Generation of near encounter spacecraft-target planet celestial geometry using two body trajectory computerized simulatio

Duxbury, T. C.

English

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N A T I O N A L  A E R O N A U T I C S  A N D  S P A C E  A D M I N I S T R A T I O N  
Technical Report 32-7338 
Near- Encounter Geometry Generation 
7: C. Duxbury 
J E T  P R O P U L S I O N  L A B O R A T O R Y  
C A L I F O R N I A  I N S T I T U T E  O F  T E C H N O L O G Y  
P A S A D E N A ,  C A L I F O R N I A  
November 15, 1968 
https://ntrs.nasa.gov/search.jsp?R=19690002138 2020-03-12T06:04:56+00:00Z
N A T I O N A L  A E R O N A U T I C S  A N D  S P A C E  A D M I N I S T R A T I O N  
Technical Report 32-1338 
Near- Encounter Geometry Generation 
T: C. Duxbury 
J E T  P R O P U L S I O N  L A B O R A T O R Y  
C A L I F O R N I A  I N S T I T U T E  O F  T E C H N O L O G Y  
P A S A D E N A ,  C A L I F O R N I A  
November 15, 1968 
TECHNlCAl REPORT 32-1338 
Copyright 0 1968 
Jet Propulsion laboratory 
California Institute of Technology 
Prepared Under Contract No. NAS 7-100 
National Aeronautics & Space Administration 
Preface 
The work described in this report was performed by the Guidance and Control 
Division of the Jet Propulsion Laboratory. 
JPL T€CHNfCAL REPORT 32-7338 iii 

Contents 
1 . Introduction . . . . . . . . . . . . . . .  
II . Two-Body Trajectory Solution . . . . . . . .  
111 . Sun Direction in RST . . . . . . . . . . . .  
IV . Spacecraft-Centered Celestial Geometry 
V . Results of Application . . . . . . . . . . .  
VI . Recommendations . . . . . . . . . . . . .  
Nomenclature . . . . . . . . . . . . . . . .  
References . . . . . . . . . . . . . . . . .  
Appendix . Near-Encounter Geometry Generation Program 
. . . .  
. . . . . . . . . .  1 
. . . . . . . . . .  1 
. . . . . . . . . .  2 
. . . . . . . . . .  5 
. . . . . . . . . .  5 
. . . . . . . . . .  6 
. . . . . . . . . .  7 
. . . . . . . . . .  8 
. . . . . . . . . .  9 
Tables 
1 . Trajectory encounter characteristics . . . . . . . . . . . . . . . .  5 
6 
6 
2 . Geometry comparison . . . . . . . . . . . . . . . . . . . . .  
3 . Effective two-body orbital parameters . . . . . . . . . . . . . . . .  
Figures 
1 . Target-planet-spacecraft vector . . . . . . . . . . . . . . . . .  2 
2 . Celestial coordinate system . . . . . . . . . . . . . . . . . . .  2 
3 . Sun and Canopus directions 
4 . VUW coordinate system 
. . . . . . . . . . . . . . . . . . .  3 
3 . . . . . . . . . . . . . . . . . . . .  
JPL TECHNICAL REPORT 32-7338 V 
Abstract 
vi 
A method is presented for generating the near-encounter spacecraft-target- 
planet celestial geometry by including the motion of the spacecraft-target-planet 
system about the sun in the two-body trajectory solution. This method has been 
incorporated in a computer program that has been used to simulate an earth- 
Mars trajectory. The computer program, which uses output data from the 
SPACE-Single Precision Cowell Trajectory Program as input, is presented along 
with the results from the trajectory studied. 
J P t  TECHNICAL REPORT 32-1338 
Nea r-Encou n ter Geometry Genera tion 
1. Introduction 
A major effort of mission analysis is concerned with 
the near-target-planet encounter phase. Knowledge of the 
pre- and post-encounter trajectory geometry is necessary 
to determine sensor look angles, science and antenna 
pointing requirements, occultation zones, and guidance 
constraints. This report describes an approximate method 
for generating the near-encounter geometry to an accu- 
racy greater than 0.1 deg during an interval of up to 
20 days from encounter. The approximate method, not 
requiring integration of the spacecraft equations of mo- 
tion, can generate a complete trajectory geometry for a 
20-day period in a matter of minutes when programmed 
on the IBM-1620 computer. 
Near-encounter motion of a spacecraft with respect to 
a target planet will be described by the hyperbola de- 
fined in a planet-centered, inertial coordinate system 
(RST) at planet encounter. Data containing the inertial 
direction in RST to celestial bodies and the classical 
elements defining the hyperbola used in the analyses 
are available in the target planet-centered conic section 
of the SPACE-Single Precision Cowell Trajectory Pro- 
gram output (Ref. 1). The Appendix lists an IBM-1620 
computer program that calculates the target-planet cone 
angle, clock angle, phase angle, and angular diameter; 
spacecraft-target-planet range; target-planet-spacecraft- 
Canopus angle; and Canopus cone angle. 
II. Two-Body Trajectory Solution 
Figure 1 shows a general planet-centered spacecraft 
vector r* in the RST coordinate system with 
cos 0 cos i sin 0' + sin 0 cos 0' 
sin i sin 0' 
cos 0 cos 0' - sin 0 cos i sin 0' 
r = T [  
where 
R = vector completing right-hand system 
S = vector along incoming asymptote 
T = vector parallel to ecliptic plane 
0 = argument of periapsis 
0' = 0 + r )  (7 = true anomaly) 
i = inclination of trajectory plane to T-R plane 
0 = orientation of impact parameter B in T-R plane 
r = target planet-spacecraft range 
*Vectors are differentiated as follows: r = vector; ? = unit vector. 
JPL TECHNICAL REPORT 32-1338 1 
T /  
Fig. 1. Target-planet-spacecraft vector 
For a specific trajectory with the accompanying RST 
coordinate system, 
i = 90 deg 
o = t a r1  ( d B )  
where 
a = semimajor axis of hyperbola 
B = magnitude of B 
These definitions of i and 0 would not necessarily hold, 
for example, when assuming an RST coordinate system 
and then defining the actual trajectory in the assumed 
system as would be done in an orbit determination 
problem. 
For a target planet with a gravitational constant p and 
radius rad, and for a hyperbolic trajectory defined by the 
aim point B and hyperbolic excess velocity V,, the fol- 
lowing equations hold for the two-body trajectory solu- 
tion (Ref. 2). 
a2 + B2 1/2 
e = (?) = hyperbolic eccentricity (4) 
T = (e)”’ (e sinh F - F )  = time past encounter 
(5) 
F = cosh-l [ (a + r) /ae] sgn (T) 
= hyperbolic eccentric anomaly (6) 
(7) rl = cos-1 [(P - ra)/rae] sgn (T) 
Given a time T, Eq. (5) can be solved by an iterative 
process, such as the Newton-Raphson technique (Ref. 3), 
to yield T. Equation (l), defining the vector r, can then 
be solved. The angle subtended by the target planet as 
seen from the spacecraft (planet angular diameter) is 
given by 
+ = 2 s i r1  (rad/r) (8) 
111. Sun Direction in RST 
To define the spacecraft-centered celestial cone angle p 
and clock angle a! of the target planet (Fig. 2), it is nec- 
essary to define the direction to the sun and Canopus in 
the target-planet RST system and then transform these 
directions to the spacecraft at time T. 
c 
4 SUN 
- b  
Fig. 2. Celestial coordinate system 
A 
Figure 3 defines the sun direction IRp and Canopus di- 
rection e in the target-planet RST system at encounter 
(T = 0). 
At a time T, other than zero, the inertial direction to 
the sun will have changed due to the target-planet’s 
motion about the sun. This change in direction can be 
expressed as a rotation of R-p about a vector W, normal 
to the target-planet plane of motion as a function of T. 
2 JPL TECHNICAL REPORT 32-J338 
S W 
t t 
J 
T 
Fig. 3. Sun and Canopus directions 
Thus, the inertial VUW coordinate system, shown in 
Fig. 4, is defined such that V = R, at T = 0, and U com- 
pletes the right-hand system. 
Sun vector R, defined in VUW at time T is given by 
COS X (T) - sin X (T) 0 
R, = R, (T) sin X ( T )  cos h (T) 0 C o  0 1 
= RP (7) J (T) 9 
where 
(T) = (t) dt 
i (T) = target-planet angular rate about the sun 
R, (T) = sun-target-planet range 
(9) 
V R i  
Fig. 4. VUW coordinate system 
For the time period in which the two-body approxima- 
tion holds 
where 
C = Kepler's area constant 
and 
RP = RP (0) 
Therefore, 
The transformation K from WW to RST is needed to 
express R, in RST. An intermediate coordinate system 
XYZ will be used in determining I(. In RST, 
- (sin & sin qs)  (cos .$) 
0 1 0 
- (sin & cos q8) 
q s  0 - sinqs 
(12) 
3 JPL TFCHNICAL REPORT 32-1338 
[ ~ ]  = L  [8] (13) 
In VUW, 
1 0 0 
( 14) 
0 - (sin y,/sin ts) (cos 
or 
[i] = M  [B 
The transformation K can be expressed in terms of L and M as follows: 
K = L-IM 
where 
- sin 5 8  sin v8 
K = I cos&, 
- sin 6 cos T 8  
cos ts  sin v S  cos y p  sin up - cos vs sin y, cos tS sin vs sin y, + cos vs cos y, sin a, 
sin ts sin t8 
sin y p  cos yp sin up 
cos ts cos vs cos y p  sin up + sin vs sin 7, cos tS cos vs sin y p  - sin v8 cos yp sin up 
sin tS sin tS 
The XYZ coordinate system is not necessarily an orthog- 
onal coordinate frame. Also, the angle a, is not included 
in the SPACE output. From the geometry, however, 
cos u p  = cos &/cos yp ( 17) 
In general, outer planets have a greater angular ve- 
locity about the sun than the approaching spacecraft 
for type I trajectories (Ref. 4). The inverse would apply 
to trajectories to the inner planets. Under these con- 
ditions, the sign of sin a, may be determined by using 
0 _< up < 180 deg for type I trajectories to the outer 
planets, and 180 5 up < 360 deg for type I trajectories 
to the inner planets. 
The sun vector R, at time T and expressed in RST 
is then 
A 
Rp = Rp K J ( T )  V (18) 
4 JPL TECHNICAL REPORT 32- I338 
Using Eq. (18), the phase angle of the target planet as 
seen from the spacecraft is given by 
The cone angle of Canopus pc is given by 
58, 
des 
155.365 
A 
(23) p c  = cos-1 (2 C) 
E.# 98, 90, YP. R p r  B, e, "0s c, 
des de9 de9 des 10' km IO3 km de9 km/s 10% km2/s 
111.001 158.327 264.227 8.955 213.3 7.124 40.22 6.955 5469.7 
4 
The spacecraft-planet direction G expressed in abc is 
given by 
IV. Spacecraft-Centered Celestial Geometry 
The direction to Canopus C can be considered constant 
and equal in either the planet-centered or spacecraft- 
centered RST system, because of the great distance to 
Canopus. The separation angle 6 between the target 
planet and Canopus as viewed from the spacecraft is 
given by 
A 
A 
6 = cos-1 (- 3.C)  (20) 
where vu, ob, and vc are the direction cosines of $. The 
target-planet cone angle p is given by 
p = cos1 (oc) (25) where 
A 
C = - (sin .& sin qc)  R + (cos tC) S - (sin .$ cos qc) T and the target-planet clock angle a: is given by 
The vector c in the spacecraft-centered celestial abc 
coordinate system (Fig. 2) is defined by transforming 
the sun direction to the spacecraft-centered RST sys- 
tem. Therefore, in spacecraft coordinates, 
a: = tan-l (%/vu) 
V. Results of Application 
The Near-Encounter Geometry Generation (NEGG) 
computer program, listed in the Appendix, was written 
to perform the previously defined computations. A 1969 
Mars trajectory was simulated by NEGG and then com- 
pared to the SPACE output. Table 1 lists the trajectory 
elements and encounter geometry used as input to NEGG. 
and by definition 
Table 2 lists the target-planet clock angle a: and cone 
angle p, the spacecraft-target-planet range T, and the 
cone angle of Canopus Be obtained from SPACE and 
NEGG for various times before encounter. Table 2 illus- 
trates that NEGG can be used as a very effective mis- 
sion analysis tool for the near-encounter phase of a 
trajectory. The shape and orientation of the trajectory 
can be changed by changing the input parameters B,  8 ,  
and V, without significantly affecting the accuracy of 
the resultant trajectory geometry. 
which can be expressed as follows: 
Table 1. Trajectory. encounter characteristics 
JPL TECHNICAL REPORT 32- I338 5 
Table 2. Geometry comparison 
encounter 
0.0 231.607 94.817 6.3 18 77.357 23 1.607 94.817 6.318 77.357 
buys before 
encounter 
20.0 
10.0 
5.0 
1 .o 
0.0 
VI. Recommendations 
The largest error in the geometry generation resulted 
from assuming that the target planet had a constant rate 
about the sun. For the Mars trajectory, the angle de- 
scribed in Eq. (11) was in error by 0.05 deg at 10 days 
before encounter. Therefore, a more exact expression for 
would improve the geometry generation. 
B, e. 
I d  km de0 
64.490 141.070 
20.220 131.131 
6.4371 62.955 
7.1316 37.052 
7.1426 36.876 
A perusal of the planet-centered conic section of the 
SPACE output can give insight into the validity of as- 
suming fixed orbital parameters. Table 3 gives the hyper- 
bolic orbital parameters B,  e, and V, that describe the 
Table 3. Effective two-body orbital parameters 
7.137 
7.057 
7.01 1 
6.996 I 6.995 
effective two-body trajectory solution for various times 
before Mars encounter for the selected trajectory. 
Table 3 indicates that the assumption of fixed orbital 
parameters is not the best choice. An improvement in 
the geometry generation could be obtained by fitting 
second-order polynomials to the orbital parameters, such 
that 
and then using the values of Eq. (27) with T to solve 
Eq. (4) ,  and then Eq. (1) for r. At more than a day from 
encounter, the direction to the planet (essentially along 
the incoming asymptote) is not affected strongly by the 
changing orbital parameters; therefore, the major im- 
provement resulting from a polynomial representation of 
the orbital parameters would be in the spacecraft-target- 
planet range. 
6 JPL TECHNICAL REPORT 32-1338 
Nomenclature 
a 
a 
b 
B 
B 
C 
C 
C 
e 
F 
i 
J 
K 
L 
M 
N 
T 
r 
R 
rad 
R P  
RP 
S 
T 
U 
V 
V 
semimajor axis of hyperbola 
celestial vector to complete right-hand system abc 
celestial vector normal to c and C 
magnitude of B 
vector from center of target ,planet to incoming 
asymptote 
celestial vector from spacecraft to sun 
Kepler’s area constant 
celestial vector from spacecraft to Canopus 
eccentricity of hyperbola 
analog of eccentric anomaly for hyperbola 
inclination of trajectory plane 
matrix which rotates sun direction about W 
transformation from VUW to RST 
transformation from RST to XYZ 
transformation from VUW to XYZ 
transformation from RST to abc 
magnitude of r 
target-planet-spacecraft vector in RST 
inertial vector to complete right-hand system RST 
target-planet radius 
magnitude of Rp 
target-planet-sun vector 
inertial vector along incoming asymptote 
inertial vector normal to S and parallel to the 
earth ecliptic plane 
inertial vector to complete right-hand system 
vuw 
spacecraft-target-planet vector in abc 
inertial target-planet-sun vector defined at en- 
counter 
projection of v on a 
projection of v on b 
projection of v on c 
inertial vector directed above and normal to 
target-planet’s plane of motion 
inertial vector equal to V 
inertial vector equal to S 
inertial vector normal to X and Y 
target-planet clock angle 
target-planet cone angle 
Canopus cone angle 
angle between S and V-U plane 
target-planet-spacecraft-Canopus angle 
true anomaly 
angle between -T and projection of C on R-T 
plane 
angle between -T and projection of R, on R-T 
plane 
direction of B in R-T plane 
angle between & and V 
time derivative of h 
target-planet gravitational constant 
angle between S and C 
angle between S and & 
angle between V and projection of S on V-U 
plane 
time past encounter 
target-planet phase angle 
target-planet angular diameter 
argument of periapsis 
w’ o + q  
JPL TECHNKAL REPORT 32-1338 7 
References 
1. White, R. J., et al., SPACE-Single Precision Cowell Trajectory Program, Tech- 
nical Memorandum 33-198. Jet Propulsion Laboratory, Pasadena, Calif., Jan. 
15,1965. 
2. Ehricke, K. A,, Space Flight-Environmental and Celestial Mechanics. D. Van 
Nostrand Co., Inc., New Jersey, Jan. 1960. 
3. Traub, J. F., Iterative Methods for the Solution of Equations. Prentice-Hall, 
Inc., Englewood Cliffs, N. J., 1964. 
4. Clarke, V. C., et al., Design Parameters for Ballistic Interplanetay Trajectories, 
Part 1 .  One-way Transfers to Mars and Venus, Technical Report 32-77. Jet 
Propulsion Laboratory, Pasadena, Calif., Jan. 16,1963. 
8 JPL TECHNICAL REPORT 32-1338 
Appendix 
Near-Encounter Geometry Generation Program 
JPL TECHNICAL REPORT 32- 1338 9 
D I M E N S I O N  C N C ~ ) ~ T W R ( ~ Y ~ ~ Y  2 V ( ? l  y T T r ( 3 * 7 l . V ( 7 ) r R P S ( 1 I  
SN(X)=SIN(X*m17453293E-o l )  
C S ( X ) = C O S ( X * . 1 7 4 5 3 2 9 5 E - 0 1 )  
U = o 1 7 4 5 3 2 9 3 E - O L  
P I = 3 . 1 4 1 5 9 2 7  
R F A D ( 5 r 2 0 1 )  7 A P y  7 A C *  F T S *  FTC, C L P Y  G P *  TH 
1 R E A D ( 5 r 2 0 0 )  PMU, R A D Y  B Y  VHY C Y  RPP 
WW=C/(RPP*RPP) 
AA=PMU/(VH*VH) 
PP=B*B /AA 
I F ( C o L E o 1 o )  WW=C 
E H = S G R T ( l o + a * B / ( A A * A A ) )  
R P = P P / (  1m+EH) 
H P = R P -R AD 
R E A D ( 5 9 2 0 1 )  T I ,  T F Y  DT 
N M = A B S ( ( T I - T F ) / D T ) + 1 . 9 5  
T I = T I * 8 6 4 0 0 0  
T F = T F * 8 6 4 0 0 0  
D T = D T * 8 6 4 0 0 0  
W R I T E ( 6 y 2 0 5 )  ZAP, ZAC, ETSI E T C Y  CLPI G P Y  TH 
W R I T E ( 6 9 2 0 6 )  AA, BI H P Y  VHY Cs R P P  
W R I T E (  6 9 2 0 2 )  
W R I T E (  6 , 2 0 3 )  
___I_______--- 
S T t i = S N ( T H )  
C T H = C S ( T H )  
S Z P = S N ( Z A P )  
CZP=CSt  ZAP 
SZC=SN ( ZAC 
C N ( 2 ) = C S ( Z A C )  
S E T S = S N ( E T S )  
C E T S = C S ( E T S )  
SGP=SN(GP) 
CGP=CS(GP) 
CC L P  =CZP/ CGP 
C N ( l ) = - S Z C * S N ( E T C )  
C N ( 3 ) = - S Z C * C S ( E T C )  
S C L P = ( R P P - ~ O E O ~ ) * S Q R T ( ~ . - C C L P # C C L P * C C L P ) / A ~ S ( R P P - ~ . E O ~ )  
I F ( C L P . L T o O o )  SCLP=-SCLP 
T F l r l  p a . 0 . I  <ri P=suri  P !  
T W R ( l , l ) = - S Z P * S E T S  
T h R ( 1 * 7 I = ( C 7 P  *SFTS++CGP*C,fI P-CFT. <*y;p I / <7P  
f W R ( Z y l ) = C Z P  
TWR L 7 - 7  
T W R ( ~ Y ~ ) = - S Z P * C E T S  
T W R ( 3 * 2 ) = ( C 7 P  *CFTS HCT,P*<f I  P+C,FTS *<Gp 1 /q7p 
T=T I -DT 
00 '75 N = l r N M  
T=T+DT 
I F ( T o G E . T F )  T = T F  
I F ( T o N E o 0 o )  GO TO 17  
C E T = l o  
SET=O. 
=CGP*Sci  P 
R=RP 
GO TO 2 0  
1 7  R=RP+VH*ABS(T)  
C H F = I R + A A ) / ( A A * E H )  
F=ALOG(CHF+SHF) 
SHF=SQRT(CHF*CHF- lo )  
18 FF=ABS(T)-AA*(EH*SHF-F)/VH 
F P F = - A A * ( E H * C H F - l o ) / V H  
F = F - F F / F P F  
Z = E X P ( F )  
R T = A A * E H + ( Z + P o / Z ) / 2 * - A A  
DR=ABS( RT-R 1 
R = R f  
C H F = ( R + A A ) / ( A A * E H )  
SHF=SQRT(CHF*CHF- lo )  
K = o 4 3 4 2 9 4 4 8 * A L O G ( R )  
I F ( l O . * * ( K - 5 ) o L T m D R I  GO TO 1 8  
C E T & ( P P / R - l o ) / E H  
SET=SQRT(lo-CET*CET)*T/ABS(T) 
10 JPL TECHNICAL REPORT 32-1338 
20 SWP=(AA*CET+B*SET) / (AA*EH)  
CWP=(B*CET-AA*SET)/(AA*EH) 
K V ( l ) = H * C W P * S T h  
R V ( Z ) = R * S W P  
RV(S)=R*CWP*CTH 
C C A L C U L A T I O N  O F  THE EFFECT O F  THE TARGET P L A N E T S  M O T I O N  ABOUT THE SUN 
SWT=SIN(WW*T) 
CWT=COS(WW*T) 
DO 21 I = l r 3  
R P S ( I ) = ( T W R ( I i l ) * C W T + T W R ( I , 2 ) + S W T ) * R P P  
PH=ARCOSt (RPS(l)*RV(l)+RPS(2)*i?V(2)+RPS(3)*RV(3))/(RPP*R) ) / U  
no 7 7  1 = i . 3  
2 1  T I C ( 3 9 I ) = R P S ( I ) - R V ( I )  
T I C M = S G R T ( T I C ( 3 9 1 ) * T I C ( 3 t l ) + T I C (  3,2)*TIC(3,2)+TIC(3,3)*TIC(393)) 
23 T I C ( 3 r I ) = T I C ( 3 r I ) / T I C M  
B C = A R C O S ( T I C ( 3 ~ 1 ) * C N ( l ) + T I C ( 3 , 2 )  *CN( 2 )  + T I C (  3 - 3 1  * r N ( 3 l ) / L J  
T I C  ( 2  9 1 ) = T I C (  3 9 2 ) *CN ( 3  ) - T I C (  393 1 *CN( 2 ) 
TDYS=T / 8 6 4 0 0 *  
W R I T E ( 6 9 2 G 4 )  TDYS, R 9  B T 9  AL, PHI P H I 9  DLTI 6 C  
~ 
7 5  C O N T I N U E  
GO TG 1 
2 0 0  FORMAT(4El0.1,2€12.4) - 
2 0 1  FORMAT(8E10.1)  
202 FORMAT ( 1HO 9 2 X  14hT I M E  95X ~ ~ H R A F ~ ~ E _ L ~ X , ~ H C O N E  t 5 X  r5HCLOCK 9 4 x 9  5hPHASE 95& 
193HPHI95X,5HDELTA95X,ZHaC) 
203 F O R M A T ( 1 H  , ~ X , ~ H ( D A Y S ) ~ ~ X I ~ H ( K M I  + 6 X , 6 ( 5 H ( D E G ) 9 4 X ) )  
204 F O R M A T ( 1 H  . F 7 * 1 9 F l Z r l r 6 F 9 * 3 )  
2 0 5  FORMATt l r i - l , 5OXr22HTRAJECTORY 1!4FORMATION/lX94HZAP=,F8*393X,4HZAC=, 
~ F ~ . ~ , ~ X , ~ H E T S = , F ~ * ~ , ~ X ~ ~ H E T C = ~ F ~ ~ ~ ~ ~ X ~ ~ H C L P = ~ F ~ D ~ ~ ~ X ~ ~ H G P = , F ~ * ~ ~ ~ X  
,2HA= 9F8. 1,5X,2Hij=,FB * 1 9 5 x 9  3HHP=rF8. 1 r5X,3HV=F7.3 9 5 X  93 
_____-__I 2 9 3 H T t i = r F 8 . 3 )  _I --- ____- 
2 C 6  FORMAT ( 1H 
1H C=9E11.495X,4HRPP=,t11*4) 
END 
JPL TECHNICAL REPORT 32-1338 11 


Near-encounter geometry generation

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