FOCAL mission to 550 thru 1000 AU: Status review 2009

ARTICLE IN PRESS Acta Astronautica 67 (2010) 521–525

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Review

FOCAL mission to 550 thru 1000 AU: Status review 2009 Claudio Maccone  Co-Chair, SETI Permanent Study Group, International Academy of Astronautics, Via Martorelli 43, 10155 Torino (Turin), Italy

a r t i c l e in fo

abstract

Article history: Received 26 October 2009 Received in revised form 12 March 2010 Accepted 15 March 2010 Available online 8 May 2010

This paper presents a 2009 status review of the ‘‘FOCAL’’ space mission studied by this author and others since 1992 and formally proposed to ESA for consideration after the year 2000. The FOCAL probe is intended to reach distances between 550 and 1000 AU to exploit the huge radio magnification provided there by the gravitational lens of the Sun, as predicted by the general theory of relativity. However, the alignment between the radio source (any star, for instance), the center of the Sun and the FOCAL spacecraft is rather strict, and so it will be necessary to send a FOCAL probe in the opposite sky direction for any stellar system we wish to observe. For instance, before humanity ever embarked in a true interstellar mission even to the closest stars, the Alpha Centauri three stars system at 4.40 light-years from us, it plainly appears that before launching a really interstellar spacecraft it will be better to send a FOCAL probe in the opposite direction of the sky. In fact, the distance it must reach is 278 times smaller than 4.40 light-years, or, in other words, assuming equal engineering problems, FOCAL will take 278 times less than the trip to Alpha Centauri. This makes the Sun focus a reasonable target for our probes to reach within this century already. This paper describes the gravitational lens of the Sun and an updated status review of FOCAL including:(1) The new book by the author, published in March 2009 and entitled ‘‘Deep Space Flight and Communications’’.(2) The utilization of the relativistic  KLT (Karhunen–Loeve Transform) instead of the classical FFT to insure optimal telecommunications with the Earth during such a relativistic flight. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Sun gravitational lens Space probe Special relativity Propulsion Telecommunications

Contents 1. 2. 3. 4. 5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Why 550 AU is the minimal distance that ‘‘FOCAL’’ must reach The huge (antenna) gain of the gravitational lens of the sun . . Relativistic communications with ‘‘FOCAL’’ optimized by KLT . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional references. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

 Tel.: + 39 0112055387.

E-mail address: [email protected] 0094-5765/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2010.03.013

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C. Maccone / Acta Astronautica 67 (2010) 521–525

1. Introduction The gravitational focusing effect of the Sun is one of the most amazing discoveries produced by the general theory of relativity. The first paper in this field was published by Albert Einstein in 1936 (Ref. [1]), but his work was virtually forgotten until 1964, when Sydney Liebes of Stanford University (Ref. [2]) gave the mathematical theory of gravitational focusing by a galaxy located between the Earth and a very distant cosmological object (quasar). In 1978, the first ‘‘twin quasar’’ image, caused by the gravitational field of an intermediate galaxy, was spotted by the British astronomer Dennis Walsh and his colleagues. Subsequent discoveries of several more examples of gravitational lenses eliminated all doubts about the gravitational focusing predicted by general relativity. Von Eshleman of Stanford University then went on to apply the theory to the case of the Sun in 1979 (Ref. [3]). His paper for the first time suggested the possibility of sending a spacecraft to 550 AU from the Sun to exploit the enormous magnifications provided by the gravitational lens of the Sun, particularly at microwave frequencies, such as the hydrogen line at 1420 MHz (21 cm wavelength). This is the frequency that all SETI radio astronomers regard as ‘‘magic’’ for interstellar communications, and thus the tremendous potential of the gravitational lens of the Sun for getting in touch with alien civilizations became obvious. The first experimental SETI radio astronomer in history, Frank Drake (Project Ozma, 1960), presented a paper on the advantages of using the gravitational lens of the Sun for SETI at the Second International Bioastronomy Conference held in Hungary in 1987 (Ref. [4]), as did Nathan ‘‘Chip’’ Cohen of Boston University (Ref. [5]). Non-technical descriptions of the topic were also given by them in their popular books (Refs. [6,7], respectively). However, the possibility of planning and funding a space mission to 550 AU to exploit the gravitational lens of the Sun proved to be a difficult task. Space scientists and engineers first turned their attention to this goal at the June 18, 1992, Conference on Space Missions and Astrodynamics held in Turin, Italy, and run by this author. The relevant Proceedings were published in 1994 in the Journal of the British Interplanetary Society (Ref. [8]). Meanwhile, on May 20, 1993, this author submitted a formal Proposal to the European Space Agency (ESA) to fund the mission design of ‘‘FOCAL’’, as the mission to 550 AU was called (Ref. [9]). The optimal direction in space to launch FOCAL was also discussed by Jean Heidmann of Paris Meudon Observatory and the author (Ref. [10]), but it seemed evident that a demanding space mission like this one should not be devoted entirely to SETI. Things like the computation of the parallaxes of many distant stars in the Galaxy, the detection of gravitational waves by virtue of the very long baseline between the spacecraft and the Earth, plus a host of other experiments would complement the SETI utilization of this space mission to 550 AU and beyond. The mission had also been dubbed ‘‘AstroSail’’ and ‘‘SETIsail’’ in earlier papers (Refs. [10,11]). In the third edition of his book ‘‘The

Sun as a Gravitational Lens: Proposed Space Missions’’ (Ref. [12]), the author summarized all knowledge available as of 2002 about the FOCAL space mission to 550 AU and beyond to 1000 AU. On October 3rd, 1999, this book had already been awarded the Engineering Science Book Award by the International Academy of Astronautics (IAA). Finally, in March 2009, the new, 400-pages and comprehensive book by the author, entitled ‘‘Deep Space Flight and Communications - Exploiting the Sun as a Gravitational Lens’’ (Ref. [19]), was published. This book embodies all the previous material published about the FOCAL space mission and updates it. On November 25th, 2009, a presentation of this work was made at the SETI Institute in Mountain View, CA, USA: it is publicly available at the web site: http://www.youtube.com/ watch?v=ObvKVe5H8pc. 2. Why 550 AU is the minimal distance that ‘‘FOCAL’’ must reach The well-known Schwarzschild solution to the Einstein field equations is the mathematical foundation upon which the theory of the gravitational lens of the Sun rests. Then, a long string of formulae can be developed that are derived in standard textbooks. But the geometry of the Sun gravitational lens is easily described: incoming electromagnetic waves (arriving, for instance, from the center of the Galaxy) pass outside the Sun and pass within a certain distance r of its center. Then the basic result following from the Schwarzschild solution shows that the corresponding deflection angle a(r) at the distance r from the Sun center (see Fig. 1) is given by aðrÞ ¼ 4GMSun =c2 r. The light rays, i.e. electromagnetic waves, cannot pass through the Sun’s interior (whereas gravitational waves and neutrinos can), so the largest deflection angle a occurs for rays just grazing the Sun surface, i.e. for r =rSun. This yields the inequality a(rSun) 4 a(r), where a(rSun) is found upon replacing r = rSun into a(r). From Fig. 1, it is clear that the minimal focal distance dfocal is related to the tangent of the largest deflection angle by tanðaðrSun ÞÞ ¼ rSun =dfocal . Moreover since the angle a is very small (its actual value is about 1.75 arcsec), the above expression may be rewritten by replacing the tangent by the small angle itself: aðrSun Þ  ðrSun =dfocal Þ. Solving this for the minimal focal distance dfocal and then invoking the previous expression for a(rSun), one then gets at once dfocal 

rSun

aðrSun Þ

¼

2 c2 rSun rSun ¼ : 4GMSun 4GMSun =c2 rSun

This basic result may also be rewritten in terms the Schwarzschild radius of the Sun rSchwarzschild ¼ 2GMSun =c2 , yielding dfocal 

2 rSun rSun rSun ¼ ¼ : 2 aðrSun Þ 4GMSun =c rSun 2rSchwarzschild

Numerically, one finds dfocal = 542 AUE550 AU E3.171 light days. This is the fundamental formula yielding the minimal focal distance of the gravitational lens of the Sun, i.e. the minimal distance from the Sun’s center that the FOCAL spacecraft must reach in order to get magnified radio pictures of whatever lies on the other side of the Sun with

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523

(r) < (rSun) (rSun)

r(z) rSun Sun

z

dfocal = zmin FOCAL spacecraft

Fig. 1. Geometry of the Sun gravitational lens with the minimal focal length of 550 AU (= 3.17 light days= 13.75 times beyond the Pluto’s orbit) and the FOCAL spacecraft position beyond the minimal focal length.

respect to the spacecraft position. A simple, important consequence of the above discussion is that all points on the straight line beyond this minimal focal distance are foci too, because the light rays passing by the Sun further than the minimum distance have smaller deflection angles and thus come together at an even greater distance from the Sun. And the important astronautical consequence of this fact for the FOCAL mission is that it is not necessary to stop the spacecraft at 550 AU. It can go onto almost any distance beyond and focus as well or better. In fact, the further it goes beyond 550 AU, the less distorted are the radio waves that passed thru the plasma fluctuations in the solar Corona. We would like to add here one more result holding good not just for the Sun, but for all stars in general. This we will do without demonstration: it can be found on page 55 of Ref. [13]. Consider a spherical star with radius rstar and mass Mstar that will be called the ‘‘focusing star’’. Suppose, that a light source also (i.e. another star or an advanced extraterrestrial civilization) is located at the distance Dsource from it. Then ask: how far is the minimal focal distance dfocal on the opposite side of the source with respect to the focusing star center? The answer is: dfocal ¼

2 rstar : 2 =D 2 ð4GMstar =c Þðrstar source Þ

This equation is the key to gravitational focusing for any pair of stars, and may well be the key to SETI in finding extraterrestrial civilizations. It could also be used to find the magnification of a certain source by any star that is perfectly aligned with that source and the Earth: the latter would then be in the same situation as the FOCAL spacecraft except, of course, that it is located much further out than 550 AU with respect to the focusing, intermediate star. Finally, notice that the last equation reduces to the previous equation in the limit Dsource-N, i.e. for the special case of light rays approaching the focusing star from an infinite distance. 3. The huge (antenna) gain of the gravitational lens of the sun Having determined the minimal distance of 550 AU that the FOCAL spacecraft must reach, one now wonders how much focusing of light rays is caused by the

gravitational field of the Sun. The answer to such a question is provided by the technical notion of ‘‘antenna gain’’ stemming out of antenna theory. A standard formula relates the antenna gain, Gantenna, to the antenna effective area, Aeffective, and to the wavelength l or the frequency n by virtue of the equation (refer, for instance, to Ref. [14], in particular page 6–117, Eq. (6–241)) Gantenna ¼

4pAeffective

l2

:

Now, assume the antenna is circular with radius rantenna, and assume also 50% efficiency. Then, 2 =2. This yields the antenna Aeffective ¼ Aphysical =2 ¼ prantenna gain as a function of the antenna radius and of the observed frequency Gantenna ¼

2 2p2 rantenna 2

l

¼

2 2p2 rantenna n2 : c2

The important point here is that the antenna gain increases with the square of the frequency, thus favoring observations on frequencies as high as possible. Is anything similar happening for the Sun’s gravitational lens also? Yes is the answer, and the ‘‘gain’’ (one maintains this terminology for convenience) of the gravitational lens of the Sun can be proved to be GSun ¼

8p2 GMSun 1 8p2 GMSun ¼ n, l c2 c3

or, invoking the Schwarzschild radius, GSun ¼ 4p2 rSchwarzschild =l. The mathematical proof of this result is difficult to achieve. The author was dissatisfied by the description of this key mathematical topic given in Refs. [1,3] and so turned to three engineers of the engineering school in his home town, Renato Orta, Patrizia Savi and Riccardo Tascone. To his surprise, in a few weeks they provided the full proof described in Ref. [13], and based on the aperture method used to study the propagation of electromagnetic waves. Using the words of these three authors’ own Abstract, they have ‘‘computed the radiation pattern of the spacecraft Antenna +Sun system, which has an extremely high directivity. It has been observed that the focal region of the lens for an incoming plane wave is a half line parallel to the propagation direction starting at a point 550 AU, whose position is related to the blocking effect of the Sun disk (Fig. 1). Moreover a characteristic of

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Line

OH radical

Neutral Hydrogen

ν

H 2O

1420 MHz

327 MHz

1.6 GHz

5 GHz

22 GHz

Wavelength λ

21 cm

92 cm

18 cm

6 cm

1.35 cm

FOCAL antenna beam width

1.231 deg

5.348 deg

1.092 deg

0.350 deg

0.080 deg

Sun Gain

57.4 dB

51.0 dB

57.9 dB

62.9 dB

69.3 dB

12-meter Antenna FOCAL Gain Combined Sun+FOCAL Gain

42.0 dB

29.3 dB

43.1 dB

53.0 dB

65.8 dB

99.5 dB

80.3 dB

101.0 dB

115.9 dB

135.1 dB

Frequency

Fig. 2. The gain of the Sun’s lens alone, the gain of a 12-meter FOCAL spacecraft antenna and the combined gain of this Sun + FOCAL Antenna system at five selected frequencies used in radio astronomy.

this thin lens is that its gain, defined as the magnification factor of the antenna gain, is constant along this half line. In particular, for a wavelength of 21 cm, this lens gain reaches the value of 57.5 dB. Also a measure of the transversal extent of the focal region has been obtained. The performance of this radiation system has been determined by adopting a thin lens model which introduces a phase factor depending on the logarithm of the impact parameter of the incident rays. Then the antenna is considered to be in transmission mode and the radiated field is computed by asymptotic evaluation of the radiation integral in the Fresnel approximation’’. One is now able to compute the total gain of the Antenna +Sun system, that is simply obtained by multiplying equations, the two equations yielding the spacecraft gain proportional to n2 and the Sun gain proportional to n GTotal ¼ GSun Gantenna ¼

2 16p4 GMSun rantenna n3 : c5

Since the total gain increases with the cube of the observed frequency, it favors electromagnetic radiation in the microwave region of the spectrum. Table in Fig. 2 shows the numerical data provided by the last equation for five selected frequencies: the hydrogen line at 1420 MHz and the four frequencies that the Quasat radio astronomy satellite planned to observe, had it been built jointly by ESA and NASA as planned before 1988, but Quasat was abandoned by 1990 due to lack of funding. The definition of dB is: N dB ¼ 10 log10 N ¼ 10 ln N=ln 10. 4. Relativistic communications with ‘‘FOCAL’’ optimized by KLT

reference frame (that is different from the acceleration with respect to the static reference frame in special relativity). Sometimes, theoretical physicists also call the hyperbolic motion ‘‘Rindler spacetime’’. This means that the motion of the FOCAL probe to 550 AU, or 1000 AU, or beyond, must be studied within the context of special relativity, and not of classical Newtonian mechanics. Thus, in this regard also the FOCAL mission will be ‘‘innovative’’, since it will be the first relativistic space mission ever. Based upon these equations, the author and his doctoral pupil (now Dr.) Luca Derosa published a paper, Ref. [18], that may be also consulted for more technical details about the various relativistic propulsion tradeoffs available as of 2007. The subject of ‘‘relativistic telecommunications’’, i.e. telecommunications between the Earth and a spacecraft moving at a relativistic speed, has received little attention so far. In his 2009 book (Ref. [19]), however, the author studied this topic in depth with the goal of letting FOCAL become the first relativistic spacecraft ever. 5. Conclusion In these few pages, we could just sketch the FOCAL space mission to 550 AU and beyond to 1000 AU. A number of issues still have to be investigated in: (1) the science related to the mission, (2) in the propulsion tradeoffs to get there in the least possible time, and (3) in the optimization of the telecommunication link. Nevertheless, it plainly appears that the Sun focus at 550 AU is the next most important target that humankind must reach in order to be prepared for the successive and more difficult task of achieving the interstellar flight. 6. Additional references

Within the special theory of relativity there is a topic called ‘‘the theory of hyperbolic motion’’ that seems to be the only case for which the equations of motions of special relativity could be solved in a closed form. In simple words, this relativistic hyperbolic motion is the special-relativity extension of Newtonian ‘‘uniformly accelerated motion,’’ with the proviso that the acceleration must be constant with respect to the moving

Three more references are given to help the reader. Ref. [15] deals with the crucial problem of propulsion, prospecting the use of radioactive decaying materials for this purpose. Refs. [16] and [17] deal with the optimal telecommunications for a relativistic spacecraft solved by using the relativistic KLT. The latter is a principal axes transformation in the Hilbert space spanned by the

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eigenfunctions of the autocorrelation of the signal+noise. This topic may currently be regarded as "too advanced" by traditional engineers used to the traditional FFT. This author, however, believes that the KLT will finally displace the FFT when the KLT higher computational burden will become affordable by new and more advanced computer technologies. References [1] A. Einstein, Lens-like action of a star by the deviation of light in the gravitational field, Science 84 (1936) 506–507. [2] S. Liebes Jr., Gravitational lenses, Physical Review 133 (1964) B835–B844. [3] V. Eshleman, Gravitational lens of the sun: its potential for observations and communications over interstellar distances, Science 205 (1979) 1133–1135. [4] F. Drake, Stars as gravitational lenses, in: Proceedings of the ¨ Bioastronomy International Conference held in Balatonfured, Hungary, June 22–27, G. Marx editor, (1987) pp. 391–394. [5] N. Cohen, The Pro’s and Con’s of Gravitational Lenses in CETI, in: G. Marx (Ed.), Proceedings of the Bioastronomy International Conference ¨ held in Balatonfured, Hungary, June 22–27 (1987) p. 395. [6] F. Drake, D. Sobel, Is Anyone Out There?, Delacorte Press, New York, 1992 (in particular pp 230–234). [7] N. Cohen, Gravity’s Lens, Wiley Science Editions, New York, 1988. [8] C. Maccone, Space Missions Outside the Solar System to Exploit the Gravitational Lens of the Sun, in: C. Maccone (Ed.), Proceedings of the International Conference on Space Missions and Astrodynamics held in Turin, Italy, June 18, 1992, Journal of the British Interplanetary Society, 47 (1994), pp. 45–52. [9] C. Maccone, FOCAL, A New space Mission to 550 AU to Exploit the Gravitational Lens of the Sun, A Proposal for an M3 Space Mission submitted to the European Space Agency (ESA) on May 20, 1993, on

[10]

[11]

[12]

[13]

[14] [15]

[16] [17] [18] [19]

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behalf of an international Team of scientists and engineers. Later (October 1993) re-considered by ESA within the ‘‘Horizon 2000 Plus’’ space missions plan. J. Heidmann, C. Maccone, AstroSail and FOCAL: two extraSolar System missions to the Sun’s gravitational focuses, Acta Astronautica 35 (1994) 409–410. C. Maccone, The SETISAIL Project, in: Progress in the Search for Extraterrestrial Life, in: G. Seth Shostak (Ed.), Proceedings of the 1993 Bioastronomy Symposium held at the University of California at Santa Cruz, 16–20 August 1993, Astronomical Society of the Pacific Conference Series, 74 (1995) pp. 407–417. C. Maccone, The Sun as a Gravitational Lens: Proposed Space Missions, third edition, IPI Press, Colorado Springs (Colorado, USA), ISBN 1-880930-13-7, 2002. R. Orta, P. Savi and R. Tascone, Analysis of gravitational lens antennas, in: C. Maccone (Ed.), Proceedings of the International Conference on Space Missions and Astrodynamics held in Turin, Italy, June 18, 1992, Journal of the British Interplanetary Society, 47 (1994) pp. 53–56. John D. Kraus, Radio Astronomy, second ed., Cygnus-Quasar Books, Powell, Ohio, 1966 (pp. 6–115 thru 6–118). C. Maccone, Radioactive decay to propel relativistic interstellar probes along a rectilinear hyperbolic motion (Rindler spacetime), Acta Astronautica 57 (2005) 59–64. C. Maccone, Telecommunications, KLT and Relativity, vol. 1, IPI Press, Colorado Springs, CO, USA, ISBN 1-880930-04-8, 1994. C. Maccone, Relativistic Optimized Link by KLT, Journal of British Interplanetary Society 59 (2006) 94–98. L. Derosa, C. Maccone, Propulsion tradeoffs for a mission to Alpha Centauri, Acta Astronautica 60 (2007) 711–718. C. Maccone, ‘‘Deep Space Flight and Communications—Exploiting the Sun as a Gravitational Lens,’’ a 400-pages treatise about FOCAL that updates all previously published material. ISBN 978-3-54072942-6 Springer Berlin Heidelberg New York, 2009. Library of Congress Control Number: 2007939976. & Praxis Publishing Ltd., Chichester, UK, 2009.