Chapter 4. Integrated Algorithm for Impact Lunar Transfer Trajectories. using Pseudo state Technique
|
|
- Phillip Lane
- 5 years ago
- Views:
Transcription
1 Chapter 4 Integrated Algorithm for Impact Lunar Transfer Trajectories using Pseudo state Technique Abstract A new integrated algorithm to generate the design of one-way direct transfer trajectory for moon missions is presented. The departure translunar state together with some unknown Earth parking orbit parameters is determined. The transfer trajectories are generated including the gravity fields of the Earth and the moon based on pseudo state technique. Because the main aim is to develop a methodology for determining an initial departure state of a lunar transfer trajectory, for simplicity, a rectilinear hyperbola that results in impact is assumed for arrival phase. The translunar injection state, that is the initial state of the transfer trajectory, is obtained by iteration on the argument of latitude of the parking orbit through Lambert problem solutions. Lambert solution is obtained using the universal algorithm presented in Chapter 3. The numerical results obtained using the integrated algorithm are analyzed and a comparison with the Lambert conic solutions is made. The role of pseudo state solution in reducing the error in achieving the target is discussed. The reduction in the error in achieving the target position is found to be more than 95%. 4.1 Introduction In lunar and interplanetary travel, the space vehicle passes through multiple gravity fields, which makes the trajectory design more complex. For a lunar mission, the space vehicle passes through the gravity fields of the Earth and the moon; the trajectory design problem becomes a complex 3- body problem. Further, the non-spherical gravity fields of the 50
2 Earth and the moon also influence the transfer trajectory design. It is well known that there is no known closed form solution to this problem. The only method that generates near-exact solution for the 3-body equations of motion is a numerical one. This method is expensive and computationally intensive as it involves exorbitant number of simulations. Also the convergence depends on the initial guess made on the initial state. Evidently, this method is not suitable for mission planning purposes. As an altemate, analytical methods based on point conic, patched conic and pseudo conic techniques can be used for quick mission design and analysis. These techniques differ on the force model used in the transfer trajectory design process: the point conic technique ignores the gravity field of the moon and considers only the Earth; the patched conic technique considers one body at a time; the pseudo state considers the Earth for full flight duration and superimposes the moon's effect. Unlike in the interplanetary transfers, for lunar transfer a different approach is required because the gravity fields of the Earth and the moon overlap. As described earlier, the transfer trajectory design process consists of two parts: (i) determining the initial departure state (ii) solving the equation of motion of the spacecraft. Further, only some of the Earth parking orbit parameters are assumed and other parameters must be appropriately determined. In this chapter, an integrated algorithm that generates the initial departure state and the unknown parking orbit parameters concurrently is developed. Appropriate departure state for the lunar transfer trajectory is generated using a new iterative procedure. The solution of the equation of motion, that is trajectory propagation is obtained using pseudo state theory. The necessity of such an algorithm is discussed. An overview of evolution of the pseudo state theory and its application in the context of interplanetary missions is provided. A comparison with the Lambert's conic method (point conic method) is also made to establish the accuracy levels obtained with the integrated algorithm. 51
3 4.2 Interplanetary and Lunar Transfer Trajectory Phases When the design of transfer trajectory is attempted using analytical techniques, the design process is split into several phases to suit the assumptions made in the modeling of forces acting on the spacecraft. The interplanetary trajectory design involves three major phases in general: departure hyperbolic trajectory phase relative to the departure planet from MSI / Plane1" -- ~i-f..,..--"" ' Figure 4.1 Interplanetary transfer trajectory phases 52
4 Figure 4.2 Lunar transfer trajectory phases the parking orbit to the mean sphere of influence (MSI) of the departure planet (phase 1), interplanetary transfer trajectory phase relative to the central body (Sun) from the MSI of departure planet to the MSI of the target planet (phase 2), and approach hyperbolic trajectory phase relative to the target planet from the MSI of target planet to the parking orbit around the 53
5 target planet (phase 3). These three phases are to be synchronized to realize an integrated mission design. Firstly, the interplanetary phase (phase 2) is obtained by treating the target planets as point masses and by solving the resulting two-body Lambert problem. Then the determined initial conditions of the transfer trajectory, assumed to be at the MSI of the departure planet, are transformed into the conditions relative to the departure planet. These conditions are asymptotic relative to the departure planet. Departure phase is designed to achieve these asymptotic conditions by proper choice of the parking orbit characteristics. Similarly, approach trajectories are obtained by selecting an appropriate aim point satisfying the arrival constraints. A large number of iterations must be carried out on these three phases. to integrate them. For lunar missions, since the gravity field of the moon lies within the gravity field of the Earth, only two phases are required to be designed for the lunar transfer trajectory (LTT). The departure phase and the cruise phase are combined in to a single phase: from the Earth parking orbit to the MSI of the moon. The second phase is selenocentric hyperbolic phase : from the MSI of the moon to the lunar parking orbit (LPG). Appropriate Earth parking orbit (EPG) characteristics are determined to achieve the combined phase. The state on the parking orbit, at which translunar injection that puts the craft on course towards the moon is executed, must be determined together with the impulse requirement for translunar injection. 4.3 Pseudo state Theory and its Evolution Several analytical methods exist for the trajectory propagation and they can be grouped, mainly, into three categories (i) Point conic based methods (ii) Patched conic based methods (iii) Pseudo-state-theory based methods. Point conic and patched conic methods ignore the presence of multiple gravity fields or consider them one at a time to design the 54
6 transfer trajectory through the sphere of influence concepts. The relative velocity vectors are matched at the patch points on the sphere of influence by iteration, in the patched conic method. The initial state obtained through these methods, when numerically propagated under realistic force model, deviate from the actual transfer trajectory and fails to meet the desired mission objectives. The pseudo state theory solves the problem by correcting the major portion of the error occurring due to patched / point conic approaches without actually going for numerical integration. The evolution of the pseudo state theory started with Wilson Jr.'s paper [23], in He explained the theory behind the innovative idea in his paper. As described in his paper, the pseudo state theory to study the motion of a space vehicle under the gravitational influences of two bodies (termed as primary body and secondary body) is outlined as: (1) Given an initial state, propagate the trajectory to the desired time (at which the state of a space vehicle is to be found under the influence of two bodies) as a conic relative to the primary body. (2) Transform this primary-eentered state to a state with respect to the secondary body. (3) Propagate back along a straight line with the velocity vector with respect to the secondary body to the initial time to find the position of the space vehicle that would have been in the absence of the primary body gravity field. (4) Propagate forward to the desired time as aconic relative to the secondary body. The new state thus obtained is equivalent to the state, which would have been obtained by simulating the trajectory numerically from the initial state under the influence of the gravity fields of both the bodies. When the step sizes are small, this method equals the numerical integration. Byrnes and Hooper [26] developed a multi conic method, a rapid propagation method that was used in the design of trajectories for the Apollo mission. 55
7 Designing the trajectory in the presenceeof the gravity fields of the two target planets ' can be considered as a three-body Lambert problem. The above multi step propagation technique was modified into a one step method by Byrnes [24] to solve the three-body Lambert problem. In this technique the three-body Lambert problem is converted into many two-body Lambert problems of connecting two states viz., a departure state and a pseudo state (corresponding to a target aim point) in a fixed time. Consideration of the pseudo state instead of the real state of the target body accounts for the influence of the target body. Unlike in the multi conic method, the sweep back propagation time is not the same as that of the forward propagation time but a fixed time is chosen during which the secondary body gravity field is assumed to be active in addition to the central force field. This vicinity within which the secondary body is assumed to be active was called as pseudo state transformation sphere by Wilson and later as pseudosphere by other authors. This pseudosphere is a secondary body-centric sphere with sufficiently large radius. A discussion on the size the pseudosphere is included in a subsequent section. Essentially, for a lunar trajectory the influence of the Earth is considered for the total flight duration and the influence of the moon is superimposed for a fraction of flight duration. The approach trajectory to the target aim point, generally a hyperbola within the pseudosphere, is obtained by iteration together with iteration for the transfer trajectory. The technique of Byrnes is more suitable to handle gravity assist trajectories around the secondary body and it must be modified to just flyby the secondary body viz., one-way transfer meeting some target constraints. The target constraints on arrival scenario create additional complexity of fixing an aim point and an appropriate approach trajectory in the solution process. To avoid this complication Sergeyevsky et al. [27] introduced a simplification on the approach trajectory by assuming that it is a rectilinear hyperbola. Because the periapsis of a rectilinear hyperbola is 56
8 the center of the secondary body and the eccentricity is one, the target aim point gets fixed as the center of the target body. This partial knowledge about the approach trajectory avoids the iteration required to obtain hyperbolic approach trajectory characteristics. He has presented an algorithm to generate transfer trajectories for interplanetary missions. In addition to its simplicity due to the assumption on the approach trajectory, this method improves the initial conditions and, hence, the transfer trajectory by correcting the major portion of errors of the point conic method. It offers better initial guesses for precision-trajectory-generation process by reducing the number of iterations for convergence. Because the algorithm is presented as applicable to. interplanetary transfer trajectories, the requirements of the parking orbit conditions such as the ascending node of the injection plane and the location of trans planetary injection to attain the transfer trajectory design are not discussed. In general, this problem is tackled separately in interplanetary missions as it offers such flexibility. 4.4 Lunar Transfer Trajectory Design In the design of lunar transfer trajectories the flexibility of interplanetary trajectory discussed in the previous section is not available because the moon (secondary body) lies within the gravity field of the Earth (primary body) itself. In the case of interplanetary missions, the orbit transfer is carried out between the orbits of the planets, and hence, the initial position of the space vehicle is the same as the position of the Earth which can be obtained from ephemeris data for the given departure time, and the parking orbit requirements are computed based on departure asymptotic conditions that are represented by excess velocity vector, V~. Battin[40] presents a mathematical formulation to obtain circular parking orbit characteristics that achieves the departure asymptotic conditions ( the right ascension 57
9 and declination of V~ ). The information about the turn angle (e~) that depends on the shape of the departure hyperbolic trajectory is used to locate the trans planetary injection point. A strategy that finds the transplanetary injection point from an elliptic parking orbit is discussed by Bell et al. [21]. The strategy searches along the parking orbit for a location minimizing the incremental velocity required for achieving the asymptotic conditions. For a lunar mission, the transfer is carried out between the parking orbit and the orbit of the moon. Only some of the orbit parameters such as semi major axis, eccentricity and inclination of the parking orbit is known. Other parameters such as argument of perigee, right ascension of ascending node are unknown. So, the initial state on the parking orbit is unknown, and must be found along with the transfer trajectory design by iteration. The absence of departure asymptotic conditions in the trajectory design of a lunar mission necessitates a different treatment for generating the translunar injection state. The treatment must also meet the requirement that the parking orbit plane should contain the target point (the state of the moon) at the time of injection. In the trajectory design process, appropriate parking orbit orientation must be chosen. After fixing the plane orientation, the location on the parking orbit at which translunar injection takes place must be determined. Search technique along the parking orbit could be followed to find the TLI location. But this involves solution of Lambert problem for each point on the parking orbit resulting in large computational time. When the parking orbit is elliptical, the search process becomes complicated because the argument of perigee of the parking orbit is unknown. Battin [40] has presented an algorithm to arrive at parking orbit requirements for circum lunar trajectories based on patched conic technique that could possibly be modified for one-way transfer trajectory. The algorithm does not allow the flight time to exceed the flight time needed for a parabolic conic connecting the 58
10 positions and, hence, puts a restriction on the type of conic (only elliptic orbits). Newton iteration is used to arrive at the transfer angle and, hence, the location for translunar injection. In this chapter, an integrated approach to obtain parking orbit conditions for translunar injection and the transfer trajectory design is presented together with elaborate algorithmic details. The analytical algorithm presents a unified approach in finding the location of TLI for both circular and elliptical parking orbits. The analytical solution of the three-body Lambert problem is obtained by finding a pseudo state of the moon and then, by solving the two-body Lambert problem involving the departure state and the pseudo state. The target aim point is chosen as the center of the moon because the main aim of this chapter is to derive translunar/earth parking orbit characteristics. The choice of target aim point fixes the approach trajectory as a rectilinear hyperbola thus avoiding the need for iteration over the approach hyperbola. The use of universal algorithm for Lambert problem solution helps to design any type of transfer trajectories viz., circular, elliptical, parabolic, hyperbolic. Two iterations are involved on two states: one on the departure state and another one on the pseudo state corresponding to the aim point. Also the information that the injection for lunar journey starts at the perigee of the transfer trajectory is derived. Although it is redundant for tangential, horizontal injection where the parking orbit and transfer trajectory lie in the same plane and the injection takes place in the horizon plane, it will be useful for conducting non-tangential non-horizontal injection studies that require out-of-plane as well as in-plane maneuvers before injection. 4.5 Selection of Earth Parking Orbit Orientation For a tangential translunar injection that minimizes the impulse requirement, the earth parking orbit plane must contain the moon's position on arrival. So, the orientation of the 59
11 parking orbit must be chosen appropriately, that is the right ascension of ascending node (Q p ) must be chosen appropriately. However, such orientation exists only when IBM I< i p, where 8 M and i p are the declination of the moon on arrival and inclination of the parking orbit respectively. There are two such orientations one containing the moon in the ascending phase and the other in the descending phase. The geometry of these planes is given in Figure 4.3. Use of Napier's formula in the spherical triangle AMF of Figure 4.3 results in The second plane is given by Figure 4.3 Geometry of parking orbit orientation 60
12 tang sm[180- (am - Q )] =.M P tan lp where am is the right ascension of the moon on arrival. 4.6 Procedure for Determination of Translunar Injection State For circular orbits, a location on the parking orbit is given by argument of latitude. The translunar injection impulse requirement is minimum when the chosen location is the perigee of the transfer trajectory. In the case of elliptic parking orbits, the impulse for translunar injection is minimum and tangential, when the injection takes place at the perigee of the parking orbit and the argument of perigee of the transfer trajectory is same as that of the parking orbit. Instead of searching all through the Earth parking orbit to find appropriate translunar conditions, this algorithm uses the above-mentioned facts. In other words, for tangential and horizontal injection, the argument of perigee of the transfer trajectory must be equal to the argument of latitude of the translunar injection point on the parking orbit. Few iterations on this parameter (OJ/) through a repeated Lambert problem solutions makes it possible for the algorithm to find the location of TLI on both types of parking orbits viz. circular, elliptical. The iterative procedure for the location of TLI on the parking orbit is given along with the integrated algorithm. 4.7 Integrated Impact Algorithm The steps of the integrated algorithm that produces the unknown parking orbit characteristics and the transfer trajectory design are as follows: 61
13 (1) Fix the following inputs: date of departure td, flight duration tf ' a duration during which the moon's gravity field also acts on the space vehicle!1t referred to as sweep back duration, semi major axis a p, eccentricity e p, and inclination ip of the parking orbit. (2) Find the geocentric position of the moon with respect to the Earth's equator on arrival (t d +tf) using lunar ephemeris data, and set the pseudo state vector R~ = R M (3) Compute the right ascension and declination of R~ with respect to the Earth's equator. (4) Compute the right ascension of ascending node of the parking orbit using the equations given in Section 4.5. The iterative procedure to find out the location on the parking orbit to initiate translunar injection starts here. (5) Assume avalue for true anomaly v p, and guess avalue for argument of perigee wp of the parking orbit and set up =w p + v p (6) Find the position R p, corresponding to the assumed parking orbit location described by (7) Solve the Lambert problem connecting two positions R p and R~ for the flight duration tf and obtain the transfer orbit characteristics (at let' it J21' wi'vj [Evidently 0 p =0t' ip = it, and vt = O. Though this information is known before the start of the iteration, these parameters are again determined by the solution procedure of Lambert problem thus becoming verification for the Lambert problem solution procedure.] (8) Replace w p+vp of the parking orbit by w t with the other parking orbit characteristics remaining the same, 62
14 (9) Find the new position R p on the parking orbit corresponding to the updated characteristics (10) Repeat the steps 7-9 till the two successive values of (1), differ only by a very small tolerance. (11) Find the arrival velocity VA of the space vehicle on the transfer trajectory (Use the equations in Section 4.8.1). (12) Find the hyperbolic excess velocity (if ~) as VA - VM where VM is the velocity of the moon on arrival epoch and compute a~, 5~ of V~ (Use the equations in Section 4.8.2). The internal iteration to obtain the parking orbit characteristics ends here. The method consisting of the above steps is based on 'point conic method' or 'Lambert conic method' in the literature. If the gravity field of the moon is ignored, the transfer trajectory design is arrived at the end of step (12). The pseudo state technique, which corrects the trajectory by including the moon's gravity field, is presented in the following steps and the iteration to find out the pseudo state starts. (13) Find the radial distance r h and velocity v" along the rectilinear hyperbola at (tf - ~t ) with V~,M, and PM as inputs using the procedure described in Section (14) Because, for a rectilinear hyperbola, radial and velocity directions are parallel, find r" V~ _ V~ (-J (-J and v" as r" =r h V~ and V h = V h V~. (15) Sweep back from (r", v h ) in a straight line with constant velocity v h for a duration of!1t and compute the pseudo state as r~ =r h - v h!1t in the selenocentric frame and transform to geometric frame using R~ =R M + r~. 63
15 (16) If the pass is not the first one for the current iteration, then proceed to step (3) with new R~. Otherwise compute the time of travel /),i from r h to the periapsis of the rectilinear hyperbola with the velocity as V_ (use the equations given in Section 4.8.4). (17) Find the time difference, =1M-M'I. If, is less than a pre fixed tolerance, the solution is reached. Otherwise proceed to (18) (18) Find the correction (ar h ) to the pseudo state; at if this is the first iteration. ar h = rh - at rh old, -,old otherwise. (19) Correct the asymptotic radial distance r h by and reset the old values to the current values with an indication that the pass is not the first one in the current iteration. (20) Repeat the steps (14) onwards until, is less than a prefixed tolerance. In a typical extemal iteratio~, steps are executed, and then again are executed. With the transfer of the internal iteration to step 3, this typical external iteration ends. The two iterations in this procedure: the first one (internal iteration) to obtain the location of TLI on the parking orbit and second one (external iteration) to obtain the pseudo state, are repeated until the convergence criteria on ( is satisfied. The process of convergence requires about four to five iterations on both internal and external iterations. 64
16 4.8 Computational Procedures for Some Parameters The procedures used in the computation of some parameters in the algorithm are compiled in this section Arrival velocity of the spacecraft. Let ai' e " ii' Q I' (01' VI be the transfer trajectory characteristics at the initial time (td ). Find the mean motion n l by n,=t: where f.le is the gravitational constant of the Earth. a, The mean anomaly of the spacecraft on arrival after flight duration tf is given by M A =n,t f Care must be taken to maintain consistency in units. Other orbital characteristics under Kepler motion do not change. So the position and velocity of the spacecraft on arrival can be found from ai' e " i"q"oj"ma' Right ascension and declination of excess velocity vector The unit excess velocity vector is given by cosa~ COSO~j [ V~ = sin~~ COSO~. smo_ So from the components of V~ I the right ascension (a_) and the declination (0_) are computed. 65
17 4.8.3 Asymptotic parameters of a rectilinear hyperbola Given V~ and!1t, the mean motion is found from and the mean anomaly is given by v 3 nil =---=- where JiM is the gravitational constant of the moon JiM M" =-n"at. The eccentric anomaly F is obtained by solving the hyperbolic form of the Kepler's equation: M" =sinh(f) - F The asymptotic radial distance and velocity are given by, and r" = Ji~ [cosh(f) - F] V~ Duration of travel on a hyperbola In the integrated algorithm, step (16) requires computation of travel time along the approach hyperbola. Given V~, r" and JiM, the semi major axis of the approach hyperbola is given by and the eccentric anomaly is obtained from If sm. h(f) r"v" ~JiM a" 66
18 and F =log(sinhf +cosh F) The corresponding mean anomaly M h is computed and the travel time is given by 4.9 Illustrations and Analysis The above algorithm has been implemented and the illustrative results with the analysis are presented in this section. The size of the earth parking orbit is selected as 300 km circular and the inclination is fixed at 45. A flight duration of 5 days is assumed for the transfer and the period for departure is chosen as January 2007, covering about one orbital period of the moon. The departure is characterized by incremental velocity, right ascension of ascending node of the parking orbit, argument of latitude on the parking orbit for TLI, and the arrival is by the hyperbolic excess velocity, right ascension and declination of the excess velocity vector with respect to the lunar equator. Generally, the accuracy of the transfer trajectory design is linked to the parameter sweep back duration in the pseudo state technique. Sweep back duration represents the size of the pseudosphere. The accuracy levels can be improved by handling this parameter judiciously. Kredron and Sweetser [32] discuss the importance of this parameter. They give empirical formulas to compute the optimal sweep back duration for interplanetary missions. But the flight duration for lunar mission being only four to five days, the optimal sweep back duration can be found by varying the sweep back durations from 0 to 5 days in small steps. Obviously, the zero sweep back duration corresponds to the design by point conic method. The transfer trajectories obtained by pseudo state technique with different sweep back 67
19 durations are numerically propagated under a force field consisting of both the Earth and the moon, and the resulting errors on the end constraint, namely reaching the target aim point in desired flight duration, are assessed. The variations in the solutions with respect to sweep back duration are shown in Figures 4.4 and 4.5 and its impact on the end constraints are in Figures 4.6 and 4.7. These plots correspond to a departure date of 171 h January 2007, which require minimum energy for translunar injection in the selected lunar cycle. These figures show that even the small differences (less than 2 deg.) in the angles results in huge errors in the end constraints. The error due to point conic solution that ignores moon's gravity field is about 5.5 hours in flight duration when the target is reached or kms in the target distance after the specified flight duration of 5 days. The inclusion of moon's gravity field in the trajectory design process improves the solution in satisfying the end constraints. Even an assumption of a nominal presence of the moon (for about only 0.5 days) reduces the errors in achieving the target drastically (about 50 %). Both the TLI angles increase almost linearly after an initial rapid increase. The errors are reduced till an optimal sweep back duration is reached, and beyond this value the errors tend to increase again. For these departure conditions, the value is about 75 % of the total flight duration, namely, 3.75 days. A further analysis for other departure dates with different relative geometry scenario and for other flight durations has also shown the optimal sweep back duration around this percentage value. It can safely be concluded that transfer trajectory by pseudo state technique assuming moon's presence for about 75 % of the total duration yields a better solution and satisfies the end constraints of the transfer trajectory. Typical lunar mission characteristics obtained using this algorithm are given in Table 4.1 and comparison is made with the Lambert conic results that are obtained using this integrated algorithm. The initial state obtained by using pseudo state technique when 68
20 propagated numerically under the gravity fields of the Earth and the moon for the full flight duration reaches a minimum distance of 423 km from the target aim point, that is the centre of the moon, in the specified arrival time. This is equivalent to 1315 km below the surface of the moon. The incremental velocity requirement does not vary between the techniques, but the angles vary by about 2 deg. As pointed out already the point conic initial state, when propagated numerically, results in an error of nearly 5.5 hours in arrival time and the space vehicle is at a very large distance from the target aim point at the prescribed time. The differences between the solutions of pseudo state and point conic techniques are plotted in Figures 4.8 and 4.9 for departure and arrival characteristics respectively. The errors in incremental velocity at departure are negligible. The errors in the argument of latitude of TLI fluctuate between -2.0 deg to +1.5 deg. The right ascension of ascending node deviates in the range [1.3 deg, 4.0 deg], indicating that the pseudo state always moves away from the moon's orbit as seen from reference x-axis. The deviation is at maximum when the moon is near its apogee and minimum when the moon is near perigee on arrival. It is also observed that the absolute deviation in ' u ' is maximum when the moon is near Earth equator and the deviation is near zero when the moon is near its maximum absolute declination. The impact of moon's gravity field on the arrival excess velocity is about 8 m/s and the variation in the angles, which fixes the direction of arrival excess velocity, is only marginal Conclusions An integrated algorithm to obtain the transfer trajectory design together with the required parking orbit characteristics is presented. Because the main aim here is to develop an algorithm and related theories for the departure state of the transfer trajectory design, the aim point is fixed as the centre of the moon. This algorijhm provides better data compared to 69
21 point conic methods forming a good basis for preliminary lunar mission design analysis with minimum computational effort. The illustrative results are presented and analyzed. The accuracy levels of the algorithm are demonstrated. The importance of the sweep back duration that represents the moon-centered pseudosphere within which the gravity acceleration of the moon is accounted is highlighted. 70
22 Table 4.1 Typical lunar transfer trajectory characteristics and comparison Parameter Integrated Algorithm using pseudo state technique Integrated algorithm using point conic method V, (km/s) L\ V (km/s) Q p = Q, (deg) u p = OJ, (deg) a, (km) e, V_ (km/s) a_ (deg) _ (deg) Closest Approach Time Closest Approach Distance (km) Distance from the moon's surface on Ohr: Om: Osec (km) :00:00 hrs 18:39 hrs Departure Date: 17 /01 / hrs 0 min 0 sec 71
23 C) GJ -g := 'S :: o C E167.3 ~ C) ~ / V JV I I / V / V ~ ~~ -, Sweep Back Duration (days) Figure 4.4 TLilocation variation with respect to the sweep back duration 72
24 ~351.1 "0 -CIJ 351 "0 g350.9 g'350.8 "0 c CIJ ~ «J ' c en ii Co) ~ E C)350.1 a: 350 / 1/ / I I / ~/ ~v ~.-'~.-"""" Sweep Back Duration (days) 5 Figure 4.5 Parking orbit orientations with respect to the sweep back duration 73
25 1 0.5 o _-0.5 en~ : ) E :0 ~ -2 'i: ~ -2.5 c,- -3 c o :; -3.5 'S: 4) -4 C -4.5 / V I I I I V ~V V... ~ ~""" ---- ~ ~ o Sweep Back Duration (days) Figure 4.6 Deviation in arrival time on reaching the target 74
26 X e 2.llI: - ~ 1.75 c ~ 2i 1.5 ~ ~1.25 ~ c 1 c.2...! ~ C 0.5 \ \\ \ '" ~ 0.25 '" " ---. """'" l,...--v o o Sweep Back Duration (days) Figure 4.7 Deviation from target distance at the specified arrival time 75
27 !<Q 3.5 E 3 ~ 2.5 CI os g 1 ~ 0.5 ~C Impulse (rnis) --- Right ascension of asc node (deg),-, -~. Argument of latitude (deg), ,.. ~....,,..... I..,....., '\, '\, " 1.('''' ''''., --,..,... / ~ ~,,,,,_,,., --'--.',...,.' ' ,.... ' Day of Departure (in Jan. 2007) Figure 4.8 Differences (Pseudo-Lambert) in the departure characteristics 76
28 _.~ ~ III.! 2 ~ :1:1 1 III W 0 ~ c 4J ~ -3 :l:: is -4,~"'--'''''''''.", " I, ; 3, ; ' ~ I ; '.,,,..,~ _- --j-, '. ",,,,,,-,--. V_infinity (m/s) 1-, --- Right ascension of V_inf (d ~g) -., - Declination of V inf (deg) I- ".',, -"---.,..., ",, ", ;' I "... _ Day of Departure ~n Jan. 2007) Figure 4,9 Differences (Pseudo - Lambert) in the arrival characteristics 77
Chapter 8. Precise Lunar Gravity Assist Trajectories. to Geo-stationary Orbits
Chapter 8 Precise Lunar Gravity Assist Trajectories to Geo-stationary Orbits Abstract A numerical search technique for designing a trajectory that transfers a spacecraft from a high inclination Earth orbit
More informationInterplanetary Mission Opportunities
Interplanetary Mission Opportunities Introduction The quest for unravelling the mysteries of the universe is as old as human history. With the advent of new space technologies, exploration of space became
More informationList of Tables. Table 3.1 Determination efficiency for circular orbits - Sample problem 1 41
List of Tables Table 3.1 Determination efficiency for circular orbits - Sample problem 1 41 Table 3.2 Determination efficiency for elliptical orbits Sample problem 2 42 Table 3.3 Determination efficiency
More informationChapter 3. Algorithm for Lambert's Problem
Chapter 3 Algorithm for Lambert's Problem Abstract The solution process of Lambert problem, which is used in all analytical techniques that generate lunar transfer trajectories, is described. Algorithms
More informationASTRIUM. Interplanetary Path Early Design Tools at ASTRIUM Space Transportation. Nathalie DELATTRE ASTRIUM Space Transportation.
Interplanetary Path Early Design Tools at Space Transportation Nathalie DELATTRE Space Transportation Page 1 Interplanetary missions Prime approach: -ST has developed tools for all phases Launch from Earth
More informationLaunch strategy for Indian lunar mission and precision injection to the Moon using genetic algorithm
Launch strategy for Indian lunar mission and precision injection to the Moon using genetic algorithm VAdimurthy, R V Ramanan, S R Tandon and C Ravikumar Aeronautics Entity, Vikram Sarabhai Space Centre,
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 5: Hyperbolic Orbits Introduction In this Lecture, you will learn: Hyperbolic orbits Hyperbolic Anomaly Kepler s Equation,
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 10. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation 2 6. Interplanetary Trajectories 6.1 Patched conic method 6.2 Lambert s problem
More informationLecture D30 - Orbit Transfers
J. Peraire 16.07 Dynamics Fall 004 Version 1.1 Lecture D30 - Orbit Transfers In this lecture, we will consider how to transfer from one orbit, or trajectory, to another. One of the assumptions that we
More informationOrbit Characteristics
Orbit Characteristics We have shown that the in the two body problem, the orbit of the satellite about the primary (or vice-versa) is a conic section, with the primary located at the focus of the conic
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) L06: Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation 2 Problem Statement? Hint #1: design the Earth-Mars transfer using known concepts
More informationSatellite Orbital Maneuvers and Transfers. Dr Ugur GUVEN
Satellite Orbital Maneuvers and Transfers Dr Ugur GUVEN Orbit Maneuvers At some point during the lifetime of most space vehicles or satellites, we must change one or more of the orbital elements. For example,
More informationThe B-Plane Interplanetary Mission Design
The B-Plane Interplanetary Mission Design Collin Bezrouk 2/11/2015 2/11/2015 1 Contents 1. Motivation for B-Plane Targeting 2. Deriving the B-Plane 3. Deriving Targetable B-Plane Elements 4. How to Target
More informationExtending the Patched-Conic Approximation to the Restricted Four-Body Problem
Monografías de la Real Academia de Ciencias de Zaragoza 3, 133 146, (6). Extending the Patched-Conic Approximation to the Restricted Four-Body Problem Thomas R. Reppert Department of Aerospace and Ocean
More informationSUN INFLUENCE ON TWO-IMPULSIVE EARTH-TO-MOON TRANSFERS. Sandro da Silva Fernandes. Cleverson Maranhão Porto Marinho
SUN INFLUENCE ON TWO-IMPULSIVE EARTH-TO-MOON TRANSFERS Sandro da Silva Fernandes Instituto Tecnológico de Aeronáutica, São José dos Campos - 12228-900 - SP-Brazil, (+55) (12) 3947-5953 sandro@ita.br Cleverson
More informationSatellite meteorology
GPHS 422 Satellite meteorology GPHS 422 Satellite meteorology Lecture 1 6 July 2012 Course outline 2012 2 Course outline 2012 - continued 10:00 to 12:00 3 Course outline 2012 - continued 4 Some reading
More informationCelestial Mechanics Lecture 10
Celestial Mechanics Lecture 10 ˆ This is the first of two topics which I have added to the curriculum for this term. ˆ We have a surprizing amount of firepower at our disposal to analyze some basic problems
More informationSECTION 9 ORBIT DATA - LAUNCH TRAJECTORY
SECTION 9 ORBIT DATA - LAUNCH TRAJECTORY --~'- SECTION 9 LAUNCH TRAJECTORY 9.1 MISSION PROFILE IUE was launched by a three-stage Delta 2914 launch vehicle from Cape Kennedy on January 26, 1978 at l7 h
More informationFlight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics AE-104, lecture hours 1-4: Interplanetary flight Ron Noomen October 5, 01 AE104 Flight and Orbital Mechanics
More informationProblem Description for the 8 th Global Trajectory Optimisation Competition. Anastassios E. Petropoulos 1
1 Background Problem Description for the 8 th Global Trajectory Optimisation Competition Anastassios E. Petropoulos 1 Outer Planet Mission Analysis Group Mission Design and Navigation Section Jet Propulsion
More informationGlobal Optimization of Impulsive Interplanetary Transfers
Global Optimization of Impulsive Interplanetary Transfers R. Armellin, Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano Taylor Methods and Computer Assisted Proofs Barcelona, June, 3 7, 2008
More informationOptimal Gravity Assisted Orbit Insertion for Europa Orbiter Mission
Optimal Gravity Assisted Orbit Insertion for Europa Orbiter Mission Deepak Gaur 1, M. S. Prasad 2 1 M. Tech. (Avionics), Amity Institute of Space Science and Technology, Amity University, Noida, U.P.,
More informationFundamentals of Astrodynamics and Applications
Fundamentals of Astrodynamics and Applications Third Edition David A. Vallado with technical contributions by Wayne D. McClain Space Technology Library Published Jointly by Microcosm Press Hawthorne, CA
More informationASEN 6008: Interplanetary Mission Design Lab Spring, 2015
ASEN 6008: Interplanetary Mission Design Lab Spring, 2015 Lab 4: Targeting Mars using the B-Plane Name: I d like to give credit to Scott Mitchell who developed this lab exercise. He is the lead Astrodynamicist
More informationInterplanetary Travel
Interplanetary Travel Interplanetary Travel Concept Patched Conic Hypothesis Departure & Arrival Manoeuvres Interplanetary Travel Concept Interplanetary travel is concerned with motion of manmade objects
More informationorbits Moon, Planets Spacecrafts Calculating the and by Dr. Shiu-Sing TONG
A Science Enrichment Programme for Secondary 3-4 Students : Teaching and Learning Resources the and Spacecrafts orbits Moon, Planets Calculating the 171 of by Dr. Shiu-Sing TONG 172 Calculating the orbits
More informationRigorous Global Optimization of Impulsive Space Trajectories
Rigorous Global Optimization of Impulsive Space Trajectories P. Di Lizia, R. Armellin, M. Lavagna K. Makino, M. Berz Fourth International Workshop on Taylor Methods Boca Raton, December 16 19, 2006 Motivation
More informationLunar Landing Trajectory and Abort Trajectory Integrated Optimization Design.
Lunar Landing Trajectory and Abort Trajectory Integrated Optimization Design Bai Chengchao (1), Guo Jifeng (2), and Xu Xibao (3) (1)(2) School of Astronautics, Harbin Institute of Technology, (451)864128766
More information10 Orbit and Constellation Design Selecting the Right Orbit
Orbit and Constellation Design Selecting the Right Orbit.7 Design of Interplanetary Orbits Faster Trajectories Ron Noomen, Delft University of Technology Using the recipe given in Table -9, one can compute
More informationLow-Thrust Trajectories to the Moon
3rd WSEAS International Conference on APPLIED and THEORETICAL MECHANICS, Spain, December 14-16, 7 257 Low-Thrust Trajectories to the Moon ANTONIO F. B. A. PRADO Space Mechanics and Control Division INPE
More informationExperimental Analysis of Low Earth Orbit Satellites due to Atmospheric Perturbations
Experimental Analysis of Low Earth Orbit Satellites due to Atmospheric Perturbations Aman Saluja #1, Manish Bansal #2, M Raja #3, Mohd Maaz #4 #Aerospace Department, University of Petroleum and Energy
More informationOrbital Dynamics and Impact Probability Analysis
Orbital Dynamics and Impact Probability Analysis (ISAS/JAXA) 1 Overview This presentation mainly focuses on a following point regarding planetary protection. - How to prove that a mission satisfies the
More informationASEN 5050 SPACEFLIGHT DYNAMICS Interplanetary
ASEN 5050 SPACEFLIGHT DYNAMICS Interplanetary Prof. Jeffrey S. Parker University of Colorado Boulder Lecture 29: Interplanetary 1 HW 8 is out Due Wednesday, Nov 12. J2 effect Using VOPs Announcements Reading:
More informationSatellite Communications
Satellite Communications Lecture (3) Chapter 2.1 1 Gravitational Force Newton s 2nd Law: r r F = m a Newton s Law Of Universal Gravitation (assuming point masses or spheres): Putting these together: r
More informationPatch Conics. Basic Approach
Patch Conics Basic Approach Inside the sphere of influence: Planet is the perturbing body Outside the sphere of influence: Sun is the perturbing body (no extra-solar system trajectories in this class...)
More informationInterplanetary Mission Analysis
Interplanetary Mission Analysis Stephen Kemble Senior Expert EADS Astrium stephen.kemble@astrium.eads.net Page 1 Contents 1. Conventional mission design. Advanced mission design options Page 1. Conventional
More informationEffect of Coordinate Switching on Translunar Trajectory Simulation Accuracy
Effect of Coordinate Switching on Translunar Trajectory Simulation Accuracy Mana P. Vautier Auburn University, Auburn, AL, 36849, USA This paper focuses on the affect of round-off error in the accurate
More informationOrbital Mechanics MARYLAND
Orbital Mechanics Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time in orbit Interplanetary trajectories Planetary launch and
More informationMARYLAND U N I V E R S I T Y O F. Orbital Mechanics. Principles of Space Systems Design
Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time and flight path angle as a function of orbital position Relative orbital
More informationEscape Trajectories from the L 2 Point of the Earth-Moon System
Trans. Japan Soc. Aero. Space Sci. Vol. 57, No. 4, pp. 238 244, 24 Escape Trajectories from the L 2 Point of the Earth-Moon System By Keita TANAKA Þ and Jun ichiro KAWAGUCHI 2Þ Þ Department of Aeronautics
More informationANNEX 1. DEFINITION OF ORBITAL PARAMETERS AND IMPORTANT CONCEPTS OF CELESTIAL MECHANICS
ANNEX 1. DEFINITION OF ORBITAL PARAMETERS AND IMPORTANT CONCEPTS OF CELESTIAL MECHANICS A1.1. Kepler s laws Johannes Kepler (1571-1630) discovered the laws of orbital motion, now called Kepler's laws.
More informationPrevious Lecture. Orbital maneuvers: general framework. Single-impulse maneuver: compatibility conditions
2 / 48 Previous Lecture Orbital maneuvers: general framework Single-impulse maneuver: compatibility conditions closed form expression for the impulsive velocity vector magnitude interpretation coplanar
More informationMARYLAND U N I V E R S I T Y O F. Orbital Mechanics. Principles of Space Systems Design
Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time and flight path angle as a function of orbital position Relative orbital
More informationNAVIGATION & MISSION DESIGN BRANCH
c o d e 5 9 5 National Aeronautics and Space Administration Michael Mesarch Michael.A.Mesarch@nasa.gov NAVIGATION & MISSION DESIGN BRANCH www.nasa.gov Outline Orbital Elements Orbital Precession Differential
More informationOPTIMAL MANEUVERS IN THREE-DIMENSIONAL SWING-BY TRAJECTORIES
OPTIMAL MANEUVERS IN THREE-DIMENSIONAL SWING-BY TRAJECTORIES Gislaine de Felipe and Antonio Fernando Bertachini de Almeida Prado Instituto Nacional de Pesquisas Espaciais - São José dos Campos - SP - 12227-010
More informationL eaving Earth and arriving at another planet or asteroid requires
Designing Interplanetary Transfers L eaving Earth and arriving at another planet or asteroid requires a spacecraft to implement a sequence of manoeuvres. These include changes of velocity needed to escape
More informationOrbit Representation
7.1 Fundamentals 223 For this purpose, code-pseudorange and carrier observations are made of all visible satellites at all monitor stations. The data are corrected for ionospheric and tropospheric delays,
More informationA SURVEY OF BALLISTIC TRANSFERS TO LOW LUNAR ORBIT
AAS 11-277 A SURVEY OF BALLISTIC TRANSFERS TO LOW LUNAR ORBIT Jeffrey S. Parker Rodney L. Anderson and Andrew Peterson A simple strategy is identified to generate ballistic transfers between the Earth
More informationRAPID GEOSYNCHRONOUS TRANSFER ORBIT ASCENT PLAN GENERATION. Daniel X. Junker (1) Phone: ,
RAPID GEOSYNCHRONOUS TRANSFER ORBIT ASCENT PLAN GENERATION Daniel X. Junker (1) (1) LSE Space GmbH, Argelsrieder Feld 22, 82234 Wessling, Germany, Phone: +49 160 9111 6696, daniel.junker@lsespace.com Abstract:
More informationChapter 2: Orbits and Launching Methods
9/20/ Chapter 2: Orbits and Launching Methods Prepared by Dr. Mohammed Taha El Astal EELE 6335 Telecom. System Part I: Satellite Communic ations Winter Content Kepler s First, Second, and Third Law Definitions
More informationOrbital Mechanics MARYLAND U N I V E R S I T Y O F. Orbital Mechanics. ENAE 483/788D - Principles of Space Systems Design
Lecture #05 September 15, 2015 Planetary launch and entry overview Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time in orbit
More informationOrbital Mechanics MARYLAND U N I V E R S I T Y O F. Orbital Mechanics. ENAE 483/788D - Principles of Space Systems Design
Planetary launch and entry overview Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time in orbit Interplanetary trajectories
More informationAS3010: Introduction to Space Technology
AS3010: Introduction to Space Technology L E C T U R E S 8-9 Part B, Lectures 8-9 23 March, 2017 C O N T E N T S In this lecture, we will look at factors that cause an orbit to change over time orbital
More informationFundamentals of Satellite technology
Fundamentals of Satellite technology Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai Orbital Plane All of the planets,
More informationAnalysis of optimal strategies for soft landing on the Moon from lunar parking orbits
Analysis of optimal strategies for soft landing on the Moon from lunar parking orbits R V Ramanan and Madan Lal Aerospace Flight Dynamics Group, Vikram Sarabhai Space Centre, Thiruvananthapuram 695 022,
More informationORBITAL CHARACTERISTICS DUE TO THE THREE DIMENSIONAL SWING-BY IN THE SUN-JUPITER SYSTEM
ORBITAL CHARACTERISTICS DUE TO THE THREE DIMENSIONAL SWING-BY IN THE SUN-JUPITER SYSTEM JORGE K. S. FORMIGA 1,2 and ANTONIO F B A PRADO 2 National Institute for Space Research -INPE 1 Technology Faculty-FATEC-SJC
More informationEasyChair Preprint. Retrograde GEO Orbit Design Method Based on Lunar Gravity Assist for Spacecraft
EasyChair Preprint 577 Retrograde GEO Orbit Design Method Based on Lunar Gravity Assist for Spacecraft Renyong Zhang EasyChair preprints are intended for rapid dissemination of research results and are
More informationChapter 13: universal gravitation
Chapter 13: universal gravitation Newton s Law of Gravitation Weight Gravitational Potential Energy The Motion of Satellites Kepler s Laws and the Motion of Planets Spherical Mass Distributions Apparent
More informationMission Design Options for Solar-C Plan-A
Solar-C Science Definition Meeting Nov. 18, 2008, ISAS Mission Design Options for Solar-C Plan-A Y. Kawakatsu (JAXA) M. Morimoto (JAXA) J. A. Atchison (Cornell U.) J. Kawaguchi (JAXA) 1 Introduction 2
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 10: Rendezvous and Targeting - Lambert s Problem Introduction In this Lecture, you will learn: Introduction to Lambert s
More informationGRAIL Takes A Roundabout Route To Lunar Orbit
The Gravity Recovery and Interior Laboratory (GRAIL) mission departed Earth from Cape Canaveral Air Force Station Space Launch Complex 17B on 2011 September 10 at 13:08 UTC, carried by a Delta II Heavy
More informationAN ANALYTICAL SOLUTION TO QUICK-RESPONSE COLLISION AVOIDANCE MANEUVERS IN LOW EARTH ORBIT
AAS 16-366 AN ANALYTICAL SOLUTION TO QUICK-RESPONSE COLLISION AVOIDANCE MANEUVERS IN LOW EARTH ORBIT Jason A. Reiter * and David B. Spencer INTRODUCTION Collision avoidance maneuvers to prevent orbital
More informationA Study of the Close Approach Between a Planet and a Cloud of Particles
A Study of the Close Approach Between a Planet a Cloud of Particles IIAN MARTINS GOMES, ANTONIO F. B. A. PRADO National Institute for Space Research INPE - DMC Av. Dos Astronautas 1758 São José dos Campos
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 4: Position and Velocity Introduction In this Lecture, you will learn: Motion of a satellite in time How to predict position
More informationA SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE
DOING PHYSICS WITH MATLAB A SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE Download Directory: Matlab mscripts mec_satellite_gui.m The [2D] motion of a satellite around the Earth is computed from
More informationObservational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws
Observational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws Craig Lage New York University - Department of Physics craig.lage@nyu.edu February 24, 2014 1 / 21 Tycho Brahe s Equatorial
More informationSection 13. Orbit Perturbation. Orbit Perturbation. Atmospheric Drag. Orbit Lifetime
Section 13 Orbit Perturbation Orbit Perturbation A satellite s orbit around the Earth is affected by o Asphericity of the Earth s gravitational potential : Most significant o Atmospheric drag : Orbital
More informationChapter 8. Orbits. 8.1 Conics
Chapter 8 Orbits 8.1 Conics Conic sections first studied in the abstract by the Greeks are the curves formed by the intersection of a plane with a cone. Ignoring degenerate cases (such as a point, or pairs
More informationLecture Module 2: Spherical Geometry, Various Axes Systems
1 Lecture Module 2: Spherical Geometry, Various Axes Systems Satellites in space need inertial frame of reference for attitude determination. In a true sense, all bodies in universe are in motion and inertial
More informationResults found by the CNES team (team #4)
3 rd Global Trajectory Optimisation Competition (GTOC3) organized by the Aerospace Propulsion Group of the Dipartimento di Energetica at Politecnico di Torino Results found by the CNES team (team #4) Presented
More informationANALYSIS OF VARIOUS TWO SYNODIC PERIOD EARTH-MARS CYCLER TRAJECTORIES
AIAA/AAS Astrodynamics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California AIAA 2002-4423 ANALYSIS OF VARIOUS TWO SYNODIC PERIOD EARTH-MARS CYCLER TRAJECTORIES Dennis V. Byrnes Jet
More informationOrbital Mechanics MARYLAND. Orbital Mechanics. ENAE 483/788D - Principles of Space Systems Design
Lecture #08 September 22, 2016 Planetary launch and entry overview Energy and velocity in orbit Elliptical orbit parameters Orbital elements Coplanar orbital transfers Noncoplanar transfers Time in orbit
More informationCelestial Mechanics and Satellite Orbits
Celestial Mechanics and Satellite Orbits Introduction to Space 2017 Slides: Jaan Praks, Hannu Koskinen, Zainab Saleem Lecture: Jaan Praks Assignment Draw Earth, and a satellite orbiting the Earth. Draw
More informationA Low-Cost Mission for LISA Markus Landgraf, Florian Renk, Pierre Joachim, Rüdiger Jehn HSO-GFA
A Low-Cost Mission for LISA Markus Landgraf, Florian Renk, Pierre Joachim, Rüdiger Jehn HSO-GFA LISA Internal Final Presentation July 8 th, 2011 CDF HSO-GFA Page 1 Overview Basic working assumptions Operational
More informationINDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
6 th International Conference on Astrodynamics Tools and Technique (ICATT) INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT LI Xiangyu, Qiao Dong, Cui Pingyuan Beijing Institute of Technology Institute of
More informationAbstract A COUPLED INTERPLANETARY ENTRY, DESCENT AND LANDING TARGETING PROCEDURE. Jeremy David Shidner, M.S., National Institute of Aerospace
Abstract Title of Thesis: A COUPLED INTERPLANETARY ENTRY, DESCENT AND LANDING TARGETING PROCEDURE Jeremy David Shidner, M.S., 006 Thesis Directed by: Dr. Robert Tolson National Institute of Aerospace In
More informationA space probe to Jupiter
Problem 3 Page 1 Problem 3 A space probe to Jupiter We consider in this problem a method frequently used to accelerate space probes in the desired direction. The space probe flies by a planet, and can
More informationMAE 180A: Spacecraft Guidance I, Summer 2009 Homework 4 Due Thursday, July 30.
MAE 180A: Spacecraft Guidance I, Summer 2009 Homework 4 Due Thursday, July 30. Guidelines: Please turn in a neat and clean homework that gives all the formulae that you have used as well as details that
More informationSession 6: Analytical Approximations for Low Thrust Maneuvers
Session 6: Analytical Approximations for Low Thrust Maneuvers As mentioned in the previous lecture, solving non-keplerian problems in general requires the use of perturbation methods and many are only
More informationPHYSICS 1030 Homework #9
PHYSICS 1030 Homework #9 (Due Dec. 5, 2018, 6:00 pm) Find the position of the planet Mars at time t D December 5, 2018, 7:50 pm EST. You will do this by following the steps shown below. (a) Convert the
More informationCHAPTER 3 PERFORMANCE
PERFORMANCE 3.1 Introduction The LM-3A performance figures given in this chapter are based on the following assumptions: Launching from XSLC (Xichang Satellite Launch Center, Sichuan Province, China),
More informationEscape Trajectories from Sun Earth Distant Retrograde Orbits
Trans. JSASS Aerospace Tech. Japan Vol. 4, No. ists30, pp. Pd_67-Pd_75, 06 Escape Trajectories from Sun Earth Distant Retrograde Orbits By Yusue OKI ) and Junichiro KAWAGUCHI ) ) Department of Aeronautics
More informationPatched Conic Interplanetary Trajectory Design Tool
Copyright by Martin James Brennan 2011 The Thesis committee for Martin James Brennan Certifies that this is the approved version of the following thesis: Patched Conic Interplanetary Trajectory Design
More informationSupplemental Questions 12U
Supplemental Questions 12U Gravitational, Electric and Magnetic Fields Questions A satellite of mass 5.00x10² kg is in a circular orbit of radius 2r around Earth. Then it is moved to a circular orbit radius
More informationAstromechanics. 10. The Kepler Problem
Astromechanics 10. The Kepler Problem One of the fundamental problems in astromechanics is the Kepler problem The Kepler problem is stated as follows: Given the current position a velocity vectors and
More informationOrbits in Geographic Context. Instantaneous Time Solutions Orbit Fixing in Geographic Frame Classical Orbital Elements
Orbits in Geographic Context Instantaneous Time Solutions Orbit Fixing in Geographic Frame Classical Orbital Elements Instantaneous Time Solutions Solution of central force motion, described through two
More informationThe Astrodynamics and Mechanics of Orbital Spaceflight
The Astrodynamics and Mechanics of Orbital Spaceflight Vedant Chandra 11-S1, TSRS Moulsari 1 1 Introduction to Rocketry Before getting into the details of orbital mechanics, we must understand the fundamentals
More informationMAHALAKSHMI ENGINEERING COLLEGE-TRICHY QUESTION BANK UNIT I PART A
MAHALAKSHMI ENGINEERING COLLEGE-TRICHY QUESTION BANK SATELLITE COMMUNICATION DEPT./SEM.:ECE/VIII UNIT I PART A 1.What are the different applications of satellite systems? *Largest International System(Intel
More informationCHAPTER 3 PERFORMANCE
PERFORMANCE 3.1 Introduction The LM-3B performance figures given in this chapter are based on the following assumptions: Launching from XSLC (Xichang Satellite Launch Center, Sichuan Province, China),
More informationSPACECRAFT FORMATION CONTROL IN VICINITY OF LIBRATION POINTS USING SOLAR SAILS
SPACECRAFT FORMATION CONTROL IN VICINITY OF LIBRATION POINTS USING SOLAR SAILS D. Novikov (1), R. Nazirov (), N. Eismont (3) (1) E-mail: dnovikov@iki.rssi.ru () E-mail: rnazirov@rssi.ru (3) E-mail: neismont@iki.rssi.ru
More informationProton Launch System Mission Planner s Guide APPENDIX F. Proton Launch System Options and Enhancements
Proton Launch System Mission Planner s Guide APPENDIX F Proton Launch System Options and Enhancements F. PROTON LAUNCH SYSTEM OPTIONS AND ENHANCEMENTS The missions presented in the previous sections represent
More informationKeplerian Elements Tutorial
Keplerian Elements Tutorial This tutorial is based on the documentation provided with InstantTrack, written by Franklin Antonio, N6NKF. Satellite Orbital Elements are numbers that tell us the orbit of
More informationDEFINITION OF A REFERENCE ORBIT FOR THE SKYBRIDGE CONSTELLATION SATELLITES
DEFINITION OF A REFERENCE ORBIT FOR THE SKYBRIDGE CONSTELLATION SATELLITES Pierre Rozanès (pierre.rozanes@cnes.fr), Pascal Brousse (pascal.brousse@cnes.fr), Sophie Geffroy (sophie.geffroy@cnes.fr) CNES,
More informationORBITAL DECAY PREDICTION AND SPACE DEBRIS IMPACT ON NANO-SATELLITES
Journal of Science and Arts Year 16, No. 1(34), pp. 67-76, 2016 ORIGINAL PAPER ORBITAL DECAY PREDICTION AND SPACE DEBRIS IMPACT ON NANO-SATELLITES MOHAMMED CHESSAB MAHDI 1 Manuscript received: 22.02.2016;
More informationLong-Term Evolution of High Earth Orbits: Effects of Direct Solar Radiation Pressure and Comparison of Trajectory Propagators
Long-Term Evolution of High Earth Orbits: Effects of Direct Solar Radiation Pressure and Comparison of Trajectory Propagators by L. Anselmo and C. Pardini (Luciano.Anselmo@isti.cnr.it & Carmen.Pardini@isti.cnr.it)
More informationPHYSICS 1030 Homework #9
PHYSICS 1030 Homework #9 (Due Dec. 6, 2017) Find the position of the planet Mars at time t D December 6, 2017, 5:00 am EST. You will do this by following the steps shown below. (a) Convert the time t to
More informationLow energy trajectories for the Moon-to-Earth space flight
Low energy trajectories for the Moon-to-Earth space flight V V Ivashkin Keldysh Institute of Applied Mathematics, Miusskaya Sq. 4, Moscow 125 047, Russia. e-mail: Ivashkin@Keldysh.ru The Moon-to-Earth
More informationIAC-16.A Jason A. Reiter a *, David B. Spencer b
IAC-16.A6.7.5 Trading Spacecraft Propellant Use and Mission Performance to Determine the Optimal Collision Probability in Emergency Collision Avoidance Scenarios Jason A. Reiter a *, David B. Spencer b
More informationUlrich Walter. Astronautics. The Physics of Space Flight. 2nd, Enlarged and Improved Edition
Ulrich Walter Astronautics The Physics of Space Flight 2nd, Enlarged and Improved Edition Preface to Second Edition Preface XVII Acknowledgments XIX List of Symbols XXI XV 1 Rocket Fundamentals 1 1.1 Rocket
More informationABOUT COMBINING TISSERAND GRAPH GRAVITY-ASSIST SEQUENCING WITH LOW-THRUST TRAJECTORY OPTIMIZATION
ABOUT COMBINING TISSERAND GRAPH GRAVITY-ASSIST SEQUENCING WITH LOW-THRUST TRAJECTORY OPTIMIZATION Volker Maiwald German Aerospace Center (DLR) Institute of Space Systems Department of System Analysis Space
More information