Tether satellite system collision study

Acta Astronautica Vol. 44, Nos. 7-12. pp. 543-551, 1999 0 1998 International Astronautical Federation Published by Elsevier Science Ltd

Pergamon

PII: SOO94-5765(99)00098-3

TETHER SATELLITE

SYSTEM COLLISION

All rights reserved. Printed in Great Britain 0094-5765/99 $ - see front matter

STUDY

V.A. Chobotov’ and D.L. Mains+ Center for Orbital and Reentry Debris Studies The Aerospace Corporation El Segundo, CA 90245-469 1

Italian-built TSS satellite radially upward from the shuttle using the same 20 km conducting tether as in the TSS-1 experiment. At 19.7 km the tether broke at the orbiter. The satellite and the 19.7 km tether moved to a 321 by 407 km altitude orbit and achieved a gravity-gradient (along the local vertical) attitude.

Abstract A study was performed to determine the probability of collision with resident space objects and tmtrackable debris for the tether component of the Tethered Satellite System (TSS) after it broke away from the space shuttle orbiter (mission STS-75) in February 1996. Both an analytical and a numerical approach were used in this study, and the results obtained with these two methods were found to be in good agreement. These results show that the deployed tether is expected to have been impacted by several particles 0.1 mm or larger in size. The probability of collision with objects 10 cm in size or larger was on the order of 10-3 per month. Since the severed tether reentered within one month after deployment, the collision hazard to other objects while in orbit was small. The analytical methods used in this study are general and can be applied to future tether collision evaluations. 0 1998 International Astronautical Federation

Published

by Elsevier

Science

Post flight inspection of the tether end showed it to be charred, with an apparent final tension failure of a few strands of Kevlar. It was established that the failure was a result of arcing and burning of the tether. At the time of the failure, the nominal load on the tether was 65 N. Although the damaged area of the insulation was destroyed due to burning, the evidence from tests and analysis suggested that foreign object penetration of the insulation layer in manufacturing or handling was the probable cause of the breach of the insulation layer. The TSS characteristics were: 1 satellite diameter satellite mass tether diameter Nomex core SN-CU conductor Teflon-FEP insulation Kevhu #29 load member Mass/length

Ltd. All rights

reserved.

1. Introduction The first Tethered Satellite System (TSS-1) mission, flown in August 1992 on STS-46, demonstrated the ability to deploy and retrieve a satellite connected to the orbiter with a tether and allow the current to flow along the tether. A length of 268 m rather than the planned 20 km was reached due to the difficulties of deploying the tether.1

1.6m 518 kg 2.87 mm

0.82E-2 kg/m

The primary objective of the TSS program was to demonstrate the feasibility of deploying and controlling long tethers in space. The science objectives included:

1) Characterization of the system current-

voltage response and demonstration of electrical power generation.

On 25 February 1996 the TSS-1R (STS-75) mission was flown.1 This was a reflight of the TSS-1 mission. The orbiter achieved a 296 km altitude at 28.45’ inclination and deployed the

2) Characterization of the satellite’s high voltage plasma sheet, current collection, and current closure.

3) Verification of the deployment control law and basic dynamics.

‘consultant ‘Senior Member of Technical Staff 543

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The study examines the probability of TSS collision with micrometeoroids and orbiting objects in space. The results are obtained by analytical and computer simulation methods. It is found that, while the extended tether is expected to be impacted by multiple particles 0.1 mm or larger in size, the probability of collision with objects 10 cm or larger in size was small (-10-3) before the TSS reentered and burned up in the atmosphere 3 weeks after deployment lhom the shuttle. The schematic diagrams of the deployed tether and the detached tether are shown in Figures 1 and 2, respectively. -

E%I S’f

ps :

).

. ..-

%

--

-- __--

2.1 Tether Collisions with Small Particles in Orbtt The gravity-gradient oriented tether was subject to impacts by small particles and collisions with larger objects while in orbit. Although there is a considerable uncertainty about the flux of small particles in low earth orbit (LEO) due to measurement limitations, NASA2 has published a grouping of data acquired at a variety of altitudes at different times. A collision prediction based on this data is therefore only an estimate which may vary by an order of magnitude or more. Based on this data, the cumulative cross-sectional area flux of man-made debris has been estimated by NASA’s EVOLVE model for the 350 km altitude as shown in Table 1.

.*-: /-.$p

YI,

.*--__--

2. Tether Collision Hazard in Orbit

./-

‘t lCLI

...- i------‘F?“_____ i i ._...._.

~

. .._-----....

I; ! 1

The estimated number of encounters for the tether is then given by the equation E = FAtT

(I)

where F = particle flux rate, At = tether projected area, and T = time. Table 1 shows the results. Table 1. Estimated Tether in Ports with Small Particles, Projected Area At = 56.6 m2

Figure 1. TSS-IR Deployed Configuration.

2.2 Tether Collisions with Tracked Obiects 2.2.1 Analytical Considerations

Figure 2. Satellite and Upper Tether Section. (Photo courtesy of NASA Web Site.)

Consider a gravity-gradient stabilized tether (TSS) of length L deployed in orbit as shown in Figure 3. The area A swept by the tether in one orbital revolution is pierced by the space objects For example, the repeatedly over time. probability that an object of diameter “a” in a circular orbit will pierce the shaded area around the deployed tether in Figure 3 is given by the ratio of the areas as

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(2)

p*=n

545

Table 2. Potential Collision Objects with Tether

27cRL

where e is arbitrary and R is the radius of the circular orbit. The probability that a tracked object of diameter a will impact within a distance a of the tether is P1. =- 2a

(3)

e

The overall probability striking the tether is therefore Pt (COVpaSS)

=

of the object

Ps ’ Pi

=- a 7tR

(4)

For N, penetrations by space objects in an extended time interval, At, the probability of collision with the tether is Pt(col/At)

t 23692

IMIRDEB

I

3.086301

I

1 16551

1 SOLWIND DEB

I

3.211662

1

1

IMIRDEB

I

23694

3.6372941

16277

BL-3 DEB

3.626414

11055

coStulos 1043

4.142943

21640

IUS RIB(l)

5.001676

6695

DELTA 1 RIB(l)

5.094293

23695

MIR DEB

5.562964

23691

MIR DEB

6.671790

=g

A numerical simulation for the case illustrated in Figure 3 was perfotmed using the U.S. Space Command SGP4 propagator (uncontrolled version) on space ObJeCt catalog dated 5 March 1996. The simulation, which covered 6 months starting beginning 1 March 1996, yielded 58,646 space object passing through area A by 24 different satellites, which are shown in Table 2. The distribution of the minimum relative distances to the tether (measured as distance x) is shown in Figures 4 and5.

1 23466

1 ATLAS2CENTAUR

1 20546

1 PEGBAT

RIB

1

19.559492

1

1

26.119773

1

16672

DELTA 1 DEB

39.491276

23559

GRlDEB

39.941679

10723

DELTA 1 wB(2)

40.366446

2956

WESTFORD NEEDLES

43.330237

40

5

1020SD4D4050708090100

minimum relative distance (km)

4. Orbit Piercing Statistics; All Orbit Piercings Over 6 Months (
Figure

4 Figure 3. Tether Geometry

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The Weibull differential function is of the form

cn40 1 30

f(x)=(i)

I 20 B )lO 0

minimumrelativedistance(km)

Figure 5. Orbit Piercing Statistics; All Orbit Piercings Over 6 Months (cl000 km).

(g)r-lexp[-(i)r]

(6)

where x is a particular value of the closest approach to the tether measured normal to the tether, and p, 7 are the scale and shape parameters, respectively. The cumulative distribution function is the integral of f(x) given by the relation F(x)= j f(x) dx

Assuming that the average diameter of the 24 objects in Table 2 is 5 meters, the probability of collision in 6 months with the tether is Pt(co1/ 6 months) =

distribution

for X<
(7)

5g.646 x 5 7c x 6728 x lo3

or 2.32 x lO-3 per month 2.2.2 Deployed Tether - Statistical Approach A method based on the frequency of close appmaches by space objects to the tether over an extended period of tune involves determination of the closest approach distances by the space objects which can collide with the tether. This is a modification of the method presented in Reference 3. The objects of interest are those identifmd in Table 2 which pass through the area swept by the tether. A numerical simulation over a 6 month time interval starting from 6 March 1996, was performed using the U.S. Space Command SGP4 ropagator (uncontrolled version) on space o%ject catalog dated 5 March 1996. This yielded the distribution of the distance between an object and the closest point on the tether at regular time intervals (e.g., one each 60 seconds). This was normalized and approximated b a Weibull probabiity density function as il rustrated in Figure 6. The minimum relative distance distributions within 1000 km are shown in Figure 7, and within 100 km in Figures 8 and 9 using 5 second propagation time steps.

iI*

800

g

600

B 400 tj r200 0 0

2000

4000

6000

80001oOOO

min. relativedistance(km)

Figum 6. Relative Distance Statistics; 60 Second Propagation Over 6 Months (<10,ooo km).

0

200

400

600

8001000

min.feWvecWtance(km) Figure 7. Relative Distance Statistics; 60 Second Propagation Over 6 Months (cl000 km).

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total data

poillt?

547

where

70 rn 60

F(r,) = 12 f(x)&

8 50 5 5 40

= probability of being within

8 30

the distance r, of the tether

g 20

and

* 10 0 0

20 rel%e min.

60 (k$ distance

100

E(t,)=+) r

Figure 8. Relative Distance Statistics; 5 Second Propagation Over 6 Months (
; I- : i -4 :

Here E(c) is the expected (mean) value of the chord of a circle with radius r,, and Vr is the mean relative velocity of objects to the tether. The distribution at closest encounter of the relative velocities and their mean value is shown in Figure 12.

i!

* 10 0

10

20

30 40 50 60 70 60 min. relative distance (km)

90 100

Figure 9. Relative Distance Statistics: 60 Second Propagation Over 6 Months (cl00 km). A plot of the cumulative numerical data (experimental) is shown as a dotted line and that of F(x) for the selected b and o parameters as a plotted line in Figure 10. On a larger scale, the results are given in Figure 11. As in the approach of References 3 and 4, the differential distribution function obtained in this analysis represents the relative fraction of time that the debris object nearest to the tether is a given distance away. The distribution tapers off at small values of distance and vanishes at a distance of zero. Since the tether is an extended object (not a point mass), the probability of being within a given radius of the tether r, can be found and then multiplied by the probability of striking the tether within r, by an object of size a. This can be done as follows. By analogy with the method of References 3 and 4. the cumulative distribution function can be used to determine an encounter rate N as N=

F (%) E 0,)

by an object within the radius r, of the tether

j - - ._/24llll-\ avaluatacl 7: -1

= characteristic dwell time

03)

0.0007 0.0008 0.0005 0.0004 0.0003 0.0002 0.0091 0 20

0

min.

reEive

di.stEce (km~

100

Figure 10. Cumulative Relative Distance Statistics; 5 Second Propagation Over 6 Months. 1

0.8 0.8 0.4 0.2 0 0

2000

8000 4000 8000 min. relative distance (km)

10000

Figure 11. Cumulative Relative Distance Statistics; 60 Second Propagation Over 6 Months.

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where the average relative velocity of 6.6 km/set is taken from Figure 12. In 6 months there would be 183/12.69 = 14.4 encounters within 10 km of the tether.

0

2

4

6

6

10

12

14

16

Relative Velocity(km/s)

Figure 12. Relative Velocity Distribution; 60 Second Propagation Over 6 Months.

For a given collision rate N within a sphere of radius r,, the probability of impacting the tether in the center of the sphere can be expressed as an area ratio of a projected cylinder area defined by the space object size (shaded area in Fig. 13) to that of a cross-sectional area of the sphere. The cylindrical projected area of vulnerability around the tether is 2a L and is oriented normal to the incoming object. Thus, the probability of impacting the tether within the sphere of radius rs is given by the ratio

Since it can be shown that E(c) is numerically equal to one quarter of the circumference of the circle (see Appendix),

2a L Pt =z

(12)

C

E(t,)

=IL’c = :x&ted (mean) time of passage (9) through a sphere of radius rc with relative velocity Vr

p

where a is the diameter of the object and L is the tether length

collision rate [Eq. (8)] thus becomes (Ref.

N=d

F(r 1 W, > 7

22.

(10)

‘IL rc

and the estimated time to encounter within the sphere of radius rc is Figure 13. Tether Collision Geometry Schematic Diagram. Tc=; =C.xr 2 Vr

s’ (1

(11)

rc

Applying the results to the problem of Figure 3, let r, = 10 km centered on the tether. Therefore,

The overall collision rate with the tether is therefore P(co1 / At) = N Pt

(13)

For example, if a = 5 m, L = 20 lan.V, = 6.6 Ws,r,= lOkm,j3=29OOkm,r=2.3

=

12.69 days/encounter

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This result compares with 2.32 x 10-S per month obtained by the method of Section 2.2.1.

Thus, the upper bound collision probability is P_(col)

= 2.51 x lO”/yr

2.2.3 Free Form Tether Configuration

= 2.09 x lO~/month

Just prior to reentry the orbiting tether/satellite configuration may assume a tether mesh form. The probability of collision with the tether then becomes a function of the tether mesh dimension and the size (length, diameter) of an orbiting object. Since the former cannot be determined, a worst case scenario may be examined for an upper bound collision estimate. A free-form TSS configuration prior to reentry may be assumed to have the shape shown in Figure 14 to permit a simple analysis. The probability of the mesh encounter with an object in the USSPACECOM catalog at reentry altitude of 100 km is P, where

=

A,,, = F

=

A,F mesh cross-sectional (including gaps)

area

object flux

In analogy with the problem known as the “Needle of Buff00 the probability of striking the tether with an elongated object of length a and mesh separation 1 is given by 2a P”G The overall probability of tether collision with an object at reentry altitude is therefore P(co1) = P,Pt If it is assumed that L >> D and n >> 1, then a tight upper bound on collision probability is given by P_(col)

=T

F

where a = object length (estimate = 2 m) L = tether length (19700 m) F = object flux (lo-7 #/mz/yr)

= 6.87 x lO”/day

AREA

A,rSD=

VD

;

c+

L=TElHERLENGTH=l9.7km

nt

NUMBER OF SEGMENTS

(n = 2,4,

B...)

Figure 14. Free Form Tether in Space (near reentry)3.

Summarv and Conclusions

A study was performed to determine the probability of collision for the TSS flown in February 1996 with space objects while in orbit. An analytical and a numerical approach were used and the results found to be in good agreement with each other. The results of the study show that the deployed tether in LEO was subject to several impacts by small particles greater than 0.1 mm in size. The probability of collision with large objects in orbit was on the order of lo-‘) per month. Since the severed tether reentered within one month after deployment, the collision hazard to other objects while in orbit was small. Finally, a general set of analytical methods were used in the study which can be applied to other tether collision hazard evaluations as needed. Acknowledgment The authors wish to acknowledge the helpful review of the paper by A. B. Jenkin, Dr. W. H. Ailor, and K. W. Meyer. Editing of the paper was provided by Mae Fuchino. Funding for the study was provided by the Center for Orbital and Reentry Debris Studies at The Aerospace Corporation.

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References 1.

TSS-1R Mission Failure Investigation y90a&Report, NASA , Fmal Rev, May 3 1, .

2.

3.

4.

5.

x, =

J 0f’ R2-

x, =.

National Research Council, Orbital Debris-A Technical Assessment m Academy Press, Washington, DC, 1995.

P(a s chord 5 b) =

Vedder, J. D., and J. L. Tabor, “New Method for Estimating Low-Earth Orbit Collision Probabilities,” J. Spacecraft and Rockets, Vol. 28, No. 2, March-April 1991. Chobotov V. A., D. E. Herman, and C. G. Johnson, “Collision and Debris Hazard Assessment for a Low-Earth-Orbit Space Constellation,” J. Spacecmft and Rockets, Vol. 34, No. 2, March-April 1997.

=

R

Xl

Skf(a, RIda

= probabiity that chord

isbetweenaandbin length From above -;(x2

; x1) = f(a,R) =

Spiegel, M. R., Probab Appendix: Expected Value of a Chord

Consider a circle of a radius “R” with a chord length “a”

X2

probabiity differential distribution function for the chord

Thus,

f(a,R) = -+q

_a+da

where the derivative of X1 is zero since it is not a function of a. The expected or mean value of the chord is

E(a)= I; af(a,R)da whema=2Rcoscp From the diagram

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a2da

2Rd4R2 - a2 4R2 cos2cp. 2R siqdcp 2R$ii%&&

2Rcos2cpdtp = =-

& (1+c;29)diq o

nR

2

= $ (circumference)