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C
0273—1177/84 $0.00 + .50 Copyright © COSPAR
2l3—2l6, 1984 reserved.
Adv. Space Rca. Vol.4, No.9, pp. Printed in Great Britain. All rights
DUST ENVIRONMENT MODELS FOR COMET P/HALLEY: SUPPORT FOR TARGETING OF THE GIOTTO S/C J. Fertig and G. H. Schwehm European Space Operations Centre, Orbit Attitude Division, Robert-Bosch-Strasse 5, 6100 Darmstadt, F.R. G. In March 1985 ESA’s GIOTTO spacecraft will fly by P/Halley’s nucleus at a distance of a few hundred kilometres. The near nucleus dust environment the probe will traverse poses a hazard with respect to physical damage as well as to attitude disturbance with the possible loss of ground station contact. To predict S/C survivability and dust impact rates for the experiments, a model of the spatial distribution of the dust in the nucleus’ vicinity is required. In the ‘dynamic’ model, the local spatial dust density is derived from exact expressions for the dust particle dynamic motion. The model has been implemented in a software system which allows for fast simulations of a cometary fly-by. INTRODUCTION In March 1986 five spacecraft from Japan, the USSR and Europe will explore Halley’s comet. ESA’s GIOTTO spacecraft will be launched in July 1985 to encounter the comet about one month after perihelion when it crosses the ecliptic plane. GIOTTO is planned to fly—by the comet more closely than the other spacecraft to provide in situ measurements of the inner coma and first high—resolution images of the cometary nucleus. The fast fly—by also renders closed—loop pre—encounter trajectory correction, e.g. based on on—board camera images, impossible. Thus only ground based observations and space data from other probes are available to locate comet Halley’s nucleus in a huge gas and dust coma. ESOC’s cometary dust environment model is part of an effort to meet this operational challenge/l/. The target point of the GIOTTO spacecraft is defined relative to this nucleus. Thus the GIOTTO probe can only reach its target if the nucleus can be located by some indirect means within the coma. This appears possible, considering the physical processes governing the coma’s formation. A numerical model of the spatial dust density distribution in a nucleus—fixed reference frame will enable us to simulate the brightness distribution in images of the coma. In addition to the targeting process, the dust density model supports the aim point selection. Here, the spacecraft probability of survival as predicted from the dust density along the reference trajectory will be an important decision making criterion. Dust particles will impinge on the probe throughout the final 50 000 to 100 000 km of its approach to the nucleus. As soon as the attitude offset due to particle impacts exceeds the antenna beam width of O.5~ ground contact will be lost. Already the impact of a 0.1 g particle on the outer rim of the shield would shift the spin axis by more than 2~. Still larger particles may penetrate both shields and damage the spacecraft. Fortunately, the probability of encountering particles that large is low. However, it becomes obvious that for risk assessment emphasis must be placed on the modelling of the spatial distribution of large dust grains as they constitute the main hazard for the spacecraft.
213
214
J. Fertig and G.H. Schwehni
COMETARY DUST ENVIRONMENT MODELLING Cometary dust particles are accelerated radially away from the nucleus by the expanding gas. After a distance of only a few nuclear radii the aerodynamic interaction ceases and the grains have reached their size—dependent terminal velocity. Subsequently, they are accelerated by solar radiation pressure in the anti—sunward direction. In earlier dust models /2,3/ the dynamic motion of dust particles in the cometary coma has been described by the ‘fountain model’. This which model only 8g)correctly are describes the dynamics of small particles (m~.~l0 strongly accelerated by solar radiation and very rapidly leave any near—nucleus domain of interest. Hence the concurrent comet orbital motion can be neglected and the particles can be assumed to travel in a homogeneous force field. Consequently, the particle trajectories in a comet fixed system are well approximated by parabolae and the entire cloud of particles is confined within a paraboloid of rotation, the dust envelope. Figure 1 shows the drastic difference in dust—cloud geometry for small (a), intermediate (b), and large (c) particles. The comet nucleus is at the origin and the comet—Sun line is parallel to the abscissa; the plane of the drawing is the comet’s orbital plane. The particles are assumed to be ejected at perihelion. In each case 12 trajectories are considered with initial—velocity vectors at azimuth intervals of 30~ in the orbital plane. The locii of the particles at 2, 16 or 32 day intervals in (a), (b), and (c) respectively, are indicated in the figures.
a
~
~6d7~\N
~T=~da~a=~1Orn
:~L~ ~ Figures la—c. Trajectories of dust particles in the plane of the comet orbit (cometocentric system). The azimuth of ejection is varied in steps of 30°. Three particle masses are considered; the respective radii a, masses mp~ terminal velocities VT, and radiation—pressure force/gravitational— attraction ratios are noted in the figures. The locus of simultaneously emitted particles after T=2, 16 or 32 days is shown. The GIOTTO trajectory is inclined by 8°with respect to the plane of the figure.
Dust Environment Models for Halley
215
12kg) particles can be thought of Simultaneously ejected lightweight (mp~10 as located at the surface of a sphere which is expanding with the dust terminal velocity, while its centre is travelling into the anti—sunward direction along a syndyne/4/. For large particles, these spheres are distorted into ellipsoids and, more importantly, their velocity of expansion may become larger than the velocity at which the centre moves. Thus, while these particles are still confined to a limited area around the nucleus due to their low terminal velocities, the shape of the overall particle cloud deviates greatly from a paraboloid of rotation. In the dust model established at ESOC, we derive the number density of dust as function of particle size, time and position in the comet fixed coordinate system. In a first step the departure time and initial velocity of all particles that reach a given position at the specified time is included. This is done by solving a linearized Lambert problem, i.e. the dust particle trajectory relative to the nucleus is expressed as a linear function of the dust departure velocity vector and of the effective change of the solar gravity constant due to radiation pressure. This liriearisation makes the Lambert—algorithm computationally highly efficient while it does not noticeably curtail the accuracy. Given all solutions for departure time and velocity, we find the particle density from the local emission characteristics and from the transformation of a unit volume element at the departure point to the position in question. The latter is calculated by taking the Jacobian of the cometocentric position with respect to departure right ascension, declination and arrival time /5/. The dust terminal velocity and the radiation pressure efficiency factor are calculated as a function of particle size using a self—consistent hydro— dynamic model /6/ or Mie—theory /7/, respectively. Both are input to our program in tabular form. Currently we assume the particle size distribution, bulk density model and emission characteristics of the nucleus as given in /5/ to render comparison with other models possible. The total dust production rate was taken as 0dust 8 X l06gs~ at .9 a.u. post—perihelion. A sample result of the particle number flux impinging or-i the spacecraft front shield during fly—by is shown in fig. 2.
-,
510 XM
~o3~
i0~
Fig. 2. Dust number flux per mass interval as function of distance from nucleus along the reference trajectory. The aimpoint is at 500 km to the sunward side of the nucleus, the fly—by velocity is 68 km/s The total range in particle mass from 10—12 to 3.55g has been split in 12 mass intervals which are represented individually. An aim—point 500 km to the sunward side of the nucleus is assumed. The results show that intermediate particles may be encountered at larger distances from the nucleus than previously thought. For these particles a second density maximum is found between envelope and point of closest approach. This is because certain directions of emission lead to a slow relative motion of intermediate particles (compare fig 1) which results in a dust accumulation.
216
J. Fertig and G.H. Schwehm
Figure 3 shows the integrated flux or dust number fluence along the reference trajectory. This is the total number of particles encountered per unit shield areaprobability as function of ofencountering distance from nucleus. Forhighest a total mass shield area 2 the a the particle in the class of 3m — 3.35g) is only 1.6%. (0.1 An impact of a particle with 0.0lg~m~~0.lg will occur with 30% probability for this assumed model.
~US~ ~
E~C~ I
~
~
.
~
10~~ — ;~—‘‘~
10-10 I0~
lrz 500KM
io~
SSIAMCE ‘ROM ~UCLEUS
~0.
10’
io~
Fig. 3. Dust number fluence per mass interval along the reference trajectory for the dust model in /5/, (Qdust 8.l06gs~). CONCLUSION We have developed a cometary dust environment model that correctly describes the spatial distribution of large dust particles with long transit times from the cometary nucleus to the spacecraft trajectory. From the dust number fluence per mass interval along the reference trajectory the expectation value for the spacecraft attitude offset has been calculated. With the assumed dust model from /5/, for the current reference trajectory with an aim point 500 km to the sunward side of the nucleus we have found that the spin axis will remain only within 6° from its nominal direction with 95% probability. This result seems to imply that the ground link will almost certainly be lost during closest approach. However, this is possibly overly pessimistic because the large particle contribution to the expected attitude offset are overemphasized, as the probability of encountering a particle above .lg is less than 2%. REFERENCES /1/
J. Fertig, F. Hechier, G. Schwehm, Navigation to a target hidden in dust: Comet Halley’s nucleus, ESA Bulletin no 38, 36—41, 1984
/2/
N. Divine, Numerical Models for Halley dust environments, ESA—SP 174, 25—30, 1984
/3/
R. Helimich and H.U. Keller, Definition of model parameters and numerical fly—by simulations, ESA—SP 174, 31—39,1981
/4/
M. L. Finson and R. F. Probstein, A theory of dust comets, and equations, Astrophysical Journal, 154, 327—352, 1968
/5/
N. Divine and R. L. Newburn, Numerical Models for cometary dust environments, Proc. Int. Conf. on cometary expl., ed. T. I. Garnbosi, Budapest 2, 81—98, 1982
/6/
R. Helimich and G. H. and fluence rates for Halley: a comparison. Gambosi, Budapest, 2,
/7/
G. H. Schwehm and M. Rhode, Dynamical effects on circumsolar dust grains, J. Geophys. 42, 727—735, 1977
I. Model
Schwehm, Prediction of dust particle number flux a ESA—GIOTTO and USSR—VEGA mission to comet Proc. mt. Conf. on Cometary Expl., ed. T. I. 81—98, 1982.
2l3—2l6, 1984 reserved.
Adv. Space Rca. Vol.4, No.9, pp. Printed in Great Britain. All rights
DUST ENVIRONMENT MODELS FOR COMET P/HALLEY: SUPPORT FOR TARGETING OF THE GIOTTO S/C J. Fertig and G. H. Schwehm European Space Operations Centre, Orbit Attitude Division, Robert-Bosch-Strasse 5, 6100 Darmstadt, F.R. G. In March 1985 ESA’s GIOTTO spacecraft will fly by P/Halley’s nucleus at a distance of a few hundred kilometres. The near nucleus dust environment the probe will traverse poses a hazard with respect to physical damage as well as to attitude disturbance with the possible loss of ground station contact. To predict S/C survivability and dust impact rates for the experiments, a model of the spatial distribution of the dust in the nucleus’ vicinity is required. In the ‘dynamic’ model, the local spatial dust density is derived from exact expressions for the dust particle dynamic motion. The model has been implemented in a software system which allows for fast simulations of a cometary fly-by. INTRODUCTION In March 1986 five spacecraft from Japan, the USSR and Europe will explore Halley’s comet. ESA’s GIOTTO spacecraft will be launched in July 1985 to encounter the comet about one month after perihelion when it crosses the ecliptic plane. GIOTTO is planned to fly—by the comet more closely than the other spacecraft to provide in situ measurements of the inner coma and first high—resolution images of the cometary nucleus. The fast fly—by also renders closed—loop pre—encounter trajectory correction, e.g. based on on—board camera images, impossible. Thus only ground based observations and space data from other probes are available to locate comet Halley’s nucleus in a huge gas and dust coma. ESOC’s cometary dust environment model is part of an effort to meet this operational challenge/l/. The target point of the GIOTTO spacecraft is defined relative to this nucleus. Thus the GIOTTO probe can only reach its target if the nucleus can be located by some indirect means within the coma. This appears possible, considering the physical processes governing the coma’s formation. A numerical model of the spatial dust density distribution in a nucleus—fixed reference frame will enable us to simulate the brightness distribution in images of the coma. In addition to the targeting process, the dust density model supports the aim point selection. Here, the spacecraft probability of survival as predicted from the dust density along the reference trajectory will be an important decision making criterion. Dust particles will impinge on the probe throughout the final 50 000 to 100 000 km of its approach to the nucleus. As soon as the attitude offset due to particle impacts exceeds the antenna beam width of O.5~ ground contact will be lost. Already the impact of a 0.1 g particle on the outer rim of the shield would shift the spin axis by more than 2~. Still larger particles may penetrate both shields and damage the spacecraft. Fortunately, the probability of encountering particles that large is low. However, it becomes obvious that for risk assessment emphasis must be placed on the modelling of the spatial distribution of large dust grains as they constitute the main hazard for the spacecraft.
213
214
J. Fertig and G.H. Schwehni
COMETARY DUST ENVIRONMENT MODELLING Cometary dust particles are accelerated radially away from the nucleus by the expanding gas. After a distance of only a few nuclear radii the aerodynamic interaction ceases and the grains have reached their size—dependent terminal velocity. Subsequently, they are accelerated by solar radiation pressure in the anti—sunward direction. In earlier dust models /2,3/ the dynamic motion of dust particles in the cometary coma has been described by the ‘fountain model’. This which model only 8g)correctly are describes the dynamics of small particles (m~.~l0 strongly accelerated by solar radiation and very rapidly leave any near—nucleus domain of interest. Hence the concurrent comet orbital motion can be neglected and the particles can be assumed to travel in a homogeneous force field. Consequently, the particle trajectories in a comet fixed system are well approximated by parabolae and the entire cloud of particles is confined within a paraboloid of rotation, the dust envelope. Figure 1 shows the drastic difference in dust—cloud geometry for small (a), intermediate (b), and large (c) particles. The comet nucleus is at the origin and the comet—Sun line is parallel to the abscissa; the plane of the drawing is the comet’s orbital plane. The particles are assumed to be ejected at perihelion. In each case 12 trajectories are considered with initial—velocity vectors at azimuth intervals of 30~ in the orbital plane. The locii of the particles at 2, 16 or 32 day intervals in (a), (b), and (c) respectively, are indicated in the figures.
a
~
~6d7~\N
~T=~da~a=~1Orn
:~L~ ~ Figures la—c. Trajectories of dust particles in the plane of the comet orbit (cometocentric system). The azimuth of ejection is varied in steps of 30°. Three particle masses are considered; the respective radii a, masses mp~ terminal velocities VT, and radiation—pressure force/gravitational— attraction ratios are noted in the figures. The locus of simultaneously emitted particles after T=2, 16 or 32 days is shown. The GIOTTO trajectory is inclined by 8°with respect to the plane of the figure.
Dust Environment Models for Halley
215
12kg) particles can be thought of Simultaneously ejected lightweight (mp~10 as located at the surface of a sphere which is expanding with the dust terminal velocity, while its centre is travelling into the anti—sunward direction along a syndyne/4/. For large particles, these spheres are distorted into ellipsoids and, more importantly, their velocity of expansion may become larger than the velocity at which the centre moves. Thus, while these particles are still confined to a limited area around the nucleus due to their low terminal velocities, the shape of the overall particle cloud deviates greatly from a paraboloid of rotation. In the dust model established at ESOC, we derive the number density of dust as function of particle size, time and position in the comet fixed coordinate system. In a first step the departure time and initial velocity of all particles that reach a given position at the specified time is included. This is done by solving a linearized Lambert problem, i.e. the dust particle trajectory relative to the nucleus is expressed as a linear function of the dust departure velocity vector and of the effective change of the solar gravity constant due to radiation pressure. This liriearisation makes the Lambert—algorithm computationally highly efficient while it does not noticeably curtail the accuracy. Given all solutions for departure time and velocity, we find the particle density from the local emission characteristics and from the transformation of a unit volume element at the departure point to the position in question. The latter is calculated by taking the Jacobian of the cometocentric position with respect to departure right ascension, declination and arrival time /5/. The dust terminal velocity and the radiation pressure efficiency factor are calculated as a function of particle size using a self—consistent hydro— dynamic model /6/ or Mie—theory /7/, respectively. Both are input to our program in tabular form. Currently we assume the particle size distribution, bulk density model and emission characteristics of the nucleus as given in /5/ to render comparison with other models possible. The total dust production rate was taken as 0dust 8 X l06gs~ at .9 a.u. post—perihelion. A sample result of the particle number flux impinging or-i the spacecraft front shield during fly—by is shown in fig. 2.
-,
510 XM
~o3~
i0~
Fig. 2. Dust number flux per mass interval as function of distance from nucleus along the reference trajectory. The aimpoint is at 500 km to the sunward side of the nucleus, the fly—by velocity is 68 km/s The total range in particle mass from 10—12 to 3.55g has been split in 12 mass intervals which are represented individually. An aim—point 500 km to the sunward side of the nucleus is assumed. The results show that intermediate particles may be encountered at larger distances from the nucleus than previously thought. For these particles a second density maximum is found between envelope and point of closest approach. This is because certain directions of emission lead to a slow relative motion of intermediate particles (compare fig 1) which results in a dust accumulation.
216
J. Fertig and G.H. Schwehm
Figure 3 shows the integrated flux or dust number fluence along the reference trajectory. This is the total number of particles encountered per unit shield areaprobability as function of ofencountering distance from nucleus. Forhighest a total mass shield area 2 the a the particle in the class of 3m — 3.35g) is only 1.6%. (0.1 An impact of a particle with 0.0lg~m~~0.lg will occur with 30% probability for this assumed model.
~US~ ~
E~C~ I
~
~
.
~
10~~ — ;~—‘‘~
10-10 I0~
lrz 500KM
io~
SSIAMCE ‘ROM ~UCLEUS
~0.
10’
io~
Fig. 3. Dust number fluence per mass interval along the reference trajectory for the dust model in /5/, (Qdust 8.l06gs~). CONCLUSION We have developed a cometary dust environment model that correctly describes the spatial distribution of large dust particles with long transit times from the cometary nucleus to the spacecraft trajectory. From the dust number fluence per mass interval along the reference trajectory the expectation value for the spacecraft attitude offset has been calculated. With the assumed dust model from /5/, for the current reference trajectory with an aim point 500 km to the sunward side of the nucleus we have found that the spin axis will remain only within 6° from its nominal direction with 95% probability. This result seems to imply that the ground link will almost certainly be lost during closest approach. However, this is possibly overly pessimistic because the large particle contribution to the expected attitude offset are overemphasized, as the probability of encountering a particle above .lg is less than 2%. REFERENCES /1/
J. Fertig, F. Hechier, G. Schwehm, Navigation to a target hidden in dust: Comet Halley’s nucleus, ESA Bulletin no 38, 36—41, 1984
/2/
N. Divine, Numerical Models for Halley dust environments, ESA—SP 174, 25—30, 1984
/3/
R. Helimich and H.U. Keller, Definition of model parameters and numerical fly—by simulations, ESA—SP 174, 31—39,1981
/4/
M. L. Finson and R. F. Probstein, A theory of dust comets, and equations, Astrophysical Journal, 154, 327—352, 1968
/5/
N. Divine and R. L. Newburn, Numerical Models for cometary dust environments, Proc. Int. Conf. on cometary expl., ed. T. I. Garnbosi, Budapest 2, 81—98, 1982
/6/
R. Helimich and G. H. and fluence rates for Halley: a comparison. Gambosi, Budapest, 2,
/7/
G. H. Schwehm and M. Rhode, Dynamical effects on circumsolar dust grains, J. Geophys. 42, 727—735, 1977
I. Model
Schwehm, Prediction of dust particle number flux a ESA—GIOTTO and USSR—VEGA mission to comet Proc. mt. Conf. on Cometary Expl., ed. T. I. 81—98, 1982.