**3. Detection methods**

A number of detection methods have been utilized to observe exoplanets. These include, but are not limited to, transient methods, direct detection, and radial velocity measurements. Each of these three basic methods is addressed in subsequent discussion. If concurrent radial velocity and transient methods measurements are available, this combination can be used to determine the planet's mass, radius, and density [23, 33].

Ref. [32] notes that in order to estimate an exoplanet's mass, the mass of the host star must be determined. The host star's mass estimate is based on its spectral type.

An exoplanet's mass can then be estimated by measuring its effects on the motion of the host star. Included in these effects is stellar wobble that periodically red shifts and blue shifts its emitted spectrum of light. Measuring these shifts as a function of time permits a determination of the orbital period. When combined with the host star's mass, the planet's orbital trajectory and velocity can be estimated. Once the star's velocity is known as a function of its wobble, then the exoplanet's mass is determined. The star's velocity is not zero because both the planet and host star orbit around their center-of-mass.

### **3.1 Transit method**

The transient method is the detection approach used by a number of devices including the Kepler Space Telescope. Using this method, an observer or instrument detects the decrease in radiation intensity when an exoplanet transits its host star. Periodic measurements create an intensity vs. time plot or a light curve. The light curve has a characteristic shape. It has a constant intensity until the exoplanet initiates its transit. As the exoplanet begins to cover a portion of the star, it blocks some the star's surface. When this occurs, the intensity is reduced and decreases to a reduced constant value. As the exoplanet blockage terminates, the intensity returns to its initial value before any light was blocked. For an exoplanet, this cycle repeats as the exoplanet periodically orbits and transits its host star. A dip or decrease in intensity indicates that the exoplanet is passing between the observer and its host star. If this intensity curve pattern recurs on a periodic basis, then an exoplanet has likely been observed [23].

The drop (D) in intensity (I) between the equilibrium or maximum value and the minimum value as the exoplanet is transiting its host star is given by the first order relationship:

$$\mathbf{D} = \frac{\mathbf{I}\_{\text{minimum}}}{\mathbf{I}\_{\text{maximum}}} = \left(\frac{\mathbf{r}}{\mathbf{R}}\right)^2 \tag{1}$$

where r is the exoplanet radius and R is the host star radius. Eq. (1) assumes the star and exoplanet are both spherical. Using this assumption, the volume (V) of the exoplanet can be obtained from Eq. (1):

$$V = \frac{4}{3}\pi r^3 \tag{2}$$

**19**

**Figure 3**.

*Solar System Planets and Exoplanets*

when implementing this method.

*Intensity profile for a large exoplanet traversing its host star.*

possible signatures of biological activity.

**3.4 Trappist-1 exoplanetary system**

reveal the exoplanet.

**Figure 2.**

**3.3 Radial velocity**

*DOI: http://dx.doi.org/10.5772/intechopen.98431*

occurs. Although direct detection is desirable, there are two basic complications

First, the star's intensity is orders of magnitude larger than the reflected and internally generated light from an exoplanet. This difference in intensity must be mitigated for the exoplanet to be observed. Second, the detection instrumentation must have the necessary angular resolution to distinguish the exoplanet from its host star. If this is not accomplished, the image will have insufficient resolution to

These issues create difficulties in the detection of exoplanets occurring in a habitable zone where liquid water exists. Terrestrial exoplanets that are close to a parent star such as a red giant would preclude imaging the surface topography. This proximity minimizes the direct observation of details including continents and oceans. Attention could be focused on observing atmospheric constituents to ascertain their elemental composition including spectroscopic evidence of any

The radial velocity approach entails measurement of the Doppler shift of light from a host star. As an exoplanet orbits its host star, it exerts a gravitational force on the star and causes a shift in its radial velocity as it moves toward and away from the observer. This radial velocity shift results in a wavelength frequency that periodically oscillates between a red shift and a blue shift. When this periodic oscillating frequency is observed, the host star likely has one or more exoplanets in its orbital system [7, 15]. The oscillating effect of red shifts and blue shifts is illustrated in

The numerous exoplanets discovered to date are a testament to improving detection methods. Although a complete description of these systems is not possible in this chapter, it is possible to illustrate one of these systems that has several interesting characteristics. Accordingly, this section addresses the Trappist-1 system that

Since the exoplanet is much smaller that its host star, the decrease in intensity is relatively small and dependent on the relative size of the planet and star. As an example, consider an exoplanet with a radius that 10% of its host star's. Using Eq. (1), the light will only dim by 1% if both bodies are spherical.

**Figure 2** illustrates the intensity profile for a transiting exoplanet across its host star. The figure assumes a large exoplanet and the intensity decrease is not normally so dramatic.

#### **3.2 Direct detection**

Direct detection entails the viewing or imaging of the exoplanet [7, 23]. This differs from the transit method because an explicit observation of the exoplanet

#### **Figure 2.**

*Solar System Planets and Exoplanets*

orbit around their center-of-mass.

**3.1 Transit method**

likely been observed [23].

exoplanet can be obtained from Eq. (1):

order relationship:

An exoplanet's mass can then be estimated by measuring its effects on the motion of the host star. Included in these effects is stellar wobble that periodically red shifts and blue shifts its emitted spectrum of light. Measuring these shifts as a function of time permits a determination of the orbital period. When combined with the host star's mass, the planet's orbital trajectory and velocity can be estimated. Once the star's velocity is known as a function of its wobble, then the exoplanet's mass is determined. The star's velocity is not zero because both the planet and host star

The transient method is the detection approach used by a number of devices including the Kepler Space Telescope. Using this method, an observer or instrument detects the decrease in radiation intensity when an exoplanet transits its host star. Periodic measurements create an intensity vs. time plot or a light curve. The light curve has a characteristic shape. It has a constant intensity until the exoplanet initiates its transit. As the exoplanet begins to cover a portion of the star, it blocks some the star's surface. When this occurs, the intensity is reduced and decreases to a reduced constant value. As the exoplanet blockage terminates, the intensity returns to its initial value before any light was blocked. For an exoplanet, this cycle repeats as the exoplanet periodically orbits and transits its host star. A dip or decrease in intensity indicates that the exoplanet is passing between the observer and its host star. If this intensity curve pattern recurs on a periodic basis, then an exoplanet has

The drop (D) in intensity (I) between the equilibrium or maximum value and the minimum value as the exoplanet is transiting its host star is given by the first

> minimum maximum <sup>I</sup> <sup>r</sup> D= = I R

where r is the exoplanet radius and R is the host star radius. Eq. (1) assumes the star and exoplanet are both spherical. Using this assumption, the volume (V) of the

> *V r* <sup>4</sup> <sup>3</sup> 3 = π

Since the exoplanet is much smaller that its host star, the decrease in intensity is relatively small and dependent on the relative size of the planet and star. As an example, consider an exoplanet with a radius that 10% of its host star's. Using Eq.

**Figure 2** illustrates the intensity profile for a transiting exoplanet across its host star. The figure assumes a large exoplanet and the intensity decrease is not normally

Direct detection entails the viewing or imaging of the exoplanet [7, 23]. This differs from the transit method because an explicit observation of the exoplanet

(1), the light will only dim by 1% if both bodies are spherical.

2

(1)

(2)

 

**18**

so dramatic.

**3.2 Direct detection**

*Intensity profile for a large exoplanet traversing its host star.*

occurs. Although direct detection is desirable, there are two basic complications when implementing this method.

First, the star's intensity is orders of magnitude larger than the reflected and internally generated light from an exoplanet. This difference in intensity must be mitigated for the exoplanet to be observed. Second, the detection instrumentation must have the necessary angular resolution to distinguish the exoplanet from its host star. If this is not accomplished, the image will have insufficient resolution to reveal the exoplanet.

These issues create difficulties in the detection of exoplanets occurring in a habitable zone where liquid water exists. Terrestrial exoplanets that are close to a parent star such as a red giant would preclude imaging the surface topography. This proximity minimizes the direct observation of details including continents and oceans. Attention could be focused on observing atmospheric constituents to ascertain their elemental composition including spectroscopic evidence of any possible signatures of biological activity.

#### **3.3 Radial velocity**

The radial velocity approach entails measurement of the Doppler shift of light from a host star. As an exoplanet orbits its host star, it exerts a gravitational force on the star and causes a shift in its radial velocity as it moves toward and away from the observer. This radial velocity shift results in a wavelength frequency that periodically oscillates between a red shift and a blue shift. When this periodic oscillating frequency is observed, the host star likely has one or more exoplanets in its orbital system [7, 15]. The oscillating effect of red shifts and blue shifts is illustrated in **Figure 3**.

#### **3.4 Trappist-1 exoplanetary system**

The numerous exoplanets discovered to date are a testament to improving detection methods. Although a complete description of these systems is not possible in this chapter, it is possible to illustrate one of these systems that has several interesting characteristics. Accordingly, this section addresses the Trappist-1 system that

#### **Figure 3.**

*Radial velocity profile for a transiting exoplanet. Positive (negative) radial velocities result in a light profile that is blue (red) shifted.*


*b Derived from Ref. [16].*

#### **Table 7.**

*Selected characteristics of Trappist-1 exoplanets.a,b*

contains seven potential Earth-like exoplanets. Trappist-1 is an ultra-cool red dwarf star with a radius that is somewhat larger than Jupiter's, but has a mass of about 84 times Jupiter's [13, 16]. It has a surface temperature of about 2600 K [16], which partially explains the nature of the habitable semi-major axes and rotation periods noted in **Table 7**.

In 2017, NASA announced the observation that seven rocky exoplanets similar in size to Earth were discovered orbiting the host star Trappist-1 [16]. These planets resided in the habitable zone and had the potential for the existence of liquid water on their surfaces. Trappist-1 is about 40 light years from Earth, and this proximity creates the possibility that its planetary systems could be imaged with future generations of telescopes [16]. Further investigation could reveal the existence of atmospheric constituents that would indicate the possible presence of life forms.

**Table 7** summarizes selected details of the Trappist-1 exoplanetary system [16, 17]. These exoplanets have nearly circular orbits, and orbit in proximity to their host star. The Trappist-1 exoplanets are in the range of 0.3–1.2 Earth masses with

**21**

*Solar System Planets and Exoplanets*

an Earth-like composition.

**4.1 Solar system probes**

purposes and target planets.

launched into Solar orbits.

**4.2 Exoplanet probes**

ing space objects including comets and asteroids.

**4. Space probes**

are noted.

*DOI: http://dx.doi.org/10.5772/intechopen.98431*

radii of 0.8–1.2 Earth radii. These rocky worlds have densities between 0.6 and 1.0 Earth densities. Their surface gravity values are also similar to Earth's (0.5–1.0 g). Using simulations, Ref. [17] reached several conclusions regarding the nature of the Trappist-1 exoplanetary system. Three of these most applicable to this chapter

First, Trappist-1c and -1e are likely to possess interiors that are mostly rocky in nature. Second, Trappist-1b, −1d, −1f, −1 g, and -1 h likely have a thick atmosphere, oceans, or ice cover. Third, Trappist-1d, −1f, −1 g, and -1 h are unlikely to have an enriched carbon dioxide atmosphere above a bare core assuming these planets have

A variety of probes have investigated Solar System planets as well as exoplanets. These devices are growing in capability, and future probes could have the capability to reveal significant details regarding the exoplanetary structure and atmospheric

There have been numerous scientific probes launched primarily by the United States, the European Union, and Russia/Soviet Union since the late 1950s [19]. This list of participating countries has expanded to include many more nations as launch capabilities extend to additional nations. The probes have included a variety of

Missions include flybys of a planet, moon, or other space objects; orbiting these bodies; atmospheric entry; impact with the space object; and soft-landing on the surface. Target space bodies include all Solar System planets, the Moon, dwarf planets, asteroids, moons of planets, asteroids, and comets. Probes have also been

The probes have expanded our knowledge of planetary systems including their masses, atmospheric composition, surface characteristics, and temperature and pressure profiles. Additional studies focused on major moons as well as other orbit-

Ref. [19] provides a detailed historical listing of space probes during 1958–2016. Since 2016, the number of probes and their sophistication has improved. Although, Mars and the Moon are popular destinations, recent data, suggesting the appearance of phosphine in the atmosphere of Venus, has increased focus of that planet [21]. The number and scale of future probes will reveal additional information regarding these planets. For this reason, this chapter has been written in a general manner and does not address specific probe objectives or data. However, some of

The Exoplanet Exploration Program's roadmap of NASA's exoplanet missions provides a summary of existing and planned probes [20]. NASA has a number of ongoing exoplanet and planned probes. Current instrumentation includes the Hubble, Spitzer, and Kepler/K2 Space Telescopes. These instruments have significantly improved knowledge of exoplanetary systems though the discovery and characterization of transiting systems. Another device, the Transiting Exoplanet Survey Satellite (TESS) launched in 2018, adds an additional tool to expand the

the chapters of this book illustrate selected probes and their capabilities.

composition of the increasing number of observed exoplanetary systems.

#### *Solar System Planets and Exoplanets DOI: http://dx.doi.org/10.5772/intechopen.98431*

radii of 0.8–1.2 Earth radii. These rocky worlds have densities between 0.6 and 1.0 Earth densities. Their surface gravity values are also similar to Earth's (0.5–1.0 g).

Using simulations, Ref. [17] reached several conclusions regarding the nature of the Trappist-1 exoplanetary system. Three of these most applicable to this chapter are noted.

First, Trappist-1c and -1e are likely to possess interiors that are mostly rocky in nature. Second, Trappist-1b, −1d, −1f, −1 g, and -1 h likely have a thick atmosphere, oceans, or ice cover. Third, Trappist-1d, −1f, −1 g, and -1 h are unlikely to have an enriched carbon dioxide atmosphere above a bare core assuming these planets have an Earth-like composition.
