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Роман Я. Кезерашвили City Tech The City University of New York Проверка общей теории относительности с использованием солнечных парусов Юбилейный семинар памяти Гурама Яковлевича Кезерашвили Институт ядерной физики, Новосибирск, 15 июня 2012

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Посвещается памяти моего брата Гурама Кезерашвили – прекрасного человека и замечательного физика

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Институт ядерной физики, Новосибирск, 15 июня What is a Solar Sail? Solar sail in Newtonian Approximation Orbits of a Solar Sail in General Relativity Non-Keplerian Orbits Lense-Thirring effect for Non-Keplerian Polar Orbits Poynting-Robertson Effect Conclusions Outline Kezerashvili, Vazquez-Poritz, Physics Letters B, 675, Kezerashvili, Vazquez-Poritz, Physics Letters B. 681, 2009 Kezerashvili, Vazquez-Poritz, Advances in Space Research, 46, 346, 2010 Kezerashvili, Vazquez-Poritz, Advances in Space Research, 48, 1778, (2011) Kezerashvili, Advances in Space Research, 48, 1683, (2011) Objective: Focus on Science To use a solar sail as a test of fundamental physics in the vicinity of the sun Fundamental Physics can be carried out as a passenger activity on space science missions performed by a solar sail propelled satellite.

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Yakov Perelman Yakov Perelman in 1915 in his book Interplanetary Journeys came to the idea to use the solar radiation pressure for the propulsion of a spacecraft. However, he concluded that light pressure is too small to overcome gravity but does not consider using sails to increase force. The father of Soviet astronautic Tsiolkovsky always thought highly of the talent and creative genius of Perelman and he wrote the preface for a new 1923 edition Perelman's Interplanetary Journeys. 4Институт ядерной физики, Новосибирск, 15 июня 2012

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Konstantin Tsiolkovsky Fridrickh Tsandler Fridrickh Tsandler in 1924 suggested and developed the theoretical concepts of solar sailing.Tsandler is also remembered as a pre-war pioneer of liquid rocket prolusion led early experiments with liquid prolusion in the Soviet Union. Tsiolkovsky worked on the idea of solar sailing in the 1920's and suggested using solar pressure to drive spacecraft. 5Институт ядерной физики, Новосибирск, 15 июня 2012

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Echo-1 Balloon Satellite demonstrated the effect of solar pressure on the trejectory Echo 1 Aluminum-coated Mylar plastic balloon was launched August 12, 1960 NASA launches Echo 1 first U.S. passive communications satellite first time NASA includes solar pressure in calculating trajectory. Solar pressure moves "sateloon" but doesn't collapse it. 6Институт ядерной физики, Новосибирск, 15 июня 2012

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Solar Sail When the solar electromagnetic radiation interacts with the solar sail material, it undergoes: i. Diffuse and specular reflection ii. Absorption iii. Absorption of solar radiation by a solar sail leads to a secondary process: the emission of the electromagnetic radiation by both sides of the solar sail. Институт ядерной физики, Новосибирск, 15 июня 2012 Incident radiation Solar Sail r Reflected radiation Acceleration due to reflection Acceleration Acceleration due to absorption 7

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Институт ядерной физики, Новосибирск, 15 июня The both forces act along the same line, fall off as 1/r 2, with the heliocentric distance. One of the most basic laws that describes motion in the solar system is Kepler’s third law, which can be derived from Newton’s law of gravitation Renormalized mass The sun emits electromagnetic radiation which produces an external force on objects via the solar radiation pressure. Therefore, we can say that objects move in the photo-gravitational field of the sun.

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Институт ядерной физики, Новосибирск, 15 июня

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10 Curved Spacetime A two-dimensional representation of a curved space. We imagine the space as being distorted as shown by the sun. Light from a distant star follows the distorted surface on its way to the earth. The dashed line shows the direction from which the light appears to be coming. light is bent by gravity General Theory of Relativity has passed experimental test The positions of the stars as seen during an eclipse. The open circles show their positions in the absence of the Sun. In 1919 Arthur Eddington experimentally found that the light from a distant star can be bent by the Sun, as predicted by General Relativity

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Институт ядерной физики, Новосибирск, 15 июня The exterior static curved spacetime of the sun is described by the Schwarzschild metric,

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Институт ядерной физики, Новосибирск, 15 июня GR: Static curved spacetime Condition for circular orbits leads for the period These expressions show that it is only the simultaneous effects of the static curvature of spacetime and the solar radiation pressure lead to a radial dependent deviation from Kepler’s third law. For our specification this yields an increase in the period of about 0.6 s. Equation of motion

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Институт ядерной физики, Новосибирск, 15 июня The external spacetime of a slowly rotating body with mass M and angular momentum J is described approximately by the large-distance limit of the Kerr metric

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Институт ядерной физики, Новосибирск, 15 июня General Relativistic Effects for Sun-bounded Orbits Equation of motion Deviation from the Kepler’s Law The first factor is the Kepler’s 3rd law in the Newtonian approximation for gravity. The second factor is due to the Solar Radiation Pressure and the static curvature of spacetime. The third factor results the combined effects of the Solar Radiation Pressure and frame dragging. GR effects and the solar radiation pressure lead to a radial dependent deviation from Kepler’s third law and increase in the period of about 0.6 s

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Институт ядерной физики, Новосибирск, 15 июня Heliocentric Polar orbits - Lense-Thirring effect The Lense-Thirring effect appears in the general relativity in the vicinity of rotating massive objects. Under the Lense-Thirring effect, light traveling in the direction of rotation of the object will move around the object faster than light moving against the rotation as seen by a observer from Earth. The orbital plane of a polar orbit which passes through the poles of the sun will precess, which is a well-known effect of frame dragging called the Lense-Thirring effect. The angle of precession for a polar orbit during one orbital period up to linear order in J: The angle of precession is increased by the Solar Radiation Pressure due to the renormalized mass The rate of precession is about 0.03 arcseconds per year

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Институт ядерной физики, Новосибирск, 15 июня The Oblate Sun We consider the effect of the mass multipoles moments of the sun on bound orbits. In particular, the dominant higher moment is the quadrupole, which is associated with the oblateness of the sun. Non Circular orbits There is the perihelion shift during one complete orbit

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Институт ядерной физики, Новосибирск, 15 июня Comparison of the Precessions Due to Spacetime Curvature and Oblate Sun These two precessions occur in opposite directions

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Институт ядерной физики, Новосибирск, 15 июня Net Electric Charge on Sun The basic components of the solar radiation that will interact with the solar sail are electromagnetic radiation with energy from a few eV to hundreds of MeV.swf.swf electrons and protons with energy from a few eV to hundreds of MeV.swf.swf The effect that a small amount of net charge Q on the sun would have on an SSP satellite with charge q can be described by using Reissner-Nordstrom metric For a solar sail with a charge q = 5 × 10 4 C an increase in period is about 230 s (0.05 s without the Solar Radiation Pressure). Thus, due to the Solar Radiation Pressure, even a small charge Q could certainly yield a measurable increase in the period, making this a potentially powerful test for net charge on the sun.

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Cosmological Constant

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Институт ядерной физики, Новосибирск, 15 июня Non-Keplerian Orbit The plane of a non-Keplerian orbit does not pass through the center of mass of the sun, and the solar sail is levitated above the sun. In the Newtonian approximation Solar Radiation Pressure leads to the renormalization of the mass We consider the effects of curved spacetime on non-Keplerian orbits. The period can be found to be Deviation from the Kepler’s Law The first factor is the same as for non-Keplerian orbits in the Newtonian approximation for gravity. The second factor is due to the simultaneous effects of the Solar Radiation Pressure and the static curvature of spacetime. The third factor results the combined effects of the Solar Radiation Pressure and frame dragging due to the rotation of the sun.

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Институт ядерной физики, Новосибирск, 15 июня Non-Keplerian Polar Orbits We are predicted an analog of the Lense-Thirring effect for non-Keplerian orbits. The frame dragging causes the plane of non-Keplerian orbits parallel to polar orbits to precess around the sun, The angle of precession can be approximated by We consider the effect of frame dragging on non Keplerian orbits which are parallel to polar orbits, and outside of the plane of the sun. The plane of non-Keplerian polar orbits undergoes the Lense-Thirring effect

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Институт ядерной физики, Новосибирск, 15 июня

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Институт ядерной физики, Новосибирск, 15 июня

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Институт ядерной физики, Новосибирск, 15 июня

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Институт ядерной физики, Новосибирск, 15 июня

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With solar-system exit velocity about 400 km/s the sailcraft reaches Sun’s Gravity Focus 550 AU, 6.5 Years Hellopause 200 AU, 2.5 Years Inner Oort Cloud 2500 AU, 30 Years M. Leipold, et.al.INTERSTELLAR HELIOPAUSE PROBE –DESIGN OF A CHALLENGING MISSION TO 200 AU, Proceedings ISSS 2010, pp , 2010.

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Poynting-Robertson Effect It is well known that the reflected, absorbed and emitted portions of the radiation can be used to propel the solar sail, due to the force of the electromagnetic pressure. What is less known is that the absorbed portion of the radiation induces a drag force on the solar sail due to the Poynting– Robertson effect, thereby diminishing its transversal speed relative to the sun. (R.Ya. Kezerashvili, J.F.Vazquez-Poritz, Adv. Space Research, 48, 1778–1784, (2011) Below is shown that a drag force decreases the cruising velocity as well as the heliocentric distance for escape trajectories and causes a solar sail to slowly spiral towards the sun for bound orbits. 31Институт ядерной физики, Новосибирск, 15 июня 2012

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32 Poynting-Robertson Effect Институт ядерной физики, Новосибирск, 15 июня 2012 In the rest frame of the solar sail, the solar radiation propagates at an angle with respect to the radial direction. Therefore, the absorbed portion of the radiation leads to a force with a component opposite the direction of motion. This is known as the Poynting–Robertson effect The rain is falling vertically and you start to walk. Although the rain is still falling vertically (relative to a stationary observer), you have to hold the umbrella slightly in front of you to keep off the rain. Because of your forward motion relative to the falling rain, the rain now appears to be falling not from directly above you, but from a point in the sky somewhat in front of you. Solar sail Drag Force Force due absorption v

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Escape Trajectories Институт ядерной физики, Новосибирск, 15 июня 2012 The Helios deep space probes would have traveled at the record speed of about 70 km/s at 0.3 AU. We extrapolate that to the following sampling of speeds We use these sets of initial conditions in order to demonstrate the Poynting- Robertson effect, though of course our orbital equations can be applied to any initial heliocentric distance and velocity. The Poynting-Robertson effect decreases the cruising velocity and the heliocentric distance 33

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Heliocentric Bound Orbits Институт ядерной физики, Новосибирск, 15 июня 2012 Table lists the percentage decrease in the heliocentric distance after one year for a solar sail directly facing the sun and in a bound orbit at various initial distances from the sun. For bound orbits, Poynting-Robertson effect decrease the heliocentric distance of the solar sail, thereby causing it to slowly spiral towards the sun. 34

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Non-Keplerian Orbits Институт ядерной физики, Новосибирск, 15 июня 2012 In the absence of the Poynting-Robertson effect, a non-Keplerian orbit would be maintained with a suitable pitch angle in the direction relative to the radial direction at the location of the solar sail A three-dimensional 10-day trajectory for a solar sail initially in a circular orbit outside of the plane of the sun at 0.05 AU, a polar angle of 65 0 an initial speed of 130 km/s and a pitch angle of We considered the Poynting-Robertson effect for a solar sail with a three-dimensional non-Keplerian orbit. 35

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Non-Keplerian Orbits Институт ядерной физики, Новосибирск, 15 июня 2012 An example, of the Poynting-Robertson effect on the radial coordinate r, coordinate and coordinate of a three-dimensional 100-day trajectory for a solar sail initially in a circular non-Keplerian orbit. A solar sail undergoes oscillatory motion in the polar direction 36

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Институт ядерной физики, Новосибирск, 15 июня Conclusions The solar radiation pressure generally augments the change in period of a Solar Sail due to various phenomena by a factor of about 1000 or more and make possible to test effects of General Relativity The SRP affects the period of the Solar Sail in two ways: by effectively decreasing the solar mass, thereby increasing the period, and by enhancing the effects of other phenomena by three orders of magnitude or more, rendering some of them detectable.

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Институт ядерной физики, Новосибирск, 15 июня Продемонстрирована эффективность исползования спутника с солнечным парусом для проверки эффектов общей теории относительности. Показано, что кривизна пространство-времени, сплюстнутость солнца и электрический заряд солнца с учетом электромагнитного давления изменяют третий закон Кеплера для гелиоцентических и не Кеплеровских орбит Для полярних орбит спутника с солнечним парусом увеличивается прецессия орбиты вследствии эффекта Lense-Thirring. Предсказан эффект Lense-Thirring для не Кеплеровских орбит, когда плоскость орбиты прецессирует вокруг солнца. Малые откланения спутника с солнечним парусом для гиперболических орбит приводит к большим откланениям в случае долгосрочних полетов. Эффект Poynting–Robertson уменьшает орбиталную скорость спутника с солнечним парусом, вызывая его движение к солнцу по спирали, а для гиперболических орбит уменшает скорость полета.

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