Роман Я. Кезерашвили City Tech The City University of New York Проверка...

Роман Я. КезерашвилиCity 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

Посвещается памяти моего брата

Гурама Кезерашвили – прекрасного человека и замечательного физика


3

• 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, 2009.Kezerashvili, Vazquez-Poritz, Physics Letters B. 681, 2009 Kezerashvili, Vazquez-Poritz, Advances in Space Research, 46, 346, 2010Kezerashvili, 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.

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

http://upload.wikimedia.org/wikipedia/commons/9/97/Yakov_Perelman.jpg

Konstantin TsiolkovskyFridrickh 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

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.


http://upload.wikimedia.org/wikipedia/commons/4/43/Echo-1.jpg

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.


Incident radiation

Solar Sail

r

Reflected radiation

Acceleration due to reflection

Acceleration

Acceleration due to absorption

7


8

The both forces act along the same line, fall off as 1/r2, 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

2

~

r

MmGFF SRPgrav

cG

LMM S

2

~

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.


9


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


11

The exterior static curved spacetime of the sun is described by the Schwarzschild metric,


12

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.

cG

LMM S

2

~

Equation of motion


13

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


14

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


15

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


16


17

The Oblate SunWe 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


18


19

Comparison of the Precessions Due to Spacetime Curvature and Oblate Sun

These two precessions occur in opposite directions


20

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

electrons and protons with energy from a few eV to hundreds of MeV .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 × 104 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.

Cosmological Constant


22

Non-Keplerian OrbitThe 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 tothe 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.


23


24

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


25


26


27


28

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 111-120, 2010.


30

Poynting-Robertson EffectIt 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 thata 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.


32

Poynting-Robertson Effect


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.

c

v 1sin

Solar sail

Drag Force

Force due absorption

v

http://upload.wikimedia.org/wikipedia/commons/5/5c/Poynting-Robertson_effect.png

Escape Trajectories


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

Heliocentric Bound Orbits


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

Non-Keplerian Orbits


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 650 an initial speed

of 130 km/s and a pitch angle of 280.

We considered the Poynting-Robertson effect for a solar sail with a three-dimensional non-Keplerian orbit.

35

Non-Keplerian Orbits


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


37

ConclusionsThe 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.


38

• 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.

Date post:	16-Dec-2015
Category:	Documents
Upload:	amira-wakeley
View:	218 times
Download:	0 times

Роман Я. Кезерашвили City Tech The City University of New York Проверка...

Documents