit.
Figure 1: The layout of Echelle spectrograph (Trifon, 2024).
The precision of the spectroscopy is low in early
stages. Thanks to the method of Échelle spectrograph,
the precision of spectroscopy has dramatically
increased (Trifon, 2024). The Fig. 1 shows the
mechanism of Échelle spectrograph. It splits the light
into blocks enabling more precise results of detection
of absorption lines. The light will first pass through
an image slicer which will split the beam into several
narrower beams. This can increase the efficiency and
resolution of the image. The light will then pass
through a collimator. Collimator is a mirror with same
Analysis and Comparison for Scenarios of Detection Exoplanets
665
focus as the telescope. Thus, the collimator will
spread the EM waves into parallel beams. After that
the beams will reflected by the Échelle grating. This
grating will have small grating constant and large
incidence angles. This helps the waves have more
overlapping wavelength intervals in the edge of the
image. As these overlapping wavelengths are not
useful as the single one, this action makes the image
contain more information and easier to interpret.
Lastly, the light will enter the cross disperser and be
focused by the camera’s CCD or CMOS. In
conclusion, this equipment, Échelle spectrograph,
provide benefits including high spectral resolution,
large wavelength coverage, compact design and
versatility.
Fitting is also a difficult part, because the signals
can submerge in the sea of noise and change shape
due to other interference. Apart from increasing the
resolution of CCD to increase the signal-to-noise ratio
(SNR), how to enhance the stability of the instrument
is also vital. Here comes to one method to overcome
these unstable factors that can lead to failure of
detection, which is the I2 cell method.
This method introduces an iodine gas cell into the
path of the beam (Trifon, 2024). This process allows
the absorption lines of the stars detected to
superimpose with the absorption lines of I2. Thus, the
absorption feature and shifts are more stable, due to
the presence of easily identified reference lines of I2.
It was implemented in HIRES spectrograph (Lizzana,
et al., 2024). This equipment achieving the precision
down to 3ms-1. The advantages of this method are
obvious. Firstly, it is inexpensive to settle, but it stills
provide a high resolution. Meanwhile, the small size,
maintenance cost and ease of use are all benefits
related. There are also some drawbacks of it like
extraction process is complicated. However other
methods like simultaneous Th-Ar calibration method
can have the same effects.
4 TRANSIT
Transit is also a common method of detecting
exoplanets. In recent studies, codes and computer are
also used to determine the probability of transit. For
instance, python code lightcurves can be used to
model and analyze the light curves. This python code
package makes use of the project “Exolock Project”.
(Bass and Daniel, 2024) This module helps to
determine the parameter including the mass of host
star, orbit radius, mass of the exoplanet, radius of the
exoplanet and the density of the star. In this module,
many data of specific exoplanets are stored and used
as the historical data. After this an analysis should be
carried out to fit the rotation of the exoplanets. The
first model can be applied is linear model. This model
assumes the planets has a circular orbit and a constant
orbiting speed. Thus, the equation to this model can
be expressed as followed:
(3)
In the equation,
is the mid-transit time while
is the orbital speed. E represents the epoch number
round to the closet integer. As a result, a mid-transit
time is obtained by fitting this model. Monte Carlo
Markov Chain sampler is applied to fit this linear
model. The second model can be used is Orbital
Decay model. This model also assumes a circular
orbit. However, it has better complexity. Unlike the
first model, the orbital decay model assumes a
changeable speed with steady changing rate. This
allows the equation to be obtained as followed.
(4)
Here,
is the orbital period and dPd/dE is the rate of
change in orbital period in each orbit. The Monte
Carlo Markov Chain sampler can also be applied to
fit this model with the actual data. While using transit
method, the tidal quality can relatively easy to be
obtained. (Wallace, et al., 2025) Applying some
translation of the formula the function can be
obtained as shown bellowed. The third model is
Apsidal model. This model assumes the orbit as an
eccentric orbit. The argument of this orbit of its
pericenter will precessing uniformly over the time.
From Gimenez and Bastero’s research the mechanism
of this apsidal model is gained as the equation shown.
(5)
Here,
is the reference time and the e is the
eccentricity. W is the argument of the pericenter. Ps
is the sideral period and dw/dE is the rate of change
in orbital period in each orbit.
5 ASTROMETRY
Astrometry method includes a precise mathematical
modeling to the motion of the stars and hence to
calculate the period and other features of the host stars.
The direction or the angle between the host star
system and earth is vital, as this will influence the
direction vector it seperates. In other words, the radial
velocity method considers the radial velocity while
the astrometry considers the tangential velocity. In
the most extreme examples, the star system which has
a planar normal to the vision from earth cannot be
IAMPA 2025 - The International Conference on Innovations in Applied Mathematics, Physics, and Astronomy
666
determined by the radial velocity method, and the star
system parallel to solar system cannot be measured
by the astrometry method. However, radial velocity
method is still more popular as the shifts of the
absorption lines are easier to be determined than the
motion of several pixels in the image (Simon, et al.,
2025). To model the motion of the star, the motion is
considered as a periodic movement due to the
Newton’s law of gravity. Scientist often use
trigonometric functions to express the motion in polar
coordinates forms (or can be said in complex numbers
forms) (Simon, et al., 2025). The equation is
expressed as followed:
(6)
In the equation, R is the wobble radius of the host star
from the barycenter. Combined these tow equations,
a new 2 dimensions expression is derived as followed.
(7)
Secondly, the light will pass through a vortex
filter. This will give an additional phase of the
original light separated from the whole expression as
shown in the combined equation. Then the left and
right quadrants are split and their difference are seen.
The equation is given as:
(8)
The denominator is the radial coordinates of the host
star from the vortex filter or detectors, whereas the θ
is the angle between the center of the detector and the
Gaussian beam. This difference is then normalized.
The purpose of this normalization is to totaling the
difference in the intensity of the left side and the right
side. The equation is shown as followed.
(9)
To simplify the calculation, the value of the
equation 2 is substituted into equation 1. The new
equation one obtained is like followed. Thus, an
equation of the difference in intensity in the form of a
polar equation is obtained and is ready to be
visualized. Finally, by taking a Fourier transform, the
equation can be expressed in the form of summation.
The equation is in the form as shown below:
(10)
When plotting the figures, a trend of dominating
terms can be seen (seen from Fig. 2). In conclusion, a
series of mathematical techniques are applied here to
implement to explores the motion or detectors the
motion in a precise way.
Figure 2: The mechanism of vortex filter (Simon, et al.,
2025).
6 COMPARISONS
Based on the previous research and introduction. The
advantages and disadvantages are clear and obvious.
Firstly, the benefits and drawbacks of radial velocity
method. Radial velocity method is the obvious most
straight forward metho. It makes use of the absorption
and emitting light lines. Thus, the shift of the
absorption line can be used to determine the radial
velocity and hence find the period and radius of the
exoplanet. This feature gives radial velocity method a
high accuracy due to precision of absorption lines in
comparison to other detection like intensity or
position. Meanwhile, the ease of applying radial
velocity method is also outstanding. Unlike, other
methods nowadays have a high reliance on computer
simulation and modeling. Radial velocity method
relies on computer in a very slight amount. For
instance, it does not need to fit with a model to get the
result. At the same time, it does not require a
prediction of the data or first step analysis on whether
this host star experience an epoch or motion.
However, this method needs large and complex
equipment this paper has mentioned before like I2
container. This restricts the size of the Telescope and
limit the devices on ground level. These complex
devices will furtherly cause high start-up and
maintenance cost and ask for higher level of
researchers that are able to understand the mechanism
behind these devices (Zakhozhay, et al., 2022).
Analysis and Comparison for Scenarios of Detection Exoplanets
667
For transit and astrometry, they have quite similar
trend of benefits and drawbacks. However, transit is
a lot more popular than astrometry due to its more
obvious phenomenon. They both require a continuous
detection. And the duration of the observation
depends on the period of the exoplanets. This gives
more uncertainty In the observation. In difference,
transit requires the detection of intensity. Thus, the
intensity is easier to model and detect the change of
them. This also allows the telescope to be brought to
space like Kepler and TESS.
However, this paper only mainly focuses on the
theory and mechanism part. It covers a limited
number of actual results. For the future, a more
precise comparison can be made based on the
observational results.
7 CONCLUSIONS
To sum up, this study gives a brief introduction on
three different methods on how to detecting
exoplanets. They are radial velocity, transit and
astrometry. A comparison also be made to give their
advantages and disadvantages. The introduction
mainly focuses on the mechanism and tools used in
detection. The comparison gives reasons and feature
on their benefits and drawbacks. In the future, it will
be beneficial to overcome these drawbacks and reach
a higher resolution. This allows more accurate
understanding on exoplanets. This paper concludes
the mechanism of these three methods including
radial velocity, and figure out the limitation of current
method.
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