Planetology - Future Explorations

includes one large and one small parabolic mirrors both highly reflective and with the same focal point. The reflectivity of a mirror is given by reflective foils (or plates) which are stretched on a lightweight parabolic support for the mirror. The light rays coming from the Sun are focalized by the large parabolic mirror onto the focal point; afterward they are reflected by the small parabolic mirror as a group of parallel rays which pass through a central hole located in the center of the large parabolic mirror. A mirror tube attached to the large parabolic mirror by means of an articulation permits the orientation of the concentrated light beam as required (see Figure 8).

The SECSL is table in space; according to the law of momentum conservation, the sum of all light impulses is zero. However, when the light beam is directed toward the target, this balance is changed, and compensation forces must be applied to keep the system in position (i.e., with the concave side of the large parabolic

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

Solar power is the key future for our civilization to expand in space. The main component of this power is electromagnetic radiation. The spectrum of solar radiation is the spectrum of a black body having a temperature of 5800 K [9]. The electromagnetic radiation is emitted in a broadband of frequencies. Electromagnetic energy is initially emitted in the range of gamma rays, as a result of nuclear fusion reactions. Gamma rays during their travel from the Sun's core to the surface are converted into low-energy photons. Thus the Sun does not emit gamma rays; it emits only X-rays, ultraviolet light, visible light, infrared light, and radio waves. The spectrum of nearly all solar electromagnetic radiation striking the Earth's

In Figure 9 the power emitted by the Sun under the form of X rays and ultraviolet is low. Most of the power is emitted in the range of visible light. Infrared and radio frequencies have less power. Assuming the SECSL is placed near the Earth, the

Both mirrors are made from gold-plated Mylar foil with remarkable reflectivity coefficient [10]. Figure 10 shows that for most frequencies, gold has a reflection coefficient of Rg = 0.98 compared to aluminium or silver. In the case of the SECSL, the best foil should be made of gold-plated fine and thin graphite fabric due to gold's remarkable reflection coefficient and graphite's high heat transfer coefficient and

If the large parabolic mirror is oriented with the reflective (concave) face

For example, if the large mirror has a radius of r = 10 m and assuming the solar

, the total collected power is

towards the Sun, the amount of energy captured is maximized.

.

mirror oriented toward the Sun).

DOI: http://dx.doi.org/10.5772/intechopen.86565

2.1 Estimating the power of a SECSL system

atmosphere ranges from 100 nm to 1 mm.

high emissivity coefficient.

irradiance is Ee = 1360 W/m<sup>2</sup>

Figure 9.

15

The spectrum of the Sun.

irradiance can be assumed to be Ee = 1360 W/m<sup>2</sup>

The role and functions of the main components:


Figure 8. Main design features of SECSL.

The SECSL is table in space; according to the law of momentum conservation, the sum of all light impulses is zero. However, when the light beam is directed toward the target, this balance is changed, and compensation forces must be applied to keep the system in position (i.e., with the concave side of the large parabolic mirror oriented toward the Sun).

### 2.1 Estimating the power of a SECSL system

includes one large and one small parabolic mirrors both highly reflective and with the same focal point. The reflectivity of a mirror is given by reflective foils (or plates) which are stretched on a lightweight parabolic support for the mirror. The light rays coming from the Sun are focalized by the large parabolic mirror onto the focal point; afterward they are reflected by the small parabolic mirror as a group of parallel rays which pass through a central hole located in the center of the large parabolic mirror. A mirror tube attached to the large parabolic mirror by means of an articulation permits the orientation of the concentrated light beam as required

1. Large parabolic mirror. Role: capture and focus sunlight onto the common

2. Small parabolic mirror. Role: receives the light rays coming from the large parabolic mirror and reflects them forming a beam of concentrated parallel

4.Spherical articulation. Role: permits the rotation of the light guide around one

5. Resistance structure. Role: keeps in position the foil forming the large parabolic

6.Connection structure. Role: aligns the mirrors so their axes are always parallel

7. Positioning engines. Role: keep the SECSL in the correct position and maintain

3.Mobile mirror tube guide. Role: directs the light beam as required.

The role and functions of the main components:

structure. The foil is stretched on this structure.

and their focal point is common.

(see Figure 8).

focal point.

Planetology - Future Explorations

rays of light.

point.

stability.

Figure 8.

14

Main design features of SECSL.

Solar power is the key future for our civilization to expand in space. The main component of this power is electromagnetic radiation. The spectrum of solar radiation is the spectrum of a black body having a temperature of 5800 K [9]. The electromagnetic radiation is emitted in a broadband of frequencies. Electromagnetic energy is initially emitted in the range of gamma rays, as a result of nuclear fusion reactions. Gamma rays during their travel from the Sun's core to the surface are converted into low-energy photons. Thus the Sun does not emit gamma rays; it emits only X-rays, ultraviolet light, visible light, infrared light, and radio waves. The spectrum of nearly all solar electromagnetic radiation striking the Earth's atmosphere ranges from 100 nm to 1 mm.

In Figure 9 the power emitted by the Sun under the form of X rays and ultraviolet is low. Most of the power is emitted in the range of visible light. Infrared and radio frequencies have less power. Assuming the SECSL is placed near the Earth, the irradiance can be assumed to be Ee = 1360 W/m<sup>2</sup> .

Both mirrors are made from gold-plated Mylar foil with remarkable reflectivity coefficient [10]. Figure 10 shows that for most frequencies, gold has a reflection coefficient of Rg = 0.98 compared to aluminium or silver. In the case of the SECSL, the best foil should be made of gold-plated fine and thin graphite fabric due to gold's remarkable reflection coefficient and graphite's high heat transfer coefficient and high emissivity coefficient.

If the large parabolic mirror is oriented with the reflective (concave) face towards the Sun, the amount of energy captured is maximized.

For example, if the large mirror has a radius of r = 10 m and assuming the solar irradiance is Ee = 1360 W/m<sup>2</sup> , the total collected power is

Figure 9. The spectrum of the Sun.

Figure 10. Reflection coefficient of metals.

$$\mathbf{P} = \mathbf{E}\_{\mathbf{e}} \cdot \boldsymbol{\pi} \cdot \mathbf{r}^2 = \mathbf{1360} \cdot \boldsymbol{\pi} \cdot \mathbf{10^2} = 427.256 \text{ kW} \tag{1}$$

• Melting temperature: tm = 1538°C, Tm = 1811 K

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

• Boiling temperature: tb = 2862°C, Tb = 3135 K

• Heat of fusion: cf = 247.3 kJ/kg

DOI: http://dx.doi.org/10.5772/intechopen.86565

power beam into the asteroid is

2.2 Heat transfer calculations

).

emissivity of carbon fabric/plate ec ≈ 1.

according to Stefan-Boltzmann law:

irradiance Ee = 1360 W/m<sup>2</sup>

is Es = 136,000 W/m2

17

• Heat of vaporization: cv = 6088.3 kJ/kg

This total energy can vaporize a mass of iron given by

<sup>M</sup> <sup>¼</sup> <sup>E</sup> E1

vaporize an iron asteroid having the mass of 100 tons in just 8 s.

obviously the SECSL beam hits the target with the speed of light.

system is capable of concentrating the sunlight by a factor of 64.

Ee � 1 � Rgf<sup>=</sup><sup>p</sup>

• Heat capacity: c = 0.45 kJ/kgK (considered the same for solid and liquid iron)

The heat quantity needed in order to vaporize 1 kg of iron can be calculated:

E1 ¼ 1 � c � ð Þþ Tb � Tc cf � 1 þ cv � 1 ¼ 0:45 � 3135 þ 247:3 þ 6088:3 ¼ 7746 kJ=kg

<sup>¼</sup> <sup>106814</sup>

Hitting the asteroid continuously (hundreds or thousands of times) in this manner, it can be deflected from a collision trajectory with the Earth. Even the trajectory of massive asteroids can be changed. Due to local vaporization of the asteroids, mass leads to the apparition of a reaction force produced by the expanding vapors. In space the construction of such a gigantic system should be easier due to the absence of gravity. Calculations done using the above equations show that an SECSL having the radius of the large parabolic mirror r = 10 km can send a beam of concentrated light into the asteroid at a power of 0.427 terawatt. Such a power can

The time required to destroy or deflect an asteroid using the SECSL system is reasonably low. Practically, the asteroid can be destroyed in a few minutes because

Simple calculations show that SECSL works properly both near the Earth (where

Assume that a SECSL placed near the Earth having the large parabolic mirror radius rLPM = 10 km and the radius of the small parabolic mirror rSPM = 1.25 km; this

Consider that the reflection coefficient for a gold-plated foil Rgf/p = 0.98 and the

rSPM <sup>2</sup>

Assume that the whole power absorbed by the gold-plated foil is radiated

� Rgf<sup>=</sup><sup>p</sup> � rLPM

) and at 0.1 AU distance from the Sun (where irradiance

<sup>¼</sup> <sup>σ</sup> � <sup>T</sup><sup>4</sup> (5)

Reading from Table 1 the power for the mirror with a radius r = 50 m, in 10 s the

E ¼ 10 � 10681:4 ¼ 106814 kJ (3)

<sup>7746</sup> <sup>¼</sup> 14 kg (4)

(2)

The total collected power is significant. However, when this radius increases, the power collected from the Sun becomes very high. Table 1 shows the correlation between the SECSL mirror diameter and the amount of collected power. As shown in the table, when the radius of the large parabolic mirror r = 50 m, the collected power is P = 10681.4 kW. Such a mirror is relatively easy to be built in space due to the absence of gravitational forces.

For a simple sample calculation, assume that a SECSL having a radius of large parabolic mirror, r = 50 m, is focused on an iron asteroid for 10 s. Consider iron properties listed in the literature [11]:


#### Table 1.

Collected solar power for different large parabolic mirror radii.

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris DOI: http://dx.doi.org/10.5772/intechopen.86565


The heat quantity needed in order to vaporize 1 kg of iron can be calculated:

$$\mathbf{E}\_1 = \mathbf{1} \cdot \mathbf{c} \cdot (\mathbf{T}\_\mathbf{b} - \mathbf{T}\_\mathbf{c}) + \mathbf{c}\_\mathbf{f} \cdot \mathbf{1} + \mathbf{c}\_\mathbf{v} \cdot \mathbf{1} = 0.45 \cdot 3135 + 247.3 + 6088.3 = 7746 \text{ kJ/kg} \tag{2}$$

Reading from Table 1 the power for the mirror with a radius r = 50 m, in 10 s the power beam into the asteroid is

$$\mathbf{E} = \mathbf{10} \cdot \mathbf{10} \mathbf{681.4} = \mathbf{10} \mathbf{6814} \text{ kJ} \tag{3}$$

This total energy can vaporize a mass of iron given by

$$\mathbf{M} = \frac{\mathbf{E}}{\mathbf{E}\_1} = \frac{106814}{7746} = 14 \text{ kg} \tag{4}$$

Hitting the asteroid continuously (hundreds or thousands of times) in this manner, it can be deflected from a collision trajectory with the Earth. Even the trajectory of massive asteroids can be changed. Due to local vaporization of the asteroids, mass leads to the apparition of a reaction force produced by the expanding vapors.

In space the construction of such a gigantic system should be easier due to the absence of gravity. Calculations done using the above equations show that an SECSL having the radius of the large parabolic mirror r = 10 km can send a beam of concentrated light into the asteroid at a power of 0.427 terawatt. Such a power can vaporize an iron asteroid having the mass of 100 tons in just 8 s.

The time required to destroy or deflect an asteroid using the SECSL system is reasonably low. Practically, the asteroid can be destroyed in a few minutes because obviously the SECSL beam hits the target with the speed of light.

#### 2.2 Heat transfer calculations

Simple calculations show that SECSL works properly both near the Earth (where irradiance Ee = 1360 W/m<sup>2</sup> ) and at 0.1 AU distance from the Sun (where irradiance is Es = 136,000 W/m2 ).

Assume that a SECSL placed near the Earth having the large parabolic mirror radius rLPM = 10 km and the radius of the small parabolic mirror rSPM = 1.25 km; this system is capable of concentrating the sunlight by a factor of 64.

Consider that the reflection coefficient for a gold-plated foil Rgf/p = 0.98 and the emissivity of carbon fabric/plate ec ≈ 1.

Assume that the whole power absorbed by the gold-plated foil is radiated according to Stefan-Boltzmann law:

$$\mathbf{E}\_{\mathbf{e}} \cdot \left(\mathbf{1} - \mathbf{R}\_{\mathrm{gf}/\mathrm{p}}\right) \cdot \mathbf{R}\_{\mathrm{gf}/\mathrm{p}} \cdot \left(\frac{\mathbf{r}\_{\mathrm{LPM}}}{\mathbf{r}\_{\mathrm{SPM}}}\right)^2 = \boldsymbol{\sigma} \cdot \mathbf{T}^4 \tag{5}$$

P ¼ Ee � π � r

the absence of gravitational forces.

Figure 10.

Crt. no.

Table 1.

16

Reflection coefficient of metals.

Planetology - Future Explorations

properties listed in the literature [11]:

Collected solar power for different large parabolic mirror radii.

Radius of large parabolic mirror, r (m)

<sup>2</sup> <sup>¼</sup> <sup>1360</sup> � <sup>π</sup> � <sup>10</sup><sup>2</sup> <sup>¼</sup> <sup>427</sup>:256 kW (1)

Radius of large parabolic mirror, r (km)

Collected solar power, P (terawatt)

The total collected power is significant. However, when this radius increases, the power collected from the Sun becomes very high. Table 1 shows the correlation between the SECSL mirror diameter and the amount of collected power. As shown in the table, when the radius of the large parabolic mirror r = 50 m, the collected power is P = 10681.4 kW. Such a mirror is relatively easy to be built in space due to

For a simple sample calculation, assume that a SECSL having a radius of large parabolic mirror, r = 50 m, is focused on an iron asteroid for 10 s. Consider iron

> Crt. no.

 5 106.8 13 1 0.004 10 427.3 14 2 0.017 15 961.3 15 3 0.038 20 1709.0 16 4 0.068 30 3845.3 17 6 0.154 40 6836.1 18 8 0.273 50 10681.4 19 10 0.427 60 15381.2 20 12 0.615 70 20935.6 21 14 0.837 80 27344.4 22 16 1.093 90 34607.8 23 18 1.383 100 42725.7 24 20 1.708

Collected solar power, P (kW)

In Eq. (1) <sup>σ</sup> = 5.67�10�<sup>8</sup> W/m2 K4 represents the Stefan-Boltzmann coefficient for black body radiation. Using the given data, thermal balance is achieved at T = 410 K (t = 137°C), which is under the maximum allowable working temperature for carbon composites with polymeric matrix (t = 280–300°C).

Considering that the thickness of the gold-plated foil is δ = 0.05 mm and the average thermal transfer coefficient for graphite is λ = 80 W/m K at t = 137°C, the temperature difference Δt needed for heat transfer from the gold reflective face to the rear carbon face is given by the following thermal balance equation:

$$\mathbf{E}\_{\mathbf{e}} \cdot \left(\mathbf{1} - \mathbf{R}\_{\mathbf{g}\mathbf{f}/\mathbf{p}}\right) \cdot \mathbf{R}\_{\mathbf{g}\mathbf{f}/\mathbf{p}} \cdot \left(\frac{\mathbf{r}\_{\text{LPM}}}{\mathbf{r}\_{\text{SPM}}}\right)^2 = \lambda \cdot \frac{\Delta t}{6} \tag{6}$$

Thermal balance at the surface of the large parabolic mirror is achieved at TLPM = 476 K (tLPM = 203°C) still under 280–300°C—the working temperature limit

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

In Figure 11 the cell design is based on triangular shapes. It can be either hexagonal or rectangular cells, i.e., if rectangular cells are used, it yields a light structure, but the stability is reduced compared to the design of triangular cells. When using gold-plated foils, the structure bars can be square and straight. If goldplated plates are used, the bars must be curved according to the parabolic surfaces of the mirrors which in this case results in a higher accuracy in focusing the light. Such a construction can be relatively easily built in space if "SpiderFab" robots are used (see Figure 12) [12]. Preliminary calculations show that the resistance structure of the large parabolic mirror can be built from 528 bars with 9.3 m in length. If the bars are square tubes made from titanium having dimensions of

composites are used instead of titanium, the mass of the large parabolic mirror decreases to about one-third due to the extremely low density of these materials.

3. Solar-thermal system for deorbiting space debris

This system is similar to the one presented in Chapter 2, composed of two parabolic mirrors, a large one and a small one (see Figure 13). Just like in the case of SECSL, the mirrors are made from very thin composite material (graphite fiber) plated with gold foils or gold plates on the concave face. The concave faces of the two mirrors face each other having the same focal point. The solar light rays which are parallel to the axis of the large parabolic mirror are reflected into its focal point and onto the small parabolic mirror and form parallel rays which are directed along the common axis. The diameter of the concentrated light beam is the same as the diameter of the small mirror ("d"). The concentrated light beam passes through a

cutout (hole) in the center of the large parabolic mirror with diameter d+

The system operates as follows: the system is oriented with the large parabolic mirror to the Sun using the attitude thrusters, while the shutter is closed. The light guide tube is aligned with the space debris, and the faces of the lens are curved at

in the large parabolic mirror is closed by a gold-plated shutter.

the appropriate radii in order to focus the light on the space debris.

. The hole

, calculations show that the total mass is 357 kg. If graphite fiber

for carbon fiber composite with polymeric matrix.

DOI: http://dx.doi.org/10.5772/intechopen.86565

2.3 SECSL mass calculation

<sup>20</sup> <sup>20</sup> 0.2 mm<sup>3</sup>

Figure 12.

19

NASA's SpiderFab robot in space.

For the given equation, the thermal difference necessary for heat transfer would be Δt = 0.001°C; the result shows that heat is quickly transferred from the goldplated face to the graphite fabric/plate due to the high thermal conductivity of the graphite and small thickness.

At the beginning of this chapter, we've stated that SECSL works properly even at 0.1 AU from the Sun, where the irradiance is 100 times stronger. Considering the same constants and mirror dimensions as before and using Eq. (1) we find that the surface temperature of the small parabolic mirror is TSPM = 1296 K (tSPM=1023°C) which is under the melting point of pure gold (1064°C).

Figure 11. SECSL equipment built using triangular cells.

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris DOI: http://dx.doi.org/10.5772/intechopen.86565

Thermal balance at the surface of the large parabolic mirror is achieved at TLPM = 476 K (tLPM = 203°C) still under 280–300°C—the working temperature limit for carbon fiber composite with polymeric matrix.

### 2.3 SECSL mass calculation

In Eq. (1) <sup>σ</sup> = 5.67�10�<sup>8</sup> W/m2

Planetology - Future Explorations

graphite and small thickness.

Figure 11.

18

SECSL equipment built using triangular cells.

K4 represents the Stefan-Boltzmann coefficient for

¼ λ � Δt

<sup>δ</sup> (6)

black body radiation. Using the given data, thermal balance is achieved at T = 410 K (t = 137°C), which is under the maximum allowable working temperature for

Considering that the thickness of the gold-plated foil is δ = 0.05 mm and the average thermal transfer coefficient for graphite is λ = 80 W/m K at t = 137°C, the temperature difference Δt needed for heat transfer from the gold reflective face to

For the given equation, the thermal difference necessary for heat transfer would be Δt = 0.001°C; the result shows that heat is quickly transferred from the goldplated face to the graphite fabric/plate due to the high thermal conductivity of the

At the beginning of this chapter, we've stated that SECSL works properly even at 0.1 AU from the Sun, where the irradiance is 100 times stronger. Considering the same constants and mirror dimensions as before and using Eq. (1) we find that the surface temperature of the small parabolic mirror is TSPM = 1296 K (tSPM=1023°C)

rSPM <sup>2</sup>

the rear carbon face is given by the following thermal balance equation:

� Rgf<sup>=</sup><sup>p</sup> � rLPM

carbon composites with polymeric matrix (t = 280–300°C).

Ee � 1 � Rgf<sup>=</sup><sup>p</sup>

which is under the melting point of pure gold (1064°C).

In Figure 11 the cell design is based on triangular shapes. It can be either hexagonal or rectangular cells, i.e., if rectangular cells are used, it yields a light structure, but the stability is reduced compared to the design of triangular cells. When using gold-plated foils, the structure bars can be square and straight. If goldplated plates are used, the bars must be curved according to the parabolic surfaces of the mirrors which in this case results in a higher accuracy in focusing the light.

Such a construction can be relatively easily built in space if "SpiderFab" robots are used (see Figure 12) [12]. Preliminary calculations show that the resistance structure of the large parabolic mirror can be built from 528 bars with 9.3 m in length. If the bars are square tubes made from titanium having dimensions of <sup>20</sup> <sup>20</sup> 0.2 mm<sup>3</sup> , calculations show that the total mass is 357 kg. If graphite fiber composites are used instead of titanium, the mass of the large parabolic mirror decreases to about one-third due to the extremely low density of these materials.

Figure 12. NASA's SpiderFab robot in space.

#### 3. Solar-thermal system for deorbiting space debris

This system is similar to the one presented in Chapter 2, composed of two parabolic mirrors, a large one and a small one (see Figure 13). Just like in the case of SECSL, the mirrors are made from very thin composite material (graphite fiber) plated with gold foils or gold plates on the concave face. The concave faces of the two mirrors face each other having the same focal point. The solar light rays which are parallel to the axis of the large parabolic mirror are reflected into its focal point and onto the small parabolic mirror and form parallel rays which are directed along the common axis. The diameter of the concentrated light beam is the same as the diameter of the small mirror ("d"). The concentrated light beam passes through a cutout (hole) in the center of the large parabolic mirror with diameter d+ . The hole in the large parabolic mirror is closed by a gold-plated shutter.

The system operates as follows: the system is oriented with the large parabolic mirror to the Sun using the attitude thrusters, while the shutter is closed. The light guide tube is aligned with the space debris, and the faces of the lens are curved at the appropriate radii in order to focus the light on the space debris.

synchronous orbit) [16] because the satellite is placed in constant sunlight. For example, heavy military or weather satellites are placed on Sun-synchronous orbits.

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

DOI: http://dx.doi.org/10.5772/intechopen.86565

out of and elastic material filled with a colourless liquid.

Gregorian-type (left) and Cassegrain-type (right) solar-thermal systems.

1

<sup>f</sup> <sup>¼</sup> ð Þ� <sup>n</sup> � <sup>1</sup>

The lens that is placed in the light tube has the role to focus the light on a very small area in order to assure very high power density. Theoretically, the energy can be focused on a geometric point. In reality due to chromatic aberration and shape errors, light is not focused quite precisely. The lens presented in Figure 15 is made

Approximating surfaces "S1" and "S2" with spheres having radii "r1" and "r2," respectively, assuming the thickness of the lends is denoted as "d" and neglecting the optical effect of transparent elastic material (which is very thin) if the refractive index of the liquid is "n," the focal distance "f" of the lens is given by the following

> 1 r1 � 1 r2

<sup>þ</sup> ð Þ� <sup>n</sup> � <sup>1</sup> <sup>d</sup> n � r1 � r2

(7)

3.2 Lens design

Figure 14.

equation [13]:

Figure 15.

21

Lens design filled with liquid.

Figure 13. Design of solar-thermal system.

When the shutter opens, the light coming from the Sun is focused by the large parabolic mirror in the common focal point and then is reflected by the small parabolic mirror toward the hole "d+ " and the light guide tube. At the end of the light tube, the light is focused by the lens in a focal point which is positioned onto the space debris. The focused light locally vaporizes/ionizes the space debris material. The thrust force created pushes the space debris toward the Earth surface where it burns in the atmosphere.

When the shutter is closed, the light rays are sent back toward the small parabolic mirror and back to the Sun.

An alternative to the parabolic mirror system is the Cassegrain-type or Gregorian-type solar-thermal system. These systems are used in manufacturing optical telescopes or radio antennas [13].

Basically, a Cassegrain reflector (see Figure 14) [14] is a combination of a large concave and a small convex (hyperbolic) mirror. This design permits placing a focal point at a convenient location behind the large parabolic mirror using a compact mechanical system.

On the other hand, the Gregorian reflector [15] uses a small concave (parabolic) mirror with a focal point that doesn't coincide with the focal point of the large parabolic mirror (see Figure 14).

Although the Cassegrain-type and the Gregorian-type solar-thermal system can focus the light in a single point placed behind the large parabolic mirror, it is more difficult to change the focal point distance and direct the concentrated light beam onto the space debris.

#### 3.1 Orbits for the solar-thermal system for space debris deorbiting

This system can be placed on a geocentric orbit, heliocentric orbit, or Sunsynchronous orbit. The most advantageous is the Sun-synchronous orbit (helioTechnologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris DOI: http://dx.doi.org/10.5772/intechopen.86565

Figure 14. Gregorian-type (left) and Cassegrain-type (right) solar-thermal systems.

synchronous orbit) [16] because the satellite is placed in constant sunlight. For example, heavy military or weather satellites are placed on Sun-synchronous orbits.

#### 3.2 Lens design

When the shutter opens, the light coming from the Sun is focused by the large

light tube, the light is focused by the lens in a focal point which is positioned onto the space debris. The focused light locally vaporizes/ionizes the space debris material. The thrust force created pushes the space debris toward the Earth surface

When the shutter is closed, the light rays are sent back toward the small para-

Basically, a Cassegrain reflector (see Figure 14) [14] is a combination of a large concave and a small convex (hyperbolic) mirror. This design permits placing a focal point at a convenient location behind the large parabolic mirror using a compact

On the other hand, the Gregorian reflector [15] uses a small concave (parabolic)

Although the Cassegrain-type and the Gregorian-type solar-thermal system can focus the light in a single point placed behind the large parabolic mirror, it is more difficult to change the focal point distance and direct the concentrated light beam

mirror with a focal point that doesn't coincide with the focal point of the large

This system can be placed on a geocentric orbit, heliocentric orbit, or Sunsynchronous orbit. The most advantageous is the Sun-synchronous orbit (helio-

3.1 Orbits for the solar-thermal system for space debris deorbiting

" and the light guide tube. At the end of the

parabolic mirror in the common focal point and then is reflected by the small

An alternative to the parabolic mirror system is the Cassegrain-type or Gregorian-type solar-thermal system. These systems are used in manufacturing

parabolic mirror toward the hole "d+

where it burns in the atmosphere.

bolic mirror and back to the Sun.

parabolic mirror (see Figure 14).

mechanical system.

Figure 13.

Design of solar-thermal system.

Planetology - Future Explorations

onto the space debris.

20

optical telescopes or radio antennas [13].

The lens that is placed in the light tube has the role to focus the light on a very small area in order to assure very high power density. Theoretically, the energy can be focused on a geometric point. In reality due to chromatic aberration and shape errors, light is not focused quite precisely. The lens presented in Figure 15 is made out of and elastic material filled with a colourless liquid.

Approximating surfaces "S1" and "S2" with spheres having radii "r1" and "r2," respectively, assuming the thickness of the lends is denoted as "d" and neglecting the optical effect of transparent elastic material (which is very thin) if the refractive index of the liquid is "n," the focal distance "f" of the lens is given by the following equation [13]:

$$\frac{\mathbf{1}}{\mathbf{f}} = (\mathbf{n} - \mathbf{1}) \cdot \left[ \frac{\mathbf{1}}{\mathbf{r}\_1} - \frac{\mathbf{1}}{\mathbf{r}\_2} + \frac{(\mathbf{n} - \mathbf{1}) \cdot \mathbf{d}}{\mathbf{n} \cdot \mathbf{r}\_1 \cdot \mathbf{r}\_2} \right] \tag{7}$$

Figure 15. Lens design filled with liquid.

In order to simplify the case of such model, consider r1 = r2 = r:

$$\frac{\mathbf{1}}{\mathbf{f}} = (\mathbf{n} - \mathbf{1}) \cdot \left[ \frac{\mathbf{1}}{\mathbf{r}} - \frac{\mathbf{1}}{\mathbf{r}} + \frac{(\mathbf{n} - \mathbf{1}) \cdot \mathbf{d}}{\mathbf{n} \cdot \mathbf{r} \cdot \mathbf{r}} \right] = \frac{(\mathbf{n} - \mathbf{1})^2 \cdot \mathbf{d}}{\mathbf{n} \cdot \mathbf{r}^2} \tag{8}$$

3.3 Estimated power, specific impulse, and thrust calculations

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

are considered constant for a wide range of temperatures:

• Melting temperature: tm = 660.3°C, Tm = 933.3 K

• Heat capacity (solid aluminium): cS = 0.9 kJ/kg K

• Heat capacity (liquid aluminium): cL = 1.18 kJ/kg K

• First ionization energy: cion = 577.5 kJ/mol (21,388 kJ/kg)

T0 = 0 K, the total heat needed to vaporize aluminium is

3.3.2 Estimated specific impulse and thrust calculations

present case, the process should be similar.

Making the appropriate substitutions in Eq. (9) results

• Boiling temperature: tb = 2470°C, Tb = 2743 K

• Heat of fusion: cf = 398 kJ/kg (10.71 kJ/mol)

• Heat of vaporization: cv = 6088.3 kJ/kg

in 1 s is presented.

materials [20].

23

The space debris is made of various metals (aluminium, titanium, carbon fiber composite, steel, etc.). For example, consider a space debris made out of aluminium. In Chapter 2 we've considered the space debris made out of iron.

Consider aluminium properties listed in the literature [19]. For simplicity they

Using Eq. (2) for 1 kg of aluminium and assuming that the starting temperature

Evap ¼ 0:9 � 2743 þ 398 þ 1:18 � ð2743 � 933:3Þ þ 10518 ¼ 15520 kJ=kg (10)

Eion ¼ Evap þ cion ¼ 15520 þ 21388 ¼ 36908 kJ=kg

In Table 3 the amount of aluminium that the system can vaporize and ionize

The process of generating reaction force due to material ablation is very complex. This effect was observed by pointing a laser to a material surface [20]. In this

In the case of laser rays, ablation takes place when the material is removed from a substrate through direct absorption of laser ray energy. As a first condition, the radiation energy must exceed a given threshold, which is less than 10 J/cm<sup>2</sup> for metals, 2 J/cm<sup>2</sup> for insulating inorganic materials, and 1 J/cm<sup>2</sup> for organic insulation

The solar-thermal system discussed here (see Table 2, case no. 1) satisfies this

0.98 � 0.98 � 88.4 = 84.9 kW, it provides an energy of 10 J in 1.18 � <sup>10</sup>�<sup>4</sup> s [20].

requirement because, even when the power of the smallest mirror is

The total energy needed to ionize aluminium atoms after vaporization is

Evap ¼ 1 � cS � ð Þþ Tb � T0 cf � 1 þ cL � ð Þþ Tb � Tm cv � 1 (9)

3.3.1 Estimated power calculations

DOI: http://dx.doi.org/10.5772/intechopen.86565

Eq. (8) shows that for a given n and d, when r ─› <sup>∞</sup> (i.e., low pressure of liquid inside the lens), f ─› <sup>∞</sup>, i.e., theoretically the system can hit the target (space debris) at any distance. However, due to aberration and imprecision of lens dimensions, this distance is limited. Lens operation is illustrated in Figure 16.

The temperature of liquid must be kept in an appropriate range for preserving the liquid state (avoiding of freezing). A resistor fed by battery charged by solar cells heats the liquid which is circulated permanently by a pump with a low speed. The electro-valve is normally opened. When hitting the space debris is necessary, the electro-valve is closed, and the liquid bends the lens to the necessary curvature. Some suitable liquids and reflective indexes are given in Table 2 [17].

The transparent elastic material can be polydimethylsiloxane (PDMS) which has good optical properties and large elongation and is highly transparent (over 96%) in the range of visible wavelengths. PDMS refractive index is nPDMS = 1.41. In a terrestrial application, such an elastomeric membrane having 60 microns in thickness was used in manufacturing convex lenses [18]. The refractive liquid used in that design was water.

Figure 16. How a lens filled with liquid operates to eliminate space debris.


Table 2. Suitable liquids for lens.

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris DOI: http://dx.doi.org/10.5772/intechopen.86565

### 3.3 Estimated power, specific impulse, and thrust calculations

#### 3.3.1 Estimated power calculations

In order to simplify the case of such model, consider r1 = r2 = r:

<sup>þ</sup> ð Þ� <sup>n</sup> � <sup>1</sup> <sup>d</sup> n � r � r

Eq. (8) shows that for a given n and d, when r ─› <sup>∞</sup> (i.e., low pressure of liquid

The temperature of liquid must be kept in an appropriate range for preserving the liquid state (avoiding of freezing). A resistor fed by battery charged by solar cells heats the liquid which is circulated permanently by a pump with a low speed. The electro-valve is normally opened. When hitting the space debris is necessary, the electro-valve is closed, and the liquid bends the lens to the necessary curvature.

The transparent elastic material can be polydimethylsiloxane (PDMS) which has good optical properties and large elongation and is highly transparent (over 96%) in the range of visible wavelengths. PDMS refractive index is nPDMS = 1.41. In a terrestrial application, such an elastomeric membrane having 60 microns in thickness was used in manufacturing convex lenses [18]. The refractive liquid used in

No. Liquid Refractive index, n Aniline 1.586 Benzyl benzoate 1.568 Ethylene glycol 1.43 Glycerin (glycerol) 1.47 Water 1.333

<sup>¼</sup> ð Þ <sup>n</sup> � <sup>1</sup> <sup>2</sup> � <sup>d</sup>

<sup>n</sup> � r2 (8)

inside the lens), f ─› <sup>∞</sup>, i.e., theoretically the system can hit the target (space debris) at any distance. However, due to aberration and imprecision of lens dimen-

sions, this distance is limited. Lens operation is illustrated in Figure 16.

Some suitable liquids and reflective indexes are given in Table 2 [17].

1 r � 1 r

1

Planetology - Future Explorations

that design was water.

Figure 16.

Table 2.

22

Suitable liquids for lens.

How a lens filled with liquid operates to eliminate space debris.

<sup>f</sup> <sup>¼</sup> ð Þ� <sup>n</sup> � <sup>1</sup>

The space debris is made of various metals (aluminium, titanium, carbon fiber composite, steel, etc.). For example, consider a space debris made out of aluminium. In Chapter 2 we've considered the space debris made out of iron.

Consider aluminium properties listed in the literature [19]. For simplicity they are considered constant for a wide range of temperatures:


Using Eq. (2) for 1 kg of aluminium and assuming that the starting temperature T0 = 0 K, the total heat needed to vaporize aluminium is

$$\mathbf{E\_{vap}} = \mathbf{1} \cdot \mathbf{c\_S} \cdot (\mathbf{T\_b} - \mathbf{T\_0}) + \mathbf{c\_f} \cdot \mathbf{1} + \mathbf{c\_L} \cdot (\mathbf{T\_b} - \mathbf{T\_m}) + \mathbf{c\_v} \cdot \mathbf{1} \tag{9}$$

Making the appropriate substitutions in Eq. (9) results

$$\mathbf{E\_{vap}} = \mathbf{0.9} \cdot \mathbf{2743} + \mathbf{398} + \mathbf{1.18} \cdot (\mathbf{2743} - \mathbf{933.3}) + \mathbf{10518} = \mathbf{15520 kJ/kg} \tag{10}$$

The total energy needed to ionize aluminium atoms after vaporization is

$$\mathbf{E\_{ion}} = \mathbf{E\_{vap}} + \mathbf{c\_{ion}} = \mathbf{15520} + \mathbf{21388} = \mathbf{36908 kJ/kg}$$

In Table 3 the amount of aluminium that the system can vaporize and ionize in 1 s is presented.

#### 3.3.2 Estimated specific impulse and thrust calculations

The process of generating reaction force due to material ablation is very complex. This effect was observed by pointing a laser to a material surface [20]. In this present case, the process should be similar.

In the case of laser rays, ablation takes place when the material is removed from a substrate through direct absorption of laser ray energy. As a first condition, the radiation energy must exceed a given threshold, which is less than 10 J/cm<sup>2</sup> for metals, 2 J/cm<sup>2</sup> for insulating inorganic materials, and 1 J/cm<sup>2</sup> for organic insulation materials [20].

The solar-thermal system discussed here (see Table 2, case no. 1) satisfies this requirement because, even when the power of the smallest mirror is 0.98 � 0.98 � 88.4 = 84.9 kW, it provides an energy of 10 J in 1.18 � <sup>10</sup>�<sup>4</sup> s [20].


#### Table 3.

The quantity of aluminium vaporized by the system in 1 s.

Another condition is related to the energy absorption mechanism. Chemical composition, microstructure, and morphology of material strongly influence the absorption of heat.

For the case where Isp has a known value, one can evaluate the thrust force by

where g0 represents the gravitational acceleration at the Earth's surface

Cm <sup>¼</sup> Tf

In case the large parabolic mirror has a diameter of rlpm = 25 m, the thrust

In both cases the thrust force is remarkably high and can deorbit space debris

This new design is inspired by the tragic loss of the Space Shuttle Columbia's crew on February 1, 2003 [24]. Columbia disintegrated over Texas and Louisiana when it reentered the Earth's atmosphere. During the launch of the space shuttle, a piece of foam insulation struck the left wing of the orbiter deteriorating its ablative protection [24]. When time came for the space shuttle to reenter the Earth's atmosphere, the damage caused by the foam insulation allowed hot air to penetrate into

According to the above reference, Cm max Al = 6�10�5 N/W for aluminium. That means that in the case of ablation of a space debris made of aluminium using a solar-

Tf <sup>¼</sup> <sup>P</sup> � Cm max Al <sup>¼</sup> <sup>88400</sup> � <sup>6</sup> � <sup>10</sup>�<sup>5</sup> <sup>¼</sup> <sup>5</sup>:3 N (13)

Tf 25 <sup>¼</sup> <sup>P</sup> � Cm max Al <sup>¼</sup> <sup>2670300</sup> � <sup>6</sup> � <sup>10</sup>�<sup>5</sup> <sup>¼</sup> <sup>160</sup>:2 N (14)

). m represents the mass of ions ejected in 1 s. \_ Momentum coupling coefficient Cm is another method for thrust evaluation [20]. This coefficient characterizes thrust production efficiency. The coefficient is determined as the thrust to laser power ratio. This parameter determines the mini-

Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris

thermal system with a power of P = 88.4 kW, the thrust force resulted is

4. A new design of space equipment for rapid disintegration in

mum light power required to produce a 1 N thrust:

Tf ¼ g0 � Isp � m\_ (11)

<sup>P</sup> (12)

the following equation:

The effect of a focused light ray on a material [22].

DOI: http://dx.doi.org/10.5772/intechopen.86565

(g0 = 9.81 m/s<sup>2</sup>

Figure 17.

force is

25

with just a few hits.

atmosphere after reentry

Heating debris must be sufficiently fast for homogenous nucleation and expansion of vapor bubbles and ions.

Some simulations done for interaction of laser rays have shown that [21]:


Note: The mentioned simulations have been conducted only for iron, not for aluminium or other materials currently used in manufacturing satellites and space equipment, but the effect should be similar (Figure 17).

In some experiments a specific impulse of around 4000 s was measured for carbon and aluminium in ionized state produced by the laser ray [23]:

During those experiments the following observations were made:


Technologies for Deviation of Asteroids and Cleaning of Earth Orbit by Space Debris DOI: http://dx.doi.org/10.5772/intechopen.86565

Figure 17. The effect of a focused light ray on a material [22].

Another condition is related to the energy absorption mechanism. Chemical composition, microstructure, and morphology of material strongly influence the

Some simulations done for interaction of laser rays have shown that [21]:

• The degree of light absorption increases as the cavity deepens.

Collected solar power, P (kW)

 5 88.4 6 2 7.5 240.3 15 7 10 427.3 28 12 15 961.3 62 26 20 1709.0 110 46 25 2670.3 172 72

Flow of aluminium vapors per second, g

Flow of aluminium ions (first level) per second, g

forms the final conical shape of the cavity.

equipment, but the effect should be similar (Figure 17).

the higher the specific impulse.

• The ablation time was 1.5 s.

the target.

24

Heating debris must be sufficiently fast for homogenous nucleation and expan-

• Maximum energy absorbed by the cavity is around 80% of the total energy of

• The radiation is multiple times reflected by the cavity, and as a result, the energy is highly concentrated at the center and the bottom of the cavity and

• The surface temperature is much higher than the normal boiling point.

• In order to be able to remove the material, it must have a homogenous boiling regime and evaporation; the power intensity must be over 108 W/cm<sup>2</sup>

Note: The mentioned simulations have been conducted only for iron, not for aluminium or other materials currently used in manufacturing satellites and space

In some experiments a specific impulse of around 4000 s was measured for

• The speed of the ejected atoms and implicitly Isp is inversely proportional to the square roots of the atomic mass of ablated material; the lighter the element

• The speed of the ejected atoms was independent of angle at 22 cm away from

carbon and aluminium in ionized state produced by the laser ray [23]: During those experiments the following observations were made:

• Thrust tends to increase with atomic mass of ablated material.

.

absorption of heat.

Case no.

Table 3.

radiation.

sion of vapor bubbles and ions.

The quantity of aluminium vaporized by the system in 1 s.

Radius of large parabolic mirror, rlpm (m)

Planetology - Future Explorations

For the case where Isp has a known value, one can evaluate the thrust force by the following equation:

$$\mathbf{T\_f = g\_0 \cdot I\_{sp} \cdot \dot{m}}\tag{11}$$

where g0 represents the gravitational acceleration at the Earth's surface (g0 = 9.81 m/s<sup>2</sup> ). m represents the mass of ions ejected in 1 s. \_

Momentum coupling coefficient Cm is another method for thrust evaluation [20]. This coefficient characterizes thrust production efficiency. The coefficient is determined as the thrust to laser power ratio. This parameter determines the minimum light power required to produce a 1 N thrust:

$$\mathbf{C\_m} = \frac{\mathbf{T\_f}}{\mathbf{P}} \tag{12}$$

According to the above reference, Cm max Al = 6�10�5 N/W for aluminium. That means that in the case of ablation of a space debris made of aluminium using a solarthermal system with a power of P = 88.4 kW, the thrust force resulted is

$$\mathbf{T\_f} = \mathbf{P} \cdot \mathbf{C\_{m\ max}}\\\mathbf{A}| = 88400 \cdot 6 \cdot 10^{-5} = 5.3 \text{ N} \tag{13}$$

In case the large parabolic mirror has a diameter of rlpm = 25 m, the thrust force is

$$\text{T}\_{\text{f}} \text{ }\_{25} = \text{P} \cdot \text{C}\_{\text{m } \text{max Al}} = 2670 \, 300 \cdot 6 \cdot 10^{-6} = 160.2 \, \text{N} \tag{14}$$

In both cases the thrust force is remarkably high and can deorbit space debris with just a few hits.

## 4. A new design of space equipment for rapid disintegration in atmosphere after reentry

This new design is inspired by the tragic loss of the Space Shuttle Columbia's crew on February 1, 2003 [24]. Columbia disintegrated over Texas and Louisiana when it reentered the Earth's atmosphere. During the launch of the space shuttle, a piece of foam insulation struck the left wing of the orbiter deteriorating its ablative protection [24]. When time came for the space shuttle to reenter the Earth's atmosphere, the damage caused by the foam insulation allowed hot air to penetrate into

the wing creating an irregular hole. Air entered the left wing with high speed, quickly became very hot when stagnating, and destroyed the internal structure of the wing.
