Trajectory and mission requirement data are presented for Earth Mars opposition and conjunction class roundtrip flyby and stopover mission opportunities available between 1997 and 2045. The opposition class flyby mission uses direct transfer trajectories to and on return from Mars. The opposition class stopover mission employs the gravitational field of Venus to accelerate the space vehicle on either the outbound or inbound leg in order to reduce the propulsion requirement associated with the opposition class mission. The conjunction class mission minimizes propulsion requirements by optimizing the stopover time at Mars

Young, Archie C.

English

NASA Technical Reports Server

N87-17730
MISSION CON_AND OPPORTUNITIES
Archie C. Young
Marshall Space Flight Center
Marshall Space Flight Center, Alabama 35812
ABSTRACT
Trajectory and mission requirement data are presented for Earth
Mars opposition and conjunction class roundtrip flyby and stopover mis-
sion opportunities available between 1997 and 2045. The opposition class
flyby mission uses direct transfer trajectories to and on return from
Mars. The opposition class stopover mission employs the gravitational
field of Venus to accelerate the space vehicle on either the outbound or
inbound leg in order to reduce the propulsion requirement associated with
the opposition class mission. The conjunction class mission minimizes
propulsion requirements by optimizing the stopover time at Mars.
INTRODUCTION
Ballistic mission profiles are convenient flight path approximations
based on the use of Instantaneous velocity impulses (AV) near the
planetary bodies to enter free-fall (coasting) trajectory segments bet-
ween the planets. The free-fall segments are represented by "two-body"
equations that result from integration of the differential equations
describing the motion of a space vehicle in the force field of a control
gravitational body. To achieve the velocity impulse, high thrust
chemical or nuclear propulsive systems were assumed with initial thrust
acceleration > 0.1g.
Data are presented for the Mars opposition and conjunction class
mission profiles. These profiles are pictorially described in Figure 1.
Two categories of the opposition class profiles were considered: a Mars
flyby wlth no landing or stay at Mars; and a Mars stopover mission with a
short stay time of 60-80 days. These are relatively high energy mis-
sions, elther at departure from or arrrlval at one of the planets. The
conjunction class mission profile requires low Hohmann energy transfer
trajectories which are achieved by optimizing the stay time, from 300 to
550 days, at Mars. Another type of Earth-Mars-Earth trajectory is the
free-fall approximately 2 year periodic orbit which may find use as an
orbttlng connecting node.
103
https://ntrs.nasa.gov/search.jsp?R=19870008297 2020-03-20T12:30:37+00:00Z
,f
8
,, _ i=-' ,_e // / _\\X g
o>z __ <
_- _ I
u zXX } i ; \
o z _
Q.0 <_ ._
""_ /I//' \ \l'IVI m I I", '_ u_
,_'k"k. /i, o _x
,, >- z"=X _ / _ o
>__ X _ I _ t / ./ z LU
,,e :Ecn_ I ..... -| 0
.= _-I I o
u_
I-< 0,. I I,_
n._. _ Z u-
u_
:;__Z / _ X\_ /i// _
zi_ _ _ 0 _ _ _/
• __ ,,,z
104
For oppositlon-class missions, a Venus swingby utillzes the gravlta-
tlonal field of Venus to either accelerate or decelerate the space
vehicle as it passes by the planet, thus reducing the high energy
requirements. An acceleration effect is desired for an outbound Venus
swlngby enroute from Earth to Mars and a deceleration effect is desired
for an inbound Venus swlngby enroute from Mars to Earth. The time con-
tained in this paper is year 1997 to year 2045.
MARS MISSION PROFILES
Mars round-trlp flyby trajectories are the Martian counterpart of
lunar flyby return flight paths. A round-trlp flyby may be attractive as
an early manned mission to Mars, which would reconnoiter the planet at
close range. In order to construct a flyby trajectory, three requisite
characteristics of the outbound and inbound transfer trajectories are as
follows: (1) the outbound arrival and inbound departure dates at Mars
must be the same, (2) the hyperbolic excess speed (V _) at Mars on the
inbound and outbound legs must be equal, and (3) the angle between the
hyperbolic excess speed of the approach and departure must be less than a
certain critical value in order not to require an excessive amount of
powered flyby maneuver. The Venus swingby profile involves one or
more gravitational encounters with Venus and often requires significantly
less _V's than direct trajectories to Mars and return.
MISSION OPPORTUNITIES
Mission opportunities for standard direct flights to Mars will occur
near the Earth-Mars opposition, and precede by 90 to 180 days the opposi-
tion dates which will occur on the average every 26 months. Because of
the eccentricity of Mars orbit, the mission trajectory profile changes
from one opposition to the next. The cyclic pattern of mission profile
variation repeats every 15 years or every 7 oppositions [1]. The rela-
tive positions of the Earth-Mars oppositions are indicated in Figure 2
for two periodic cycles of oppositions from year 1997 to 2031. The
slight inclination of the Mars orbit wlth respect to the ecliptic plane
causes an interplanetary transfer trajectory also to be inclined to the
ecliptic, but this effect is small compared to the effect caused by the
eccentricity. The relative position of Earth and Mars for an opposition
class mission causes the energy requirement to be excessive because the
flight time for a near-Hohmann outbound leg is such that, at Mars
105
Z,c_w
0
I
mr
)-
mr
O
UL
z
o_
0,.
0
mr
=E
I
-l-
m-
w
cq
ILl
mr
UL
106
arrival, Earth is ahead of Mars in heliocentric longitude, i.e., Hars
arrival occurs after opposition. This makes it impossible to employ a
near-Hohmann transfer for the Inbound leg; the required heliocentric
transit angle must greatly exceed the Hohmann transfer angle of 180 deg.
Thus, it is never possible to leave Earth on a minimum energy Inbound
leg. The relative position of Earth at Nars arrival can be adjusted with
a swtngby of Venus enroute to Mars on an outbound leg or swlngby of
Venus enroute to Earth on an inbound leg. The major advantage of making
a swingby of Venus is that the hyperbolic encounter with the planet
changes the velocity of the space vehicle relative to the Sun. The
magnitude of the velocity change can be large enough to make a signifi-
cant desirable change in the heliocentric trajectory. The high energy
level required can be avoided in the conjunction class mission mode where
near-Hohmann transfers can be used on both the outbound and inbound leg
by adjusting the stay time at Mars appropriately.
The availability of a Venus swtngby mode can be determined by the
following facts [1]: (1) The space vehicle will normally pass inside or
near the orbit of Venus either on the outbound leg or on the inbound leg
of a direct roundtrlp mission to Nars. Figure 3 illustrates these condi-
tions for an outbound leg and an inbound leg. (2) The gravity field of
Venus is sufficiently powerful to significantly shape the Interplanetary
transfer trajectory in a desirable way. (3) The angular rate of Venus
orbit is large compared to that of Nars, so that Venus is generally
available either on the outbound leg or on the inbound leg. The initial
step in determining a Venus swtngby trajectory profile for a given mis-
sion opportunity is the determination of the relative heliocentric posi-
tion of the three planets, Venus, Earth, and Mars.
INTERPLANETARY TRAJECTORY CALCULATIONS
The computer program used in this work to compute the interplanetary
trajectory characteristics is based on the restricted two-body (patched
conic) approximation of the interplanetary space vehicle trajectory.
While the vehicle is within the sphere of influence of Venus or Mars, the
swlngby planet or flyby planet respectively, it is assumed to be on a
free-flight hyperbolic trajectory about Venus or Hars, and gravitational
effects of all other bodies are neglected. There is no change of energy
with respect to the swlngby or flyby planet, Venus or Hats. Conservation
107
_e4
IE I,- _1
"(.9'>
_0
rr _ N if)
<
:[
ZX
UJ
z x U')
/
C_
U.I
c£
ILl
Ix:
mira
1.1..
108
of energy requires that the magnitude of the vehicle's velocity, relative
to Venus or Mars, as It leaves the sphere of influence of Venus or Mars
must equal to the magnitude of its velocity as it enters the sphere of
influence approaching Venus or Mars. If the required angle of deflec-
tion, bend angle, at Venus or Mars Is too large to be achieved by con-
straining the perlapsls altitude to one-tenth of the planet radii, a
propulsive maneuver Is effected in conjunction wlth the Venus or Mars
gravity field to glve the required bend angle.
Independent optimization of each leg is possible when the con-
Junction class roundtrlp mission is considered. The outbound leg takes
place near one opposition and by adjusting the stopover time at Mars
appropriately, the inbound leg wlll take place near the following opposi-
tion. Examination of single leg trajectory data [2] indicates that If
the outbound and inbound legs of a roundtrlp mission could be optimized
separately, then departure and arrival hyperbolic excess speeds at both
Earth and Mars of less than 0.10 to 0.15 EMOS (Earth Mean Orbital Speed
of 97,700 ft/sec) could be attained. The total mission time for conjunc-
tion class missions Is greater than the mission tlme of the Venus swlngby
opposition class mission (950 to 1004 days for conjunction class compared
to 558 to 737 days for Venus swingby).
REPRESENTATIVE MISSION PROFILES
Tables 1, 2 and 3 present summary data for the Mars flyby, opposi-
tion class stopover mission with Venus swlngby, and conjunction class
missions for missions between 1998 and 2045. Representative proflles are
presented for the three missions descrlbed In Figure 3.
The one year flyby mission departs Earth April 2, 1999 wlth excess
hyperbolic velocity, C3 , of 99.5 km2/sec 2. A flight tlme of 128 days
brings It to a Mars flyby date on August 8, 1999. A propulsive maneuver,
requiring a AV of 0.406 km/sec, Is made at Mars to achieve the necessary
turn angle at Mars for the Earth return trajectory. The Earth return
date Is April 2, 2000 wlth the interplanetary trajectory having a hyper-
bolic energy of 156 km2/sec 2. The Earth departure and return C3's of
99.5 and 156 km 2 /sec 2, respectively, are very hlgh for a Mars mission.
However, these C3 values can be reduced by optimizing the total mission
time and by making efficient midcourse maneuvers.
109
21m4-85
MARS 1-YR ROUND-TRIP MISSIONS (OPPOSITION CLASS)"
LAUNCH C3 _ V@ MARS C3 • EARTH RETURN A VTOT
DATE (km/BEC)2 (kin/SEe) (km/SEC)2 (km/SEC)
2/28/87 159.6 0.802 237 18.239
4/2/99 99.5 0.406 156 13.639
5/22/01 63.5 0.425 156 10.846
6/8/03 71.6 1,723 134 13.299
10/15/05 122.6 3.806 253 20.518
• DATA FROM REFERENCE 6
TABLE 1. MARS FLYBY MISSION
2965-85
STOPOVER TIME EQUAL 60 DAYS
TIME PERIOD 1996 TO 2031
MISSION EARTH LAUNCH DATE TOTAL TRIP TIME (DAYS)
DOUBLE SWINGBY MARCH 1996 733
OUTBOUND SWINGBY JANUARY 1998 666
INBOUND SWINGBY JANUARY 2001 708
OUTBOUND SWINGBY AUGUST 2002 Bt0
OUTBOUND SWINGBY JUNE 2004 659
INBOUND SWINGBY SEPTEMBER 2007 658
DOUBLE SWINGBY JANUARY 2009 736
OUTBOUND SWINGBY NOVEMBER 2010 650
INBOUND SWINGBY NOVEMBER 2013 634
INBOUND SWINGBY NOVEMBER 2015 677
OUTBOUND SWl NGBY APR I L 2017 638
INBOUND SWINGBY JUNE 2020 594
,OUTBOUND SWlNGBY OCTOBER 2021 B36
OUTBOUND SWINGBY SEPTEMBER 2023 614
INBOUND SWINGBY NOVEMBER 2026 570
• DOUBLE SWINGBY MARCH 202R 737
OUTBOUND SWINGBY JANUARY 2030 654
TABLE 2. MARS STOPOVER MISSION WITH VENUS SWINGBY.
110
IIi
The 1999 opposition outbound Venus swingby is characterized by a
hyperbolic transfer angle between Earth and Venus of over 180 deg, wlth
the transfer angle between Venus and Mars of less than 180 deg. The
total transfer angle of the two trajectory transfers is slightly greater
than 360 deg. Of paramount importance is the fact that the average
angular rate of the outbound leg is much greater than that of Earth in
its orbit. Thus, Earth is behind Mars at Nars arrival, i.e., Mars
arrival occurs much sooner than oppositions. This situation permits, as
shown, a near-Hohmann type Mars-Earth trajectory to be utilized on the
inbound leg. However, the Earth return hyperbolic energy, C 3 , is
slightly high with a value of 81.52 km2/sec 2 This C3 level could be
lowered by effectively applying a propulsive mldcourse maneuver on the
Mars-Earth transfer leg. The total mission time for the year 1999 out-
bound Venus swlngby opposition opportunity is 661 days.
Aerobraklng is commonly asserted to be a means of reducing
propulsion requirements for Mars missions. Earth return wlth aerobrake
entry has been analyzed and results show that with an Earth return C 3
greater than 25 km2/sec 2 the g-load will be in excess of 5 g's. This
high g-load cannot be tolerated by the astronauts. Earth return with C3
greater than 25 km2/sec 2 will require propulslve braking In order to stay
within the g-load constraint.
CONCLUSION
Optimum trajectory transfers for opposltlon class mission to Mars
for flyby and stopover missions have been computed for attractive launch
and arrival dates between years 1997 and 2031. Also, Optimum transfer
for conjunction class missions to Mars have been computed for attractive
opportunities for years 1997, 1999, 2001, and 2030 to 2045.
It is posslble to employ an outbound or inbound Venus swingby for
every Earth-Nars opposltlon; opposltlons occur approximately every 26
months. Venus swlngby permits the heliocentric transfer trajectory to be
nearly tangential relative to Earth and Mars orbit upon planet departure
and arrlval, thus reducing the required propulsive maneuver energy
requirement. The mission time is increased from 20 to 50 percent
employing the Venus swlngby mode over the direct flights to Mars.
Optimum roundtrlp trajectories for the conjunction class misslon to
Mars and return can be achieved by adjusting the stopover time at Nars.
112
Near-Hohmann type trajectories can be employed both on the outbound and
inbound leg with the conjunctions class mission. Data have been
developed for years 1997, 1999, 2001 and one Earth-Mars synodic period
between years 2030 and 2045 which consists of seven launch opportunities
associated with the oppositions occuring during this time period.
Free-fall periodic orbits which travel back and forth between Earth
and Mars on a scheduled interval may be attractive for use as a regularly
scheduled transportation system between Earth and Mars.
REFERENCES
1. Sohn, R. 0.: Venus Swtngby Mode for Manned Mars Mis-
sion. Journal of Spacecraft and Rockets, Vol. 1, No. 5,
September - October 1964.
2. Space _ Handbook, Vol. 3-Planetar¥
Handbook, NASA SP-35, Prepared for the George C.
Marshall Space Flight Center, 1963.
3. Holltster, Waiter M. and Prusslng, John E.: Optimum
Transfer to Mars via Venus. AIA/ION Astrodynamtcs
Specialist Conference, September 16, 1965.
4. Deerwester, Jerry M.: Initial Mass Savings Associated
with the Venus Swlngby Mode of Mars Round Trips. AIAA
2nd Aerospace Sciences Meeting, January 25, 1965.
5. Integrated Manned Interplanetary Spacecraft Concept
Definition, Vol. 1, The Hoeing Company, NASA Contract
NAS1-6774, January 1968.
6. So]dner, John: Mars Mission Working Paper, Science
Application, Inc., April, 1985.
7. Young, Archle C., Mulqueen, John A., and Skinner, James
E.: Mars Exploration, NASA TM-86477, August, 1984.
113


Mars mission concepts and opportunities

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server