**1. Introduction**

Aeroassist maneuvers are a family of maneuvers that use aerodynamic forces to change a spacecraft orbit and they include atmospheric entry, aerocapture, aerobraking, and aerogravity-assist. Atmospheric entry is used for in situ explorations, both for robotic and human missions. Atmospheric entry at Mars has been attempted many times by multiple space agencies. Entry at Mars was considered a challenging task mainly due to the unique atmospheric structure [1]. The atmosphere is substantial that aerothermodynamic heating is a consideration, yet the atmosphere is very thin that the aerodynamic drag is barely enough for entry vehicles to decelerate to a velocity at high altitude to safely initiate the final descent stage for a soft landing (i.e., parachute or retro-propulsion).

The concept of using atmosphere to change orbit can be traced back to the earliest publication by London in 1961 [2], which later evolved intro three main categories—aerobraking, aerocapture, and aerogravity-assist. Aerobraking is a maneuver where spacecraft uses atmospheric drag to reduce its orbital period, and it can be used for orbit transfer vehicles from GEO to LEO, or after initial orbit insertion for planetary missions. In the context of Mars missions, aerobraking maneuver is considered free in terms of system requirement because no additional system/mass is needed to perform the maneuver. All the prior aerobraking spacecraft use solar panel as the drag device to decelerate. However, aerobraking

maneuver is not free in terms of operational cost. Due to the long duration of aerobraking maneuver—on the order of months, constant ground operation is required in the past for aerobraking maneuver, which requires hours of staffs and dedicated time with the Deep Space Network (DSN) for position tracking [3].

*<sup>L</sup>* <sup>¼</sup> <sup>1</sup> 2 *ρV*<sup>2</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.93281*

*Aerocapture, Aerobraking, and Entry for Robotic and Human Mars Missions*

ysis of trajectories during atmospheric fly-through or entry.

convective heat rate with an arbitrary gas mixture:

gravitational acceleration.

1.8980 � <sup>10</sup>�<sup>8</sup>

*f V*ð Þ approaching zero.

**2.3 Vehicle designs**

**Figure 1.**

**35**

**2.2 Aerothermodynamic heating**

heating rate, *<sup>q</sup>*\_*<sup>r</sup>* is W/cm<sup>2</sup> follows [6]:

*ACL*, *<sup>D</sup>* <sup>¼</sup> <sup>1</sup>

where *CL* is the aerodynamic lift coefficient, and *A* is the aerodynamic reference area of the vehicle. The angle of attack, *α*, affects the value of *CL* and *CD*, and is assumed constant as the trim angle of attack. *<sup>g</sup>* <sup>¼</sup> *<sup>μ</sup>=r*<sup>2</sup> is the radial component of the

These equations of motion are used throughout this chapter for numerical anal-

As the spacecraft flies through the atmosphere at hypersonic speed, the aerothermodynamic heating can be substantial for entry and aerocapture. Aerothermo-

convective and radiative. Sutton and Graves [5] developed an empirical relation for

*<sup>q</sup>*\_*<sup>c</sup>* <sup>¼</sup> *<sup>k</sup>*ð Þ *<sup>ρ</sup>=Rn* <sup>0</sup>*:*<sup>5</sup>

where *Rn* is the nose radius in m. *<sup>q</sup>*\_*<sup>c</sup>* has the unit of W/cm<sup>2</sup> and *<sup>k</sup>* has a value of

where *f V*ð Þ is provided for velocities between 6000 m/s and 9000 m/s and is shown in **Figure 1**. At low speed, radiative heating becomes insignificant due to

Thermal protection system (TPS) is an important vehicle component for all aeroassist maneuvers to protect the spacecraft from the heat generated during the atmospheric pass. Entry and aerocapture can share the vehicle designs as both maneuvers result in very high heat, which warrants TPS. However, aerobraking maneuvers have been achieved without a dedicated TPS and solar panels had been used as the drag device to reduce orbital period; therefore, the following discussion

, *ρ* is the atmospheric density. The empirical relation for radiative

0*:*526

dynamic heating consists of mainly two types of dominating heat transfers:

*<sup>q</sup>*\_*<sup>r</sup>* <sup>¼</sup> <sup>2</sup>*:*<sup>35</sup> � <sup>10</sup><sup>4</sup>*<sup>r</sup>*

*Coefficient value f V*ð Þ *as a function of velocity for radiative heating relation [6].*

2 *ρV*<sup>2</sup>

*ACD* (7)

*V*<sup>3</sup> (8)

*<sup>n</sup> <sup>ρ</sup>*<sup>1</sup>*:*<sup>19</sup>*f V*ð Þ (9)

Aerocapture is an orbit insertion maneuver. Upon first approaching a planet upon hyperbolic trajectory, the spacecraft passes the body's atmosphere once to decelerate and achieve a captured orbit after the single pass. Aerocapture maneuver has been studied in the literature but has never been tested or demonstrated in flight. Aerocapture at Mars is considered side-by-side with aerobraking or direct propulsive orbit insertion.

Aerogravity-assist is a maneuver for interplanetary transfer and most often considered for fast transfer time to the outer solar system for which Mars can be used as a destination to perform aerogravity-assist maneuver, therefore aerogravity-assist will not be discussed in detail in this chapter.

The structure of the chapter is as follows: in Section 2 we discuss the mathematical models and summarize the key parameters for aeroassist maneuvers and vehicles. In Section 3, aerobraking technology is presented along with a new perspective on aerobraking at Mars. In Section 4, we discuss Mars entry technology and the system performance and requirements for future missions. In Section 5, we discuss the performance and system requirements for aerocapture.

#### **2. Mathematical models**

#### **2.1 Equations of motion**

Assuming a nonrotating body in the body-centered and body-fixed reference frame, the equations of motions for entry, aerocapture, and aerobraking are as follows [4]:

$$\dot{\theta} = \frac{V \cos \chi \cos \chi}{r \cos \phi} \tag{1}$$

$$\dot{\phi} = -\frac{V\cos\chi\sin\chi}{r} \tag{2}$$

$$
\dot{r} = V \sin \chi \tag{3}
$$

$$
\dot{V} = -\frac{q}{\beta} - \mathbf{g}\sin\chi\tag{4}
$$

$$\dot{\chi} = -\frac{q(L/D)}{V\beta}\cos\sigma + \left(\frac{V}{r} - \frac{\mathbf{g}}{V}\right)\cos\chi\tag{5}$$

$$\dot{\chi} = \frac{q(L/D)}{V\beta} \frac{\cos \sigma}{\cos \chi} + \frac{V}{r} \cos \chi \sin \chi \tan \phi + \frac{\text{g}}{V} \frac{\cos \chi}{\cos \chi} \tag{6}$$

where *θ* and *ϕ* are the longitude and latitude in a spherical surface model; *r* the radial distance from the center; *χ* is the heading angle measured clockwise from the direction of local parallel; *V* is the velocity of the vehicle; *γ* is the flight path angle (positive above local horizon); *σ* is the bank angle, which is the rotation angle about the relative velocity vector; *β* ¼ *m=*ð Þ *CDA* is the ballistic coefficient where *m* is the vehicle mass and *CD* is the aerodynamic drag coefficient; and *<sup>q</sup>* <sup>¼</sup> ð Þ <sup>1</sup>*=*<sup>2</sup> *<sup>ρ</sup>V*<sup>2</sup> is the dynamic pressure, where *ρ* is the density of the atmosphere, and *L* and *D* are the lift and drag forces respectively and are defined as:

*Aerocapture, Aerobraking, and Entry for Robotic and Human Mars Missions DOI: http://dx.doi.org/10.5772/intechopen.93281*

$$L = \frac{1}{2}\rho V^2 A C\_L, \qquad D = \frac{1}{2}\rho V^2 A C\_D \tag{7}$$

where *CL* is the aerodynamic lift coefficient, and *A* is the aerodynamic reference area of the vehicle. The angle of attack, *α*, affects the value of *CL* and *CD*, and is assumed constant as the trim angle of attack. *<sup>g</sup>* <sup>¼</sup> *<sup>μ</sup>=r*<sup>2</sup> is the radial component of the gravitational acceleration.

These equations of motion are used throughout this chapter for numerical analysis of trajectories during atmospheric fly-through or entry.

#### **2.2 Aerothermodynamic heating**

maneuver is not free in terms of operational cost. Due to the long duration of aerobraking maneuver—on the order of months, constant ground operation is required in the past for aerobraking maneuver, which requires hours of staffs and dedicated time with the Deep Space Network (DSN) for position tracking [3]. Aerocapture is an orbit insertion maneuver. Upon first approaching a planet upon hyperbolic trajectory, the spacecraft passes the body's atmosphere once to decelerate and achieve a captured orbit after the single pass. Aerocapture maneuver has been studied in the literature but has never been tested or demonstrated in flight. Aerocapture at Mars is considered side-by-side with aerobraking or direct

Aerogravity-assist is a maneuver for interplanetary transfer and most often considered for fast transfer time to the outer solar system for which Mars can be

The structure of the chapter is as follows: in Section 2 we discuss the mathematical models and summarize the key parameters for aeroassist maneuvers and vehicles. In Section 3, aerobraking technology is presented along with a new perspective on aerobraking at Mars. In Section 4, we discuss Mars entry technology and the system performance and requirements for future missions. In Section 5, we discuss

Assuming a nonrotating body in the body-centered and body-fixed reference frame, the equations of motions for entry, aerocapture, and aerobraking are as

*<sup>θ</sup>* <sup>¼</sup> *<sup>V</sup>* cos *<sup>γ</sup>* cos *<sup>χ</sup>*

*<sup>ϕ</sup>*\_ ¼ � *<sup>V</sup>* cos *<sup>γ</sup>* sin *<sup>χ</sup> r*

> *V r* � *g V*

cos *<sup>γ</sup>* sin *<sup>χ</sup>* tan *<sup>ϕ</sup>* <sup>þ</sup> *<sup>g</sup>*

*<sup>V</sup>*\_ ¼ � *<sup>q</sup>*

*<sup>V</sup><sup>β</sup>* cos *<sup>σ</sup>* <sup>þ</sup>

where *θ* and *ϕ* are the longitude and latitude in a spherical surface model; *r* the radial distance from the center; *χ* is the heading angle measured clockwise from the direction of local parallel; *V* is the velocity of the vehicle; *γ* is the flight path angle (positive above local horizon); *σ* is the bank angle, which is the rotation angle about the relative velocity vector; *β* ¼ *m=*ð Þ *CDA* is the ballistic coefficient where *m* is the vehicle mass and *CD* is the aerodynamic drag coefficient; and *<sup>q</sup>* <sup>¼</sup> ð Þ <sup>1</sup>*=*<sup>2</sup> *<sup>ρ</sup>V*<sup>2</sup> is the dynamic pressure, where *ρ* is the density of the atmosphere, and *L* and *D* are the lift

*<sup>γ</sup>*\_ ¼ � *q L*ð Þ *<sup>=</sup><sup>D</sup>*

cos *σ* cos *γ* þ *V r*

*<sup>χ</sup>*\_ <sup>¼</sup> *q L*ð Þ *<sup>=</sup><sup>D</sup> Vβ*

and drag forces respectively and are defined as:

*<sup>r</sup>* cos *<sup>ϕ</sup>* (1)

*r*\_ ¼ *V* sin *γ* (3)

*V*

cos *χ* cos *γ*

*<sup>β</sup>* � *<sup>g</sup>* sin *<sup>γ</sup>* (4)

cos *γ* (5)

(2)

(6)

\_

used as a destination to perform aerogravity-assist maneuver, therefore

aerogravity-assist will not be discussed in detail in this chapter.

the performance and system requirements for aerocapture.

propulsive orbit insertion.

*Mars Exploration - A Step Forward*

**2. Mathematical models**

**2.1 Equations of motion**

follows [4]:

**34**

As the spacecraft flies through the atmosphere at hypersonic speed, the aerothermodynamic heating can be substantial for entry and aerocapture. Aerothermodynamic heating consists of mainly two types of dominating heat transfers: convective and radiative. Sutton and Graves [5] developed an empirical relation for convective heat rate with an arbitrary gas mixture:

$$
\dot{q}\_c = k(\rho/R\_n)^{0.5} V^3 \tag{8}
$$

where *Rn* is the nose radius in m. *<sup>q</sup>*\_*<sup>c</sup>* has the unit of W/cm<sup>2</sup> and *<sup>k</sup>* has a value of 1.8980 � <sup>10</sup>�<sup>8</sup> , *ρ* is the atmospheric density. The empirical relation for radiative heating rate, *<sup>q</sup>*\_*<sup>r</sup>* is W/cm<sup>2</sup> follows [6]:

$$\dot{q}\_r = 2.35 \times 10^4 r\_n^{0.526} \rho^{1.19} f(V) \tag{9}$$

where *f V*ð Þ is provided for velocities between 6000 m/s and 9000 m/s and is shown in **Figure 1**. At low speed, radiative heating becomes insignificant due to *f V*ð Þ approaching zero.

#### **2.3 Vehicle designs**

Thermal protection system (TPS) is an important vehicle component for all aeroassist maneuvers to protect the spacecraft from the heat generated during the atmospheric pass. Entry and aerocapture can share the vehicle designs as both maneuvers result in very high heat, which warrants TPS. However, aerobraking maneuvers have been achieved without a dedicated TPS and solar panels had been used as the drag device to reduce orbital period; therefore, the following discussion

**Figure 1.** *Coefficient value f V*ð Þ *as a function of velocity for radiative heating relation [6].*

on vehicle designs is applicable to aerocapture and entry. Heritage blunt-body rigid aeroshell designs have been proven for both robotic and manned missions. Most robotic missions used ballistic entry vehicles, which have no active guidance or control (e.g., Mars Pathfinder, Mars Exploration Rovers (MER), and Mars Phoenix), whereas lifting body entry vehicles are used for manned missions and some Mars missions; for example, Mars Science Laboratory used a lifting vehicle in order to meet the landing accuracy requirement and Apollo entry capsules met the safe g-load limit acceptable to humans.

require a high accuracy in hypersonic flow modeling and the uncertainties at hypersonic speed can be very difficult to predict; therefore, they have mostly been

Magnetohydrodynamics flow control is another means to actively control the trajectory, which uses the Lorentz force (i.e., the interaction between the plasma field from the hypersonic entry and magnetic field) [19]. It has been shown useful for entry trajectory control and similar is applicable for aerocapture trajectory control. Last but not the least is applying propulsion during aerocapture maneuver to create propulsive "lift" force in order to achieve the necessary trajectory control [20].

Aerobraking maneuver was first successfully demonstrated at Venus with Magellan mission in 1993 after completing its prime mission. Magellan used aerobraking maneuver to reduce its orbital period from 3.23 h to 1.57 h. Following the Magellan's success, three Mars missions have used aerobraking as an enabling technology to reduce the propellant requirement to enter the target science orbits. The three missions are Mars Global Surveyor (MGS), Mars Odyssey, and Mars Reconnaissance Orbiter (MRO), which were launched in 1996, 2001, and 2005 respectively. **Table 2** summarizes the spacecraft parameters and aerobraking performances for selected aerobraking missions. As shown, the fuel mass saving for all three Mars missions are all over 1000 m/s, which is very significant compared with the launch mass. According to the rocket equation, the propellant mass follows an exponential relation to the required Δ*V*, the amount of fuel savings can be consid-

Aerobraking operation includes mainly three phases—walk-in phase, main phase, and walk-out phase. The walk-in phase follows the initial Mars orbit insertion, and reduces the periapsis altitude within Mars atmosphere. During the main phase of aerobraking, the spacecraft uses atmospheric drag to reduce the energy and apoapsis altitude. Past missions have used the solar panel as the main drag device. The

**Spacecraft Magellan MGS Odyssey MRO** Destination Venus Mars Mars Mars Launch mass, kg 360 1060 725 2180 Propellant mass, kg 2414 385 348.7 1149 Payload mass, kg 154 78 44.5 139 AB Δ*V* saving, m/s 1220 1220 1090 1190 AB fuel saving, kg 490 330 320 580 AB duration 70 days 6 months 2.5 months 5 months Period before AB, h 3.2 45 18 34 Period after AB, h 1.6 1.9 2 1.9 AB periapsis range, km 171.3–196.9 100–149 107–119 97–110 Dynamic pressure, N/m<sup>2</sup> 0.2–0.3 0.6a 0.2–0.3 — Heat rate, W/cm<sup>2</sup> ——— 0.75–1.6

*Dynamic pressure is reduced to 0.2 N/m<sup>2</sup> after the failure of solar panel hinge.*

*Performance and spacecraft parameters for past Venus and Mars missions using aerobraking.*

studied in paper and has not been implemented in missions.

*DOI: http://dx.doi.org/10.5772/intechopen.93281*

*Aerocapture, Aerobraking, and Entry for Robotic and Human Mars Missions*

**3. Aerobraking at Mars**

ered enabling for MGS and Odyssey.

*a*

**37**

**Table 2.**

With lifting vehicle design, the guidance and control actively modulate the direction of the lift vector thus to control the trajectory, which is also called bank modulation. The lifting vehicles are typically designed with a nominal L/D with center-of-mass offset or asymmetric heatshield, and are also equipped with thrusters to control the orientation of the lifting vector. **Table 1** lists some lifting body entry vehicles. Vehicle design with spherical section and sphere-cones are most popular and have been used for all entry missions and they can provide L/D of more than 0.3. These rigid body aeroshells are shown feasible for both entry and aerocapture missions for various planetary bodies [8–10].

Adaptable Deployable Entry and Placement Technology (ADEPT) [11] and Hypersonic Inflatable Aerodynamic Decelerator (HIAD) [12] are deployable entry systems that are currently being developed. Both ADEPT and HIAD are applicable to a range of mission sizes from small satellites to larger payloads. Ellipsled vehicle design, or mid-L/D vehicle, has been proposed as a means to increase vehicle control authority (e.g., for ice giants missions [8]) or deliver higher payload mass, such as for human Mars architectures. Starbody waverider can achieve higher nominal L/D (>5.0) than other designs and is mostly useful for interplanetary transfer maneuvers such as aerogravity-assist; therefore, it is only referenced here for comparison [7, 13]. Higher L/D vehicles are available, but in the context of Mars missions, they have very limited applications.

Drag modulation, in addition to bank modulation, is another design that provides the vehicle control authority. Drag modulation uses ballistic vehicles but with additional drag skirt that can be modified to change the vehicle's ballistic coefficient, thus achieving trajectory control in the atmosphere. Such vehicles would require a large ratio for the designed low and high values of ballistic coefficients. Drag modulations can be used for both entry and aerocapture at Mars [14, 15].

Angle-of-attack modulation has also been investigated for Mars entry [16] and shown feasible for aerocapture missions [17]. Direct force control is yet another control mode for entry vehicles, which uses active flaps to create moments and controls the angle-of-attack and side slip angles [18]. Both of the control modes


#### **Table 1.**

*Performance and spacecraft parameters for past Venus and Mars missions using aerobraking.*

*Aerocapture, Aerobraking, and Entry for Robotic and Human Mars Missions DOI: http://dx.doi.org/10.5772/intechopen.93281*

require a high accuracy in hypersonic flow modeling and the uncertainties at hypersonic speed can be very difficult to predict; therefore, they have mostly been studied in paper and has not been implemented in missions.

Magnetohydrodynamics flow control is another means to actively control the trajectory, which uses the Lorentz force (i.e., the interaction between the plasma field from the hypersonic entry and magnetic field) [19]. It has been shown useful for entry trajectory control and similar is applicable for aerocapture trajectory control. Last but not the least is applying propulsion during aerocapture maneuver to create propulsive "lift" force in order to achieve the necessary trajectory control [20].
