gravity-based static liquid orbital astronomical macro-optics

For Presentation Mon., Oct. 4, 2004, Afternoon, in Rm. 17, Session No. 13, Vancouver, B.C., Canada, at

Int’l Astronautical Federation 55th Congress; Paper No. IAC-04-J.1.08

GRAVITY-BASED STATIC LIQUID ORBITAL

ASTRONOMICAL MACRO-OPTICS By John H. Bloomer

Pres., DISCRAFT Corp.

1990 SE 157th Dr., Portland, OR 97233, USA; Ph. (503)251-6914 ; FAX (503)252-2383

August 27, 2004

ABSTRACT

Inexpensive large space astronomical-quality (telescope) optics, and an optical method for

collecting/handling/transporting energy of nearby stellar sources (in arbitrary quantity for arbitrary

wavelength range) continuously in space for terminals in space and on nearby associated planetary

surfaces, are desired. For energy-transfer, radially and transversely moving or stationary terminals within

practical cost/time-frame/engineering limitations, would be necessary. For diameter-size of the precision

(giant) optics required for both astronomy and electromagnetic energy-handling, there is no substitute.

However, the cost of “diffraction-limited” (or geometrically optically unimprovable for given wavelength-

and-diameter) optics even here on earth, goes up by the fourth power of the diameter. Most of the cost

is due to the expense of achieving by grinding and polishing a solid surface such that its normally-directed

overall deviations are less than the Rayleigh limit of /4 (or 5 × 10-6 inches for green light), and such that

its surface also is polished to exhibit an overall molecular-thick “Beilby” layer. But such a smooth “Beilby”

layer, one due to “surface tension”, is exhibited already by any non-reactive liquid surface in any

equilibrium gravity-field (e.g., such as water under 1G), and it is also a characteristic of any non-reactive

liquid in space zero-g occupying a precision cylindrical container, to exhibit a “perfectly” spherical

(precision) surface with radius-of-curvature determined by the contact angle and diameter of the

container. But a precisely (astronomically so) spherical surface (albeit on a liquid in space zero-g) is

geometrically very near a precise (astronomically so) paraboloid, for example. Too, the order-of-

magnitude of the force needed, at the precision needed, to turn such a spherical surface into such a

paraboloidal surface, can be shown to be lent by ordinary gravity of special but reasonably-sized,

bulkheads shaped & placed in space zero-g just for the limited purpose of statically (continuously)

“pulling” that spherical surface into that (“desired”) paraboloidal surface. Of course any desired

(geometrical) surface whatsoever can thereby as well be achieved simply by implementing the

appropriate gravitational normal potential function at every surface point, via a specific geometry of

bulkhead enclosing a “massive” liquid of a given specific gravity. Astronomical-quality orbital telescope

optics thus theoretically can be fashioned equally well for “passive” or “active” use, and as well one can

thereby form laser-end-mirrors. Of course the cost of such a technology promises to confer orders-of-

magnitude savings over large ordinary solid astronomical space optics fabricated by any conceivable

system of segmentation, alignment, actuators, holograms, spinning, grinding or polishing, on earth or in

space. The diameter-size of such boundary-constrained precision static liquid astronomical surfaces in

orbit, can apparently be indefinitely extended by use of this inventor’s “calibration islands” concept for

control of a surface-tension “membrane” in zero-g, comparable in effect to NASA’s “New Generation

Space Telescope” concept for control of a solid membrane. The NASA system would consist of a

membrane-backing matrix of tiny turnbuckle “actuators” capable (point-by-point) of pulling a solid

(membrane) spherical space mirror into a precision paraboloid, but implemented of course (NASA-wise)

electro-mechanically rather than physico-chemically, with therefore a certain consequent unit-cost

penalty. Too, inventor’s physico-chemically self-functioning “calibration islands” in liquid space optics,

should be needed in orders-of-magnitude less areal density (therefore at proportionally less expense)

than NASA’s (similarly-normally-driven) “actuators” in solid (membrane) space optics. Reflective (mirror)

liquid-metal described here is gallium, whereas refractive (corrector) clear-plastic liquid described is Dow-

Corning silicone No. 200. Development from Ta Li’s variational approach, of a fundamental

synthesis/analysis equation linking optical, gravitational & physico-chemical parameters, is given.

I. STATIC ADAPTIVE LIQUID SPACE MACRO-OPTICS: INTRODUCTION

In 1965, I published via American Astronautical Society1, a treatise showing one should be able to

fabricate for space zero-gravity operation, a diffraction-limited, static-liquid-surfaced, mirror-and-

corrector Maksutov (Fig. 1) catadioptric system, namely a 300-inch diameter orbital telescope (going the

Palomar 200-inch one better!) This instrument would rely on physical chemistry of liquids in zero-gravity

for precision optical sphericity, and on special masses emplaced in the spacecraft to literally and

permanently gravitationally deviate those spherical surfaces to “figure” them as required. The Maksutov

System at the given aperture requires very little figuring (retouching) indeed of its spherical-surfaced

mirror and spherical-surfaced refractive (lens) corrector. But literally any other optical system – especially

the various paraboloidal-primary ones – can as well be built to operate in space in this manner I showed.

[Cost – even on the ground – of major astronomical (SOLID) optics goes up by the fourth power of the

diameter; and, like football teams, “there is no substitute for size in major optics”!]

Later in ’65 I published a summary of the AAS conclusions in a paper for the SPIE 10th Symposium2.

I claimed in a subsequent publication, that we could as a result build and operate far larger inverted

(propulsion) laser-beaming astronomical optical systems, far less expensively, in space than on the

ground3. This was ’66 when – fired by invention of the laser (of ’63) – I showed that rapid-transit

interplanetary – and even interstellar – missions could be powered by sun-driven orbital lasers mated to

(inverted-telescope) optical systems incorporating my giant new lightweight high-precision, “beam-

tightening” lowcost mirrors. I even suggested as an afterthought, that such a propulsion system aimed at

earth, could serve as a “solar power satellite” (I didn’t call it that), one that would even oversupply all our

present energy needs globally (star-rocketry requires far more energy than that currently used for all

purposes on earth).

FIG. 1. Maksutov Catadioptric Wide-Angle System

But in those days I couldn’t seem to elicit any interest in any of this, so in ’69 I put it all aside to begin

designing aircraft.

Then in the ‘Nineties, I reviewed, revived and revised my astronomical, propulsion and power satellite

systems, as exhibited by various new publications referenced below4,5,6,7,8.

II. TO BEGIN WITH, WHAT IS (STATIC) LIQUID SPACE OPTICS?

Clean, chemically nonreactive, reflective static liquids (metals for example), inside clean, precision

cylindrical, circular cylindrical, straight, toroidal or spherical boundaries in zero-g, will attain minimum

potential energy (i.e., spherical) surfaces, which will exhibit at every point on the boundary the precise

characteristic contact angle for that liquid on that solid (irrespective of the amount of gravitational or

equivalent force acting). See Figures 2, 3, 4.

Sy’ S’ Sy’

d2 d1

y

fy f

y

n

R3

R2 R1

D

A B d1/D = 0.1

d2/D = 1.111.14

nD = 1.5163

= 64.1

R1/D = -0.6120.66

R2/D = - 0.6120.66 - 0.0565 - 0.007A

R3/D = - 2.1070.983

© 1966 BY J.H. BLOOMER DWG. BY J.H. BLOOMER ALL RIGHTS RESERVED

MAKSUTOV SYSTEM (AFTER D.D. MAKSUTOV, JOSA, MAY, 1944) FIGURE 1


EXPERIMENTAL CONFIGURATIONS OF LIQUIDS IN 1-G & ZERO-G FIGURE 2

(AFTER PETRASH & OTTO)

LIQUID CHARACTERIZED

BY:

0o CONTACT ANGLE 45o CONTACT ANGLE 90o CONTACT ANGLE 135o CONTACT ANGLE 180o CONTACT ANGLE

CYLINDRICAL TANK

(VAPOR)

(LIQUID)

(LIQUID)

(VAPOR)

ZERO-G

1-G

(AFTER PETRASH & OTTO)

= 45o

= 135o

= 90o

= 0o

= 180o

(VAPOR)

(LIQUID)


CONFIGURATIONS (EXPERIMENTAL) OF LIQUIDS IN ZERO-G. FIGURE 3

SPHERICAL TANKS PART-FILLED WITH LIQUIDS OF

VARIOUS CONTACT ANGLES

FIG. 2. Liquid Contact Angles @ 1g and 0g

FIG. 3. Liquid Contact Angles in Spherical Tanks

FIG. 4. Water Menisci in Tank @ Constant Contact Angles

Figure then of such a spherical “mirror,” will be purely and precisely spherical within the constraints

(controllable, as will be known) of the surface instantaneous axial section total circularity deviation,

where the latter is inherently due to a number of closely related influences as quantized by this author.

This quantization proceeded from analysis and application of results of a variational treatment by Ta Li of

liquid rocket fuel in zero-g and near-zero-g9.

Most useful applications of such a space-optical art, however of course will require parabolization of such

objects, introduced here by a totally new and revolutionary paradigm in space mechanics: It actually is

proposed here to figure these optics (with real-time control) by applying local gravity itself – of calibrated

liquid-metal masses and geometries – thereby achieving the tiny ultrahigh-precision axial modifications

required to change a (liquid) spherical large astronomical telescope mirror in space, into a paraboloidal

one (Fig’s 5, 6). In a sense, manufactured optics (in space) will then become infinitely “accommodating,”

much like the human eye.

FIG. 5. Error Due to Axial Effective Gravity (Begin)


MENISCI FOR WATER FOR VARIOUS LOAD FACTORS N (AFTER E. BENEDIKT). FIGURE 4

INFINITELY LONG TROUGH

N = 1

N = 0.5

N = 0.05

N = 0.0

N

(WATER)

N = VERTICAL LOAD IN G’S

= CONTACT ANGLE

C = CHARACTERISTIC = /lv R3 = RADIUS OF MIRROR F = FOCAL LENGTH D = APERTURE

= F/D N = LOAD IN g0’S

= (c,R3,N,D) = ERROR = 1 + 2

3

0

10

2

1 DCNg

FIG. 6. Practical Example of Gallium Paraboloid Due To Gravitational Deviation of Meniscus

1/8” Deviation (Gravitational) or “error”

(Difference Between Limb & Vertex “Elevation” By Fundamental Analytic/Synthetic (“Error”) Equation)

(NOT TO SCALE)

2.5 ft Gallium Mirror Mass

Solid Boundary Ring

88.2o Contact Angle (of Natural Gallium Spherical Surface with Boundary)

0.57o Paraboloidal Field-of-View

Focus of Paraboloid

Initial Spherical Surface (Radius = 3,695 ft, Imposed by Contact Angle) Before Gravitational Deviation

Final F/100 Paraboloid Surface After

Gravitational Deviation (Gallium, free liquid)

2500 ft paraboloid FOCAL LENGTH

PRODUCTION OF F/100 ORBITAL PARABOLOID “FIRST-CUT” BY GRAVITATIONAL-FORCE-FIGURING (“PANCAKE” SURFACE, SHAPE+POSITION SHOWN ARE ONLY SYMBOLIC). ZERO-G

FIG. Date: 1999


ERROR DUE TO A FINITE AXIAL LOAD Ng0. FIGURE 5

Ng0

½”

25-ft dia. paraboloidal

mirror

20,000-lb Mercury

Figuring Mass (“pancake”)

FIG. 5. Error Due to Axial Effective Gravity (Conclude)

III. SELF-FORMING (LIQUID) SPACE OPTICS

The self-forming, free liquid surface static orbital macro-optic paradigm introduced here, could ultimately

succeed in lowering cost – especially when commercial large-optics-fitted solar-power-satellites are

common – by whole orders of magnitude, even negating or reversing the sign of the cost (See Fig’s 7, 8).

To do so, however, intense R&D effort will evidently need to be directed along wholly new lines, i.e., in

physical chemistry, surface chemistry, space physics and mathematical physics of the gravitational

potential and of space liquid systems’ total energy.

FIG. 7. Adjustment & Operation of “Calibration Islands”

“HIGH” CASE I. MIRROR SURFACE “LEVEL”, “HIGH” AT CALIBRATION PT.

CASE II. MIRROR LIQUID SURFACE “LEVEL” “LOW” AT CALIBRATION PT.

ACTUAL LIQUID “LEVEL” SURFACE

DESIRED “LEVEL” SURFACE

NON-WETTING MENISCUS

NON-WETTING CONE: REPELS MENISCUS

LIQUID GALLIUM

CAPILLARY RESULTANT FORCE

“DOWN”

WETTING CONE: ATTRACTS MENISCUS

CALIBRATION POINT

“CALIBRATION ISLAND”

J. H. BURGE ET AL JOSA/SPIE VOL. 3356 3/98 PICOMOTOR ACTUATOR SETS CALIBRATION POINT

NON-WETTING CONE: REPELS MENISCUS

CALIBRATION POINT

WETTING CONE: ATTRACTS MENISCUS

LIQUID GALLIUM

CAPILLARY RESULTANT FORCE

“UP”

ACTUAL LIQUID “LEVEL”

DESIRED “LEVEL” SURFACE

WETTING MENISCUS

“CALIBRATION ISLAND”

CALIBRATION ISLANDS IN LIQUID SPACE OPTICS FIGURE. Date: Aug. ‘04

FIG. 8. Matrices of “picomotor actuators” recommended for NASA/AFRL & Bloomer “Membranes”, RESP.

8 M.

8 M.

ONE “PICOMOTOR ACTUATOR” (A LA BURGE ET AL) PER LECSO MIRROR 8-M.-DIA. AREA, TO FIX PHYSICO-CHEMICAL SELF-ADJUSTMENT POINT OR “CALIBRATION ISLAND LEVEL” FOR INSTANTANEOUS CORRECTION OF “HEIGHT” OF MIRROR LIQUID SURFACE (SURFACE TENSION) “MEMBRANE”

PRINCIPLE BY J. H. BURGE ET AL, SPIE J., 3/98: “NEXT GENERATION OF SPACE TELESCOPES” DESIGN AFTER “LIGHTWEIGHT MIRROR TECHNOLOGY USING A THIN FACESHEET WITH ACTIVE RIGID SUPPORT”

ADAPTED PRINCIPLE (GREATLY EXPANDED) BY J. H. BLOOMER, INVENTOR, YR. 2000: METHOD FOR INDEFINITELY EXPANDING DIAMETER OF “LIQUID EPIHYDROSTATIC CAPILLARY SPACE OPTICS” (LECSO)

AFRL/NASA 8-M.-DIA. MIRROR PICOMOTOR ACTUATOR (BACKSIDE) LAYOUT WITH 2500 ACTUATORS INDIVIDUALLY CONTROLLED (50 ACTUATORS PER M2): EVERY INTERSECTION AN ACTUATOR

BLOOMER 8-M.-DIA. LECSO DIFFRACTION-LTD. MIRROR (OR 8-M.-DIA. AREA IN LARGER OPTIC) FITTED W/ ONE ACTUATOR-CONTROLLED “CALIBRATION ISLAND”

COMPARISON OF NGST RIGID-MEMBRANE MIRROR W/ JHB LIQUID MEMBRANE ONE FIGURE 8. DATE: AUG 27 ‘04

IV. LIQUID SPACE OPTICAL SUPPORT STRUCTURES NOT CRITICAL

A free-surface shallow liquid-optic “pool” in zero-g in space, incidentally constrained as it is only by

capillary forces and self-gravitation, does not care what minor strains and misalignments are suffered by

its support structure – especially when support structure itself has been formed in channels by first

capillary action then solidification. High precision and high rigidity of this structure are not required (See

Fig’s 9, 10, 11, 12).

FIG. 9. Why Liquids Can’t “Leak” in Liquid Space Optics

FIG. 10. Non-Propagation of Liquid Space Optic Boundary Small Imperfections (Begin)


WHY LIQUIDS CANNOT “LEAK” OUT OF BOUNDARIES. FIGURE 9

ANY MOTION OF THE LIQUID MASS OUT OF THE ENVELOPE SHOWN BY THE SOLID-LINE MENISCUS REQUIRES A NON-UNIFORM CHANGE IN CONTACT ANGLE AROUND THE BOUNDARY AT CONSTANT TOTAL POTENTIAL ENERGY (HENCE CONSTANT TOTAL SURFACE AREA). THIS IS IMPOSSIBLE.

ACTUAL MENISCUS HYPOTHETICAL DEVIATION

cF

sF

FIG. 11. Non-Propagation of “Dimple” in Liquid Space Optic Boundary

AT P:

(1) Fs = INWARD NORMAL FORCE DUE TO SURFACE TENSION = 2M =

21

11

RR .

(2) Fc = OUTWARD (MOLECULAR, COHESIVE) NORMAL FORCE FROM PRESSURE OF LIQUID

INTERIOR =

21

11

RR .


SURFACE TENSION, BOUNDARY ERRORS, COHESIVE FORCE IN ZERO-GRAVITY. FIGURE 10

11

FIG. 10. Non-Propagation of Liquid Space Optic Boundary Small Imperfections (Conclude)

FIG. 12. Why Toroidal Channels Give Precision Circularity

V. GRADED LIQUID SPACE OPTICAL EXPERIMENTS PLANNED

A logical consequence of the identification of vast liquid-space-optics potential, is an initially purely

scientific research and development program, one which might proceed somewhat along the lines of the

experimental apparatus described in Fig’s 13, 14, 15, 16, 17, 18, 19, 20, concluding in the ultimate, the

“Liquid Optics Test Satellite” (or LOTS) shown in Fig’s 16, 17, 18, 19, 20.

VI. LI’S FOUNDATIONAL DIFFERENTIAL EQUATION

Total liquid orbital mirror axial-section circularity deviation is permitted convenient expression by the

“error” approximation derived from Li’s math model, which is a function of the net (paraxial) gravitational

attraction (or acceleration) as independent variable, itself a sum of the deliberately introduced gravity-

figuring force plus (shown sufficiently minizable) perturbations such as extraneous self-gravitation (of

spacecraft parts), gravity gradient (of earth, for example), attitude control torques, etc.10. This deviation

expression – based on our adoption of the first few terms of Li’s rapidly converging power series solution

12

to his variational differential equation (which expresses the accelerated optical system’s resulting total

paraxial deviation from spherical) – is found to be directly proportional severally to (paraxial) net effective

gravitational force (independent variable), to the difference (parameter) between the density of the

liquid metal and its vapor, and to the cube of the mirror diameter (a second parameter); while on the

other hand deviation is at the same time shown proportional inversely to the liquid-mirror surface

tension (third parameter) and to the mirror focal ratio or f-number, (fourth parameter).

This approximate equation for paraxial overall surface deviation from circularity (or sphericity) is derived

from Li’s formulation as follows:

FIG. 13. Initial 1G Tests of Liquid Space Optics

VII. OPTICAL INTERPRETATION OF LI’S DEVELOPMENT OF ZERO-G EPIHYDROSTATICS

Final development of the ultimate general mathematical tool of “zero-gravity epihydrostatical optics,” is

due to a treatment by Dr. Ta Li9. The following development by Li, illustrated in Fig. 21, is characterized by

liquids in containers whose interiors are in the form of surfaces of revolution.

“1” FORWARD

“0” REVERSE

1”

5”

S

L

P

L

M

O

T

F

D

E

R

F

H

K

B

A

A

Q

G

C

I

J

1 0

1 0

OPTICS ZERO-G SIMULATION VIA MATCHED LIQUID DENSITY

FIG. 14. Zero-g Drop Test From a Tower

1

4

FIG. 15. Zero-g Drop Test From Balloon

1

5

FIG. 16. Liquid Optics Test Satellite Erection in Orbit

lv, ls and sv are respective surface tensions at the liquid-vapor, liquid-solid, and solid-vapor interfaces,

in dyne/cm; in the plane of Fig. 21, the “horizontal boundary” is the intersection of the surface (liquid-

vapor interface) with the toroidal annulus shown. u = u(x) is the vapor-annulus interface, v = v(x) is the

liquid-annulus interface, and z = z(x) is the liquid-vapor interface, where u=u(x) and v=v(x) are known and

z=z(x) is sought.

The total potential energy K of the system consists of the sum of surface energies and the effective (net)

central-force-field or contact-force potential energy, where

111

0

220

0

2/12

0

2/12 112

xxx

lv xdxvzngxdxuxdxzK , (1)

while thermodynamic equilibrium implies:

1

02

x

xdxzuV

, (2)

where:

16

= ratio of vapor volume to container volume

V = Volume of container

g0 = Sea-level acceleration of gravity = 980.665 cm/sec2

= lv

lssv

= (liquid - vapor),

C = lvlv

vaporliquid

liquid = density of fluid

vapor = density of vapor above liquid

Above equations (1) and (2) define an isoperimetric problem in the calculus of variations with a mobile

upper limit. The total energy K is to be minimized and the resulting differential equation (the “solution”)

will itself be solved to provide a fundamental design formula, or expression. This expression will be critical

both in the analysis of systematic errors engendered by net residual acceleration (all sources combined),

and in the synthesis of diffraction-limited optical surface figures by designing masses (shapes, sizes and

positions) which will deviate the optical surfaces slightly by gravitational attraction.

Minimization of K can be facilitated by introduction of the “Bond Number” (dimensionless physico-

chemical constant characteristic of the system):

lv

RngB

20

0

, (3)

where:

n = load factor = sea level g’s of acceleration operating on system,

R = radius of curvature of liquid-vapor interface

Applying standard techniques of the variational calculus, Li found the differential equation

0

212

1 Bd

d

d

d

d

d

/

, (4)

where:

0

20

1

B

Rzz

R , (5)

and

2

2

R

x , (6)

FIG. 17. LOTS Final Erection In Orbit

1

7

FIG. 18. LOTS Interior Assembly Components

1

8

FIG. 19. LOTS Interior Assembly Pictorial FIG. 20. LOTS Rendering Showing Downlink Antenna

Z-AXIS

LIQUID IN CONTAINER OF REVOLUTION IN LOW GRAVITY FIELD FIGURE 21


FIG. 21. Model for Li’s Treatment of Zero-gravity Epihydrostatics

Li’s solution for ordinate (height) z(x) of the meniscus surface at a lateral distance x (ABSCISSA) from the

vertex, was the infinite series,

...

62

00

4

0

2

26

1

3

2012

3

1

24

2

1

22

R

xBB

R

xB

R

xz . (7)

This equation is the required solution to the characteristic (Euler) differential equation of the given

variational problem.

From Fig’s 21 and 5, we define:

0000 1010 BB zxzzxz

, (8)

where:

z0(x1) = ordinate of the (spherical) liquid surface at x=x1 when Bond No. B0=0 n=0 or “zero

gravity”; see Fig’s 21 and 5;

z0(0)=0= ordinate of the vertex (at x=0) of the (spherical) liquid surface when Bond No. B0=0 n=0

or “zero gravity”;

10xzB ordinate of the (non-spherical) liquid surface at x=x1 when B0 ≠ 0 n ≠ 0 (“non-zero-

gravity”);

00Bz ordinate of the (non-spherical) liquid surface at x=0 when B0 ≠ 0 n ≠ 0 or “non-zero-

gravity”.

We also define:

R0 = radius of curvature of unperturbed liquid surface,

x1 = radius of the meniscus “aperture”

= f/number = focal ratio = F/D,

F = focal length,

D = aperture,

g = ng0 ,

0BR = radius of curvature at the vertex of the (non-spherical) surface of revolution

obtained when n (and therefore B0) is finite.

Substituting various approximations in (8) and substituting for the Bond No., B0 from (3), reducing and

neglecting higher-order terms, we find

0

410

5

2

1

R

xng

lv

. (9)

If the liquid meniscus surface is considered an optical surface (reflector or refractor) we may redefine the

parameters of as follows:

R3 = R0 = radius of curvature of an optical mirror or lens,

F = R3/2 = focal length for paraxial rays striking an optic of curvature radius R3,

D = 2x1 = aperture of optical system,

= f/no. = focal ratio = F/D =

1

3

4

1

x

R.

Further substituting in (9) and reducing, we find, finally

3

0

10

2

1 DCng . (10)

We may define (10) as “the fundamental expression of liquid space optics,” equally useful for analysis and

synthesis.

From (10) note that, as you would expect, the error imposed by the net axial acceleration, is inversely

proportional to both liquid-vapor surface tension and f/no. , where telescopes with large f/no.’s already

have relatively flat primaries. Hence they are going to be, if liquid, less susceptible to net axial

acceleration, which is felt merely as a flattening influence anyway.

Note also from (10), the error will be directly proportional to net axial acceleration, ng0 , and not

surprisingly will be directly proportional to the third power of the liquid space optical system’s primary

diameter, nominally.

From Fig. 5, note that flattening at the circumference of liquid optic under a net downward acceleration,

is reflected by positive quantity 1101 0xzxz B , whereas concomitant flattening at the vertex of

the liquid optic under the same net downward acceleration, is reflected by positive quantity

00 02 0zzB .

VIII. DEVIATION EQUATION FOR LIQUID-SPACE-OPTIC ANALYSIS AND ROUGH SYNTHESIS (RECAP):

3

0

10

2

1 DCng ,

= total paraxial overall mirror (or lens) surface deviation from sphericity, measured as

the sum of flattening at both limb and vertex occasioned by a net gravitational

acceleration (see Fig. 5);

n = net paraxial load in g0’s;

g0 = 980.665 cm/sec2;

C = lv

vaporliquid

liquid = density of optical liquid;

vapor = density of optical liquid vapor above its liquid mass;

lv = surface tension of liquid (reflective or refractive);

D = optic diameter;

= f/no. (i.e., ratio of focal length to diameter of primary mirror).

IX. FIRST ROUGH CUT AT PARABOLIZING A NATURALLY SPHERICAL LIQUID SPACE (ZERO-G) OPTICAL SURFACE

When for example n at each point on the mirror surface is about 10-8 (earth gravities) on the zero-g liquid

gallium mirror illustrated in Fig. 6 (paraxially), and when in addition mirror diameter D is 25 ft as

illustrated (defined by the solid boundary ring shown), we pull the liquid spherical (minimum potential

energy) surface backward such as to create (roughly) a parabolic mirror with a focal ratio of = f/100 (the

contact angle on the precision cylindrical boundary is exactly 88.2o). This can be achieved by the mercury

“pancake” of 25 ft. diameter and ½-inch thickness as shown, at a distance of 2.5 ft behind the mirror

(although other elements, masses, and positions can be selected, and can be optimized to reduce weight

and eliminate toxicity).

Field-of-view of this telescope would be 0.57o, which is perhaps about maximum for standard

astronomical paraboloid reflectors, hence presumed probably equally practical for both ordinary imaging

and laser-beaming. Focal length is 2500 ft. Deviation to achieve this parabolization is (accomplished):

8

121 inch.

X. NECESSITY OF “CALIBRATION ISLANDS” TO INDEFINITELY ENLARGE DIAMETERS OF STATIC LIQUID SPACE OPTICAL PRIMARY MIRRORS

It is possible that the physico-chemical method shown in Fig. 7 may succeed in indefinitely extending

diameter of static liquid primaries, wherein we’ve taken a leaf from the NASA/AFRL “NGST” (Next

Generation Space Telescope) book11. AFRL/NASA evidently favor a matrix of individually controllable

“actuators” as shown in Fig. 8. to pull a solid membrane into diffraction-limited performance (primary-

mirror-wise). Quantity would be some 50 per square meter. In the static liquid “epihydrostatic capillary”

space optical method, however, capillary (surface tension) forces may actually drastically reduce the

necessity for such actuators, say from 2500 per 8-meter diameter mirror (as shown in Fig. 8) to only 1 per

8-meter-diameter mirror (also shown in Fig. 8). If indeed such devices can work (with appropriate physical

chemistry) to enlarge (diffraction-limited in visible light) operation of liquid space optics, then it appears

astronomy is in for an enormous boon: But it does appear such devices will be necessary to enlarge liquid

space optic diameters much above 25 ft, (if they’re to operate diffraction-ltd.), since LSO primaries rely on

their boundaries (and precision of same), to control their surfaces (and precision of same). But the ratio

of boundary units to area units of the surface, is

RR

R 222

.

Thus, for a given f/no., liquid, and net equivalent gravity, the “error” grows with 1st to 3rd pwr. of optic

diameter. Thus, some kind of “calibration islands” will be needed for very large (diffraction-limited) LSO

units, evidently.

XI. REFERENCES

1) Bloomer, J.H., “The 300-Inch Diffraction-Limited ‘Orbiting Eye’,” American Astronautical Society

(Space Electronics Symposium Vol. 6), Ed. By C.M. Wong, Los Angeles, CA. (USA), 1965.

2) Bloomer, J.H., “Liquid Space Optic Optics,” Society of Photo-optical Instrumentation Engineers,

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