The trajectory design for the Dark Ages Radio Explorer (DARE) mission concept involves dropping the DARE spacecraft off in a generalized geosynchronous transfer orbit (GTO) as a secondary payload. From GTO, the spacecraft is then required to enter a near-equatorial lunar orbit that is stable (i.e., no station-keeping maneuvers are required) and yields the required number of cumulative hours (1,000) for science measurements while in the lunar farside radio quiet cone over a span of three years. Preliminary and expected results of the corresponding trajectory design are presented herein

Burns, Jack O.

Dono Perez, Andres

Faber, Nicolas T.

Galal, Ken F.

Genova, Anthony L.

Mitchell, Scott

Yang, Fan Yang

NASA Technical Reports Server

 1 
TRAJECTORY DESIGN FROM GTO TO                                   
NEAR-EQUATORIAL LUNAR ORBIT FOR THE                                                
DARK AGES RADIO EXPLORER (DARE) SPACECRAFT 
Anthony L. Genova,* Fan Yang Yang,† Andres Dono Perez,‡                         
Nicolas T. Faber§, Ken F. Galal, ¶ Scott Mitchell, # Jack O. Burns, **, †† 
The trajectory design for the Dark Ages Radio Explorer (DARE) mission con-
cept involves dropping the DARE spacecraft off in a generalized geosynchro-
nous transfer orbit (GTO) as a secondary payload. From GTO, the spacecraft is 
then required to enter a near-equatorial lunar orbit that is stable (i.e., no station-
keeping maneuvers are required) and yields the required number of cumulative 
hours (1,000) for science measurements while in the lunar farside radio quiet 
cone over a span of three years. Preliminary and expected results of the corre-
sponding trajectory design are presented herein. 
 
PRELIMINARY AND EXPECTED RESULTS 
The goal of the proposed paper is to show that the Dark Ages Radio Explorer (DARE) space-
craft can ride as a secondary payload to geosynchronous transfer orbit (GTO) and reach the re-
quired near-equatorial circular science orbit around the Moon. The DARE mission is currently in 
the concept development phase with partners including NASA Ames Research Center (ARC), the 
University of Colorado Boulder, and Ball Aerospace and Technologies Corporation. The reason 
why the DARE spacecraft will plan to enter lunar orbit is so that it can observe away from the 
Moon’s surface into the Dark Ages while in a unique radio-quite zone shielded from noise and 
other interference. Preliminary details and expected results are presented herein. 
 
 
 
* Trajectory Designer, Mission Design Division, NASA Ames Research Center, Moffett Field, CA 94035, MS202-1 
† Trajectory Analyst, Mission Design Division, Science and Technology Corporation, NASA Ames Research Center,  
        Moffett Field, CA 94035, MS202-1 
‡ Trajectory Analyst, Mission Design Division, Universities Space Research Association (USRA), NASA Ames  
         Research Center, Moffett Field, CA 94035, MS202-1 
§ Project Manager, Mission Design Division, Millennium Engineering and Integration Co., NASA Ames  
         Research Center, Moffett Field, CA 94035, MS202-1 
¶ Aerospace Engineer, Programs and Projects Division, NASA Ames Research Center, Moffett Field, CA 94035 
# Mission Design Engineer, Ball Aerospace and Technologies Corp., Boulder, CO 80301 
** Professor, Department of Astrophysical and Planetary Sciences, Univ. of Colorado Boulder, Boulder, CO 80309 
†† Principal Investigator, NASA Lunar Science Institute, NASA Ames Research Center, Moffett Field, CA 94035 
https://ntrs.nasa.gov/search.jsp?R=20190000895 2019-08-30T09:59:09+00:00Z
 2 
Radio-Quiet Region Definition 
     The concept of a radio-quiet region has a significant role for radio astronomy. The interfer-
ences that man made radio-emissions create in our environment yield huge challenges for the ob-
servation of determined frequency spectrums. A high resolution is needed to address important 
challenges in the fields of astrophysics and cosmology. Several studies have characterized and 
defined the existence of a place in the solar system that is free of radio interference from any local 
source; Maccone
 
et al.
1, 2
 stipulated in various publications the characteristics of a radio-quiet 
zone located on the farside of the Moon. This region is extended above the surface, forming a 
cone that is free of major interferences on its interior. It is this lunar farside cone that is of interest 
to the DARE spacecraft, which will look at frequencies in the 40-120 MHz range and will thus 
need to be shielded from any noise in this range in order to study the 21 cm signal and resolve the 
turning points during the Dark Ages
3
.  
     This location is very unique in the Solar System since the Moon acts as a shield not only from 
the emissions that come from Earth but also from the Sun. Radio-emissions from potential solar 
bursts and other solar activity can be a serious threat for DARE’s required science observation. It 
was also necessary to account for emissions from the GEO belt and diffraction effects produced 
by the spherical shape of the Moon during wave propagation. Figure 1 shows a representation of 
two separate radio quiet cones calculated by considering the emissions from both the Sun and the 
Earth. As it appears in the image, the full radio quiet region is located only within the intersection 
between these two cones. It is only when the DARE spacecraft is located in this radio-quiet re-
gion that science observation are permitted. 
     After the geometric and physical calculation of the cone shapes, the Analytical Graphics Inc. 
(AGI) Systems Tool Kit (STK) was used to generate a computer based model that calculated the 
time that the spacecraft was in the radio-quiet region. DARE orbital dynamics were performing 
high-fidelity propagation of the lunar orbit. Specifically, the STK model utilized a High Precision 
Orbit Propagator (HPOP) based on the LP150Q lunar gravity model. In order to improve the ac-
curacy, the order and degree chosen were both 70, with the addition of third body perturbations 
from the Earth and the Sun as well as solar radiation pressure. The movement of the radio quiet 
cones at every time during the simulations was computed by an external propagator. A set of ro-
tating coordinates was used to account for Earth and Sun orbital movement and to locate the apex 
of both cones to be shielded at any time from their respective parent bodies. 
                          
Figure 1. Radio-Quiet Region shown as intersection between Earth and Sun cones on Lunar Farside. 
 3 
Lunar Orbit Altitude and Inclination 
In 2005, Ramanan & Adimurthy
4
 studied the impact of inclination on the orbital lifetime of 
low altitude lunar orbits. In our study we were able to characterize equivalent inclination win-
dows that create instability in the spacecraft orbit. These unstable windows are located above re-
gions of large mass concentrations (or mascons) within the Moon's crust, seen in Fig. 2 which 
plots the minimum perilune altitude of a 200 km circular orbit after two years of high-fidelity 
propagation for all lunar orbit inclination values. 
     The DARE mission requires the spacecraft to obtain a total integration time of at least 1,000 
hours (plus contingency) in the radio-quiet region while maintaining a minimum perilune altitude 
above 40 km throughout a three year science mission duration. In addition, the orbit has to be 
reached with the limited spacecraft ΔV budget as a secondary payload orbiting the Earth signifi-
cantly inclined to the lunar equatorial plane. An extensive study was performed to calculate an 
orbit that could provide the required science time while complying with stability and ΔV re-
quirements for the DARE spacecraft. The study showed that an orbit of 125 km at inclinations 
between 24.5 and 28 degrees comply with the requirements of maintaining at least a 40 km min-
imum perilune altitude and obtaining at least 1,000 hours (plus contingency) in the radio-quiet 
region for all values of right ascension of the ascending node (RAAN). Evidence to support this 
statement is found in Fig. 3a and 3b. 
     Retrograde lunar orbits are also analyzed in Fig. 3c and 3d. Although these orbits were only 
analyzed for 2.5 year of science duration (not the nominal three years), it is quite clear that such 
orbits are far less stable than their posigrade counterparts. As it stands, no retrograde inclinations 
are acceptable for DARE's science orbit, but a small acceptable inclination range around 153 de-
grees may be acceptable after extending the analysis to three years. For simplicity, this study will 
focus on acceptable posigrade inclinations between 24.5 and 28 degrees, with 26 degrees desig-
nated as the nominal science orbit inclination for discussion purposes. 
 
                                       
Figure 2. Minimum Perilune Altitude vs. Lunar Orbit Inclination for an initially circular lunar orbit 
at 200 km altitude with RAAN set to zero. 
 4 
  
Figure 3. Orbit Inclination and Stability with regard to time spent in the Radio-Quiet Region. 
 
Nominal Trajectory Design and Analysis 
The orientation of the initial orbit (GTO) must be discussed before designing the nominal tra-
jectory. Qauntus et al.
5
 support the use of the Ariane V launch vehicle since its standard launch 
times for possible GTO payload are seen in Fig. 4a, with a favorable perigee located in Earth’s 
shadow after launch. Additionally, the local launch times of historical launches to GEO (via 
GTO) are seen in Fig. 4b, with two clusters of data forming near local times of midnight and 
6pm. The latter is equivalent to 10pm or 11pm UTC (depending on the time of year) and thus 
10:30pm UTC is chosen as the baseline launch time for the DARE spacecraft. (It is of note that a 
preliminary analysis has been performed for a launch at any time of a single day, with results in-
dicating higher total ΔV requirements upon initial lunar encounter.) 
Fortunately, having the orbit perigee in Earth’s shadow allows the apogee to be located in a 
favorable Sun-Earth WSB quadrant with regard to returning to the Moon
6, 7
. Working with a 
spacecraft ΔV capability of 1,655 m/s, Sun-Earth WSB transfers from GTO to the Moon were 
computed for every day in a launch period from April 1 to October 1, 2020. The ΔV breakdown 
is seen in Fig. 5, where most values are below the current 1,655 m/s limit. 
 5 
 
 
Figure 4. Local Launch Time of Payloads to GEO (via GTO) from mid-2011 to early 2014. 
 
                        
             Figure 5. Breakdown of ΔV for Launch Dates between April 1 and October 1, 2020. 
 6 
 
Unfortunately, many lunar return trajectories approach the Moon in orbit planes significantly 
inclined to the lunar equatorial plane (Fig. 6). Since the declination of the arrival asymptote 
(DAA) at the Moon is as high as about 75 deg (in magnitude), the lunar encounter is used as a 
flyby opportunity to change the orbital plane (not perform LOI) to allow the inclination range of 
24.5 to 28 degrees to be achieved within the DARE spacecraft’s ΔV budget. To demonstrate this 
design element, a lunar return case with |DAA| = 67 degrees is selected from Fig. 5, since the ar-
rival at the Moon is nearly the steepest (i.e., |DAA| is close to the maximum 75 deg and thus re-
quires the largest plane change to achieve an acceptable science orbit). For this case, launch oc-
curs on May 8, 2020, where the spacecraft is dropped off in GTO (Fig. 7a, A). After incremental-
ly raising apogee to escape the Van Allen radiation belts and phase with the Moon, the spacecraft 
would travel to an apogee (Fig. 7a, B) near the Sun-Earth WSB (1.4 million km from Earth in this 
case) and perform a maneuver ΔV of 30 m/s to target a 3,900 km altitude flyby “under” the lunar 
south pole on August 26, 2020 (Fig. 7a, C). Once in an acceptable orbital plane, the DARE 
spacecraft would wait in a 3:2 lunar resonance orbit and perform the LOI maneuver on October 
16, 2020 (Fig. 7a, D and 7b). The total deterministic ΔV for this case is 1,512 m/s (1,632 m/s to-
tal, which is currently 23 m/s below the 1,655 m/s limit), with the primary cost of the lunar flyby 
being the approximate two months of duration (i.e., not ΔV). 
 In the proposed paper it will be shown that for any of the considered GTO cases, at most one 
lunar flyby is needed to target the acceptable inclination range within the ΔV budget of the 
DARE spacecraft. 
 
    
Figure 6. Declination of the Arrival Asymptote upon initial Lunar Encounter. 
 
 7 
 
   
Figure 7. Nominal Trajectory Design from Launch to Lunar Orbit. Lunar flyby design element 
demonstrated on case with |DAA| = 67 deg. Trajectory shown in Earth-centered, Earth inertial   
frames with view normal to (a) and edge-on (c) the lunar orbit plane. View of LOI and first science 
orbit (26 deg inclination and 125 km altitude) in a Moon-centered, Moon inertial frame (b). 
 
REFERENCES 
1Maccone, C., “The Quiet Cone above the Farside of the Moon”. International Academy of Astronautics, Via 
Martorelli,43, Torino, Italy. Acta Astronautica 53 (2003) pp. 65-70. 
2Maccone, C, “Protected antipode circle on the Farside of the Moon”. International Academy of Astronautics, Via 
Martorelli, 43, Torino, Italy. Acta Astronautica 63 (2008) pp. 110-118. 
3Burns, J. O., et al., “Probing the first stars and black holes in the early Universe with the Dark Ages Radio Explorer 
(DARE),” Advances in Space Research 49 (2012) pp. 433-450. 
4Ramanan R. V., and Adimurthy V. 'An Analysis of near-circular lunar mapping orbits'. J. Earth Syst. Sci. 114, No.6, 
December 2005, pp. 619-626. 
5Quantus, D., Spurmann, J., Dekens, E., and Pasler, H., “Weak Stability Boundary Transfer to the Moon from GTO as 
a piggyback payload on Ariane 5,” CEAS Space J (2012) 3:49–59. 
6Yamakawa, H., Kawaguchi, J., Ishii, N., and Matsuo, H., “On Earth-Moon Transfer Trajectory with Gravitational 
Capture,” Advances in the Astronautical Sciences, Univelt, San Diego, CA, Vol. 85, Part I, 1993, pp. 397-416. 
7Penzo, P., Bender, D., and Cassell, C., “Multiple Lunar Swingbys for Small Body and Planetary Missions,” Advances 
in the Astronautical Sciences, Univelt, San Diego, CA, Vol. 89, Part I, pp. 317-330, 1995. 


Trajectory Design from GTO to Near-Equatorial Lunar Orbit for the Dark Ages Radio Explorer (DARE) Spacecraft

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