# Will Hawking reach Alpha Centauri?

The Alpha Centauri system consists of a pair of stars A and B (the first is slightly larger, the second is slightly smaller than the Sun), separated by 24 AU (comparable to the distance from the Sun to Uranus), and the red dwarf Proxima, located 735 times farther. Proxima justifies its name “Nearest” - 4.22 light years to it, and the distance to A and B is close to 4.37 St. Over the past 5 years in this star system were found 3 planets similar in size to the Earth: $b$ and $c$ revolve around alpha centauri b, another $b$ belongs to Proxime www.openexoplanetcatalogue.com/planet/Alpha%20Centauri%20B%20c . Apparently, only Proxima $b$ more or less reliably detected, but due to the instability of red dwarfs, the occurrence of life on it is unlikely. The other two planets (if they actually exist) are too close to their star, having orbital periods of several days. However, these data are not reliable. In the future, they can change greatly, just as the first mass estimates of Pluto have decreased tenfold. In addition, exoplanets are primarily found very close to the stars - where they are easier to detect. Therefore, the fact that they are found too hot inspires confidence in the existence of other planets.

Quote from an article on the BBC website:
Russian businessman Yuri Milner and famous British scientist Stephen Hawking are launching a \$ 100 million Breakthrough Starshot project, the goal of which is to deliver mini-robots to the nearest Alpha Centauri star system in 20 years.

Tiny nanosatellites will need to reach speeds of up to 160 million km / h in order to reach Alpha Centauri in 20 years and send data to Earth.

Interstellar space flights have long been a dream of many, but the technical problems associated with such an expedition are extremely complex.

However, Professor Hawking said in an interview with the BBC that this dream could turn into reality faster than we think.

“If we want to survive as a species, we need to reach other stars,” he says.
“According to astronomers, there is a reasonable probability that a planet resembling Earth rotates around one of the stars in the constellation Alpha Centauri,” the scientist notes. “But we will learn more about this in the next two decades with the help of telescopes located on Earth and in space.”

“The technological progress made over the last two decades and in the future makes it possible for the next generation,” says Hawking. "

The company was selected spectacular - the names "Stephen Hawking" and "Freeman Dyson" are worth something! Back in the early '70s, Dyson theorized how to get to Alpha Centauri using thermonuclear explosions . In the next 15 to 20 years, they intend to send a swarm of micro probes to the star system closest to us, in order to get a picture of Alpha Centauri B planes in a quarter of a century (few of the project participants will live, alas).

The participation of the Russian billionaire Milner in this project gave grounds for enthusiasm in the spirit of “Russia will send a probe to Alpha Centauri”, although Russia, in fact, has nothing to do with it. This idea was born in the depths of DARPA (Pentagon Agency), working on phased laser arrays as weapon systems. Such an array is a set of fiber-optic amplifiers through which a divided laser beam passes. The control system of the phases of parallel rays allows you to focus the total beam, as well as control it for aiming. In addition to the obvious idea of ​​collecting several lasers into one “Gatling setup”, the key role here is played by controlled interference of amplified rays, which makes it possible to emulate even a converging (!) Beam of photons. In other words, the diffraction pattern on the surface orthogonal to the beam is such that the bright spot at its center has a small size compared to the size of the laser array, and its brightness is many times greater than the other light maxima. At the same time, a significant part of the energy emitted by the phased array accounts for this bright spot, the size of which may decrease with distance from the installation.

The corresponding military project DARPA bears the glorious name Excalibur (do not confuse it with Excalibur from the time of the IDF ). The Breakthrough starhot plan is organically linked to it, the details of which are set out in the article with the ambitious title “ Road Map to Interstellar Flight ”.

It is proposed to create a phased array of 100 million infrared lasers ( $\ lambda \ approx 1$ µm) located on a square section of the Earth with a side of 10 km - one laser each with a power of ~ 1 kW per 1 square meter. meter. The interference of these rays should generate an electromagnetic wave with a slightly concave front edge, shown in the figure above purple. It is assumed that the angle of convergence of the beam thus obtained will be ~ $10 ^ {- 9}$ glad, and the flow of power through its cross section is ~ 100 GW. The maximum width of this beam is ~ 10 m, i.e., the brightest diffraction maximum on the surface normal to the beam gradually decreases from ~ 10 m to ~ 1 m as the surface moves away from the array by ~ 10 million km.

It is assumed that a microprobe with a mass of 1 gram and a sail of 0.85 m of the same mass under the pressure of light in 3 minutes will reach a speed of 43,000 km / s, passing 4 million km. At this moment, the beam diameter will be equal to the sail size, and the probe acceleration will reach a maximum of 23,700g (!). In the future, the bright spot on the sail is reduced, but the acceleration remains unchanged and fantastically large. After another 76 seconds, the probe will pass about 4 million km, and the acceleration will stop (the beam will be turned off). At a cruising speed of 61,000 km / s, i.e., about 20% of the speed of light, the probe will fly to Alpha Centauri, which will last 20 years.

The probe is a substrate with chips, a battery, a video camera and a micro-laser for transmitting information to Earth. There are devices that (and if) can be made quite miniature (the total mass of the probe is 1 g without a sail). It is assumed that the sail or reflector can be used as a focusing antenna for laser pulses with a power of ~ 1 W. Although it is not even clear in principle how to implement this idea. If the reflector has the shape of a paraboloid of rotation, and the point source of light is in its focus, then a narrowly directed beam can be obtained. But its divergence will be much more order $10 ^ {- 5}$ glad (diffraction limit at $\ lambda = 1$ um and aperture ~ 1 m has order $10 ^ {- 6}$ ), which the authors of Breakthrough starhot were too optimistic on the basis of evaluations of the possibility of feedback.

The phased array can be used as a receiving antenna (the arriving photons will pass amplifiers in the opposite direction, generating an avalanche of quanta that will be detected). It is believed that the probe microlaser, using focusing with the help of a reflector, will provide the array irradiation with a flow of photons with a density of 650 pieces per second. According to the authors of the project, when encoding one bit of information with one quantum, this will allow transmitting data to the Earth at a speed of 650 bps.

Breakthrough starhot involves the launch of thousands of microprobes, which at the same time will increase the reliability of the project. However, it will not be possible to control the operation of thousands of probes due to the 4-year delay in receiving signals. Therefore, they will have to make decisions on their own, for which they need sensors and a sufficiently powerful microprocessor, and most importantly, engines for orienting and correcting trajectories as they approach Alpha Centauri. Probes need to interact with each other, so you need a reliable radio communication. Laser pulses are not suitable for searching for "partners", since for such a connection you need to know where to send the beam.

And they will have to look for each other, and at distances, perhaps millions of kilometers. Dispersion of probes on the way to Alpha Centauri will be huge, without any possibility to correct their trajectories from the Earth as they approach. It is important to keep in mind that they will not have any opportunity to slow down upon arrival, so they will have to make decisions and act very quickly (the flight time near an earth-like planet will be a fraction of a second). And for this you need energy and optics for navigation - on a probe weighing 1 gram!

In this regard, another fundamental problem arises: how does a probe with a mass of ~ 1 g find the sun without optics for astronavigation? It should be noted that due to the divergence of the beam from the probe, it will cover an area in the Solar System billions of kilometers, so you need to aim at the Sun. But how will the microprobe see it? No

Thus, the problem of collecting and transmitting information from microprobes to Earth is fantastically complex. It is unlikely that it can be overcome in principle, if you are not satisfied with the signals that the probes have flown near the destination. Although even such messages will be extremely difficult to get! If the angle of divergence of the beam from the probe is $2.2 \ cdot 10 ^ {- 5}$ happy, then with a power of 1 W, a phased array of 10 per 10 km will actually spill 650 photons arriving from Alpha Centauri in a second (the rest will pass by due to the divergence of the beam). But it does not take into account the dispersion on the way to the Earth and in the atmosphere, as well as the photon background from the Sun and surrounding objects. How to distinguish the infrared photon, arrived from the probe for 40 000 billion km, from any other with the same wavelength? The author of the Roadmap does not provide answers to these questions.

Another fundamental difficulty is related to the fact that during acceleration of the probe it is necessary to ensure the correct orientation of the reflector with respect to the beam. How to exclude the influence of fluctuations of the wave field and the surface defects of the sail, which appear under the action of irradiation with an energy density of ~ 100 GW per square meter? The slightest deviation of the sail or its deformation may lead the probe far away from the target or even throw it out of the beam. Therefore, it is necessary to control the position of the sail (reflector) in the acceleration process, when the acceleration reaches a whopping 20,000g or more. We need sufficiently powerful orientation engines that are able to overcome inertial forces, and they must have a total mass less than a gram. Since the acceleration distance is close to 10 million km, the delay of signals at the end of this path will reach 30 seconds in each direction. It is clear that timely correction of the orientation and shape of the sail is impossible, therefore, steady acceleration of the probe in the direction of the beam is an open problem.

Overall, the Breakthrough starhot plan is pretty well thought out. It builds on real progress in the development of phased laser arrays achieved at DARPA. This organization is certainly interested in the results that will be obtained in the course of efforts to resolve the fundamental difficulties associated with the implementation of this idea. However, contrary to the enthusiasm of Hawking and Dyson, it does not look feasible.

Obviously, one weak spot escaped the attention of enthusiasts. On closer examination, it turns into a huge tear, through which the Breakthrough starhot can fall into the abyss of unrealizable fantasies. This is due to the problem of reflection of radiation with a power of ~ 100 GW per ~ 1 sq. M. meter sail. A tenth of all US power plants will feed the laser array with energy for 5 to 10 minutes, which it will concentrate on a sail smaller than a meter in size! What will allow the reflector to not evaporate with such a monstrous heating?

At first glance, everything here is well thought out. The sail is supposed to be made of nanomaterials like graphene in the form of a film ~ 1 micron thick, having a reflection coefficient of 99.999%. The coefficient of 99.995% has already been achieved, success in this direction inspires faith in the fact that the desired reflection can be achieved. Acceleration above 20 000g such a film can withstand, and its micro-thickness is essential for this (the internal stress of the material with a density $\ rho$ and thick $h$ in the direction of acceleration $a$ equally $\ rho ha$ Pa). Suppose that the film reflects 99.999% of radiant energy. Then she gets ~ 1 MW of heat, which you need to get rid of. In space, this can only be done through radiation, which governs the Stefan-Boltzmann law:



Where $I$ - radiation intensity (W / m2) from the surface heated to temperature $T$ Kelvin $\ sigma = 5.67 \ cdot 10 ^ {- 8}$ - Stefan-Boltzmann constant (in SI). According to this formula, for the emission of excess heat with a capacity of 1 MW per 1 sq. Km. meter surface, it should have a temperature of 2 050 K.

Due to Kirchhoff radiation law, the following occurs:



Where $r (\ omega, T)$ - emissivity of the body (i.e., the spectral density of the heat flux), $\ alpha (\ omega, T)$ - its absorption capacity (the proportion of incident radiation with a frequency of $\ omega$ absorbed at temperature $T$ ) and $f (\ omega, T)$ - spectral density of blackbody radiation at a temperature $T$ . It follows that the mirror with absorbing $\ alpha (\ omega, T) = 10 ^ {- 5}$ (= 0.001%) will have emissivity in $10 ^ 5$ less time than an absolutely black body at the same temperature and frequency. Therefore, at a surface temperature of 2050 K (1 MW per 1 sq. M necessary for removal of excess heat), the mirror will emit in the spectrum of a laser beam in $10 ^ 5$ times less energy than a black body would emit at the same temperature in the same spectrum. Therefore, when $T = 2050K$ the mirror will radiate in $> 10 ^ 5$ times less energy than a black body in the whole spectrum.

Therefore, in order to ensure the removal of excess heat, it is necessary to raise the temperature of the mirror more than in $(10 ^ 5) ^ {1/4} = 17.78$ times

Thus, even if a mirror is capable of reflecting 99.999% of laser radiation of 100 GW per 1 square meter, then its surface temperature should be above 36,500 K. Note that the same result is obtained by the Stefan-Boltzmann law, if its left side is equal to the flow radiation to the film (100 GW per square meter). Obviously, no nanomaterial can withstand such a temperature for several minutes. In other words, a film reflecting 99.999% of radiation with moderate energy will melt and evaporate under a shower of photons of 100 GW.

The Breakthrough starhot project is another, desperate attempt to come up with something in a situation where the Universe does not want to let a person out of the solar system, only allowing itself to passively observe itself. Apparently, like all other projects to achieve the nearest stars, it will remain an unrealizable fantasy.

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