Ppt on My Thesis Work

8/13/2019 Ppt on My Thesis Work

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OUTLINE OF THE PRESENTATION:

General Transfer Orbit of SpacecraftFlyby Technique

Transfer Orbit for Jupiter Flyby to Reach Uranus

Flyby Mechanics

Planetary Grand TourFlyby Anomaly

Anomalous Data Analysis by John D. Anderson

Literature Review

Explanation of Flyby Anomaly Considering Velocity

Dependent Inertial Induction

Discussion and Conclusion

References


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General Transfer Orbit of Spacecraft:


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Flyby Technique:

Flyby is the technique of increasing or decreasing the

velocity of a spacecraft by passing it nearer to a

planet. As the spacecraft approaches a planet, it will

be slung around the planet and leave with a different

heliocentric velocity direction and magnitude.


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Transfer orbit for Jupiter Flyby to Reach

Uranus:


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Flyby Mechanics:


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Planetary Grand Tour:

A space craft Pioneer, was sent by the NASA scientists

in the year 1976 for a outer space tour to visit the

outer planets- Jupiter, Uranus, Neptune and Pluto. This

was done by using the flyby of Jupiter, Uranus andNeptune. Grand Tour had exploited the alignment of

Jupiter, Saturn, Uranus, Neptune, and Pluto, an event

that would occur in 1976, and not reoccur for 175 years


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Grand Tour Orbit:


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Flyby Anomaly:

Between 1990 and 2005 John D. Anderson, senior scientist

of Jet Propulsion Laboratory (NASA) noticed an anomalous

velocity change during the earth flyby in case six spacecrafts

Galileo 1, Galileo 2, NEAR, Cassini, Rosetta, MESSENGER.

Though this anomalous velocity is very small, the reason

behind this anomaly is still unknown to the scientists. This

unusual change of velocity is called Flyby Anomaly.


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Earth flyby parameters at closest approach for Galileo,

NEAR, Cassini, Rosetta and MESSENGER :Parameter GLL-I GLL-II NEAR Cassini Rosetta MGER

Date 12/8/90 12/8/92 1/23/98 8/18/99 3/4/05 8/2/05

H (km) 960 303 539 1175 1976 2347

(deg) 25.2 -33.8 33.0 -23.5 20.20 46.95

(deg) 296.5 354.4 47.2 231.4 246.8 107.5

(km/s) 13.740 14.080 12.739 19.026 10.517 10.389

(km/s) 8.949 8.877 6.851 16.010 3.863 4.065

DA (deg) 8.949 8.887 6.851 16.010 3.863 4.056

I(deg) 142.9 138.7 108.0 25.4 144.9 133.1

(deg) 266.76 219.35 261.17 334.31 346.12 292.61

(deg) -12.

52 -34.

26 -20.

76 -12.

92 -2.

81 31.44

(deg) 219.97 174.35 183.49 352.54 246.51 227.17

(deg) -34.15 -4.87 -71.96 -4.99 -34.29 -31.92

(kg) 2497 2497 730 4612 2895 1086

(mm/s)3.92 -4.6 13.46 -2 1.80 0.02


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Literature Review:So many researchers tried to explain this anomalous

velocity and the acceleration causing this anomaly by

taking different types of approach which are discussed

below.

An attempt has been made to explain this anomaly

in which it was thought that the interplanetary dust is

slowing down probes motion. It was found that

interplanetary dust has density less than 1024

gm/3. But the calculations show that only a density

3105larger than that of the interplanetary dust could

account for the anomalous acceleration, therefore this

attempt to explain the phenomenon failed.


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Another consideration to explain this phenomenon

was the drag of atmosphere. The drag is given by the

formula

= 2/

Where k is the probes drag coefficient, is the density of

the atmosphere, is the velocity of the spacecraft, is

the effective area and is the mass of the spacecraft.

The drag acceleration at a height of 1000 km is in theorder of 108/2, which is too small to explain the

anomaly.

h h h h h l h


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Researcher thought whether ocean or solid Earth

tides have impact on the change in velocity of the

spacecraft. The acceleration caused by tides turns out to

be at most 105 /s2, again small to provide an

explanation. The solid Earth tides are much smaller than

the ocean tides so they cannot account for the flyby

anomaly either.

The Earth albedo accounts for an effect of109m/s2,

the charging of the probe with electricity an effect of at

most 108m/s2 and the magnetic moment an effect ofonly 41015m/s2 all three of them are much too

small as compared to the unexplained acceleration.


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The effect from the solar wind is also negligible whichhas influence of less than3 1 09m/s2. John D. Anderson et al analyzed the above flyby dataand found an empirical relationship in 2008 in terms of

the respective declinations and of the incomingand outgoing osculating asymptotic velocity vectors.

The empirical relationship is given by-

= K (cos cos ).Where is the hyperbolic excess velocity, is theanomalous velocity. The proportionality coefficient K isexpressed as

K =2

= 3.099 X 10 6


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Explanation of flyby anomaly consideringVelocity Dependent Inertial Induction:


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Introduction:

The term Inertial Induction was coined by D.W. Sciama.

He noticed the similarity between Coulombs force law

for two charged particles and the inverse square law of

gravitation for two particles; he proposed an

acceleration dependent term in the law of gravity. If the

two charged particles with opposite charges 1and 2separated by a distance rpossess a relative accelerationa

Then the attractive force F between them is given by

F =122 + 122


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Where and c are the dielectric constant of the free space

and the speed of light respectively.

Sciama consider the gravitational interaction to be same.Thus two particles with gravitational masses 1 and 2

separated by a distance r will attract each other with a

force

F =12

2 +

12

2

Here a is the relative acceleration between the two

particles.


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In the above fig it is shown that Particle 2 has anacceleration a with respect to particle 1 and a makes an

angle with the line joining the two particles. So theequation becomes

F = 122 + 122 f ()

Inclination Effect in Inertial Induction


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Machs principle suggests interactive gravitational forces

depend on relative motion and motion means not only

acceleration but velocity also. An extension of Machs

principle is proposed by A. Ghosh to include an interactive

force which depends on the relative velocity of two

objects, over and above the static gravitational pool and

the acceleration dependent inertial induction effect. He

named this effect as velocity dependent inertial

induction. The simplest model of dynamic gravitationalinteraction between two bodies can be represented as

Velocity Dependent Inertial Induction:


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F= 2 22 2 () 2 ()Where,

() = cos() = . , ()= cos()= . Here the second term is due to velocity dependent

inertial induction.


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Let us consider the source of anomalous

acceleration of Earth flyby Spacecrafts is

the velocity dependent inertial drag onthe spacecraft due to the Earth. The

force on a spacecraft due to its relative

rotation with respect to the Earth can

be derived as shown below.

Explanation of Flyby Anomaly from Velocity

Dependent Inertial Induction:


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Force on the spacecraft due to velocity dependent inertial induction of Earth


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Now let us consider an elemental mass of Earth dm at a

distance r from the centre. The force on the spacecraft due

to velocity dependent inertial induction from dm can beexpressed as

d

=

.2

2

2

cos

cos

Where, cos = . and is the relative velocity of thespacecraft with respect to dm at point Q. So,

= Where, = Velocity of the spacecraft

= Velocity of the elemental mass dm


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From fig. above

=

= = and= r sin cos + r sin sin + r cos is the position of Q with respect to the centre of the

Earth O. Using the above relation we get

= X = X (r sin cos + r sin sin +r cos )= sin ( sin i + cos j)


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Position vector of the spacecraft

=

cos

+

sin

= X= x ( cos + sin )=

(

sin

+ cos

)

So,

=

= ( sin sin sin )+( sin cos + cos )


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Again from the fig. we get

=

= ( cos sin cos )+ sin sin sin cos

2=

2 +

2

2sin

cos(

)

Now,

cos

=

.

= ()sin sin


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Elemental mass of the Earth is given by

dm = ()2 sin = 222 2The unit vector in the direction of is= 2=

2+22 sin cos ()1

2 +

2+22 sin cos()1

2

cos 2+22 sin cos()12


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The component of is given as

= 2 sin 22 x22()2 2 2()22 x

cos

2

+2

2 sin cos()12

=

22 ()

2x

5 3 cos 2()2+22 sin cos ()52 0 0 20


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The density () of the Earth varies according to thefollowing relation

() = (18 10) 1 03 for 0 0.213.143 5.714 103 0.2 0.559.667 6.557 103 0.55 1 Where = Similarly we can determine X and Y components of theanomalous force then by dividing these forces by mass of

the spacecraft we can get the anomalous acceleration ofthe spacecraft due to velocity dependent inertial

induction.


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Determination of anomalous velocity due

to VDII from the calculated acceleration:

Here we considered the perturbing force causing the

anomaly is due to velocity dependent inertial induction and

the acceleration for this perturbation can be calculated

using the above theory. The equation of motion of aspacecraft considering this perturbation is given by

=

3+

Here is the calculated perturbed acceleration due to

VDII. Now anomalous velocity due to VDII is calculated by

numerically integrating the above equation for 1 hour using

MATLAB.

l


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Results :

Anomalous Flyby data analysis of various spacecraft using Velocity Dependent Inertial Induction

Name of the

Space-craft

Galileo I Galileo II NEAR Cassini Rosetta Messenger

(kg) 2497 2497 730 4612 2895 1086(rad/s) 7.27X105

(rad/s)1.872X103 2.107X103 1.84X103 2.5189X103 1.262X103 1.878X103

R(m) 7.33X106 6.681X106 6.97X106 7.553X106 8.334X106 8.752X106

(deg) 3.839 3.82 4.55 5.892 6.04 5.107

(m/)

=4.2892X1010 =3.5387X1010 =1.6871X1010A =5.81X

8.9381X10105.4650X10103.6805X1010

1.11X1.5965X10108.2318X10103.2186X10108.9817X

1.740X1095.3097X10104.1275X10101.8654X

2.80X10107.7202X10118.2075X10113.018X

2.0675X10105.3788X10101.4815X10105.9499X

(mm/s) 2.02x 3.98x 2.34x -4.3424x -7.7259x 6.8402x

(mm/s)

3.92 -4.6 13.46 -2 1.8 0.02


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= Angular velocity of the spacecraft at closest approach in

rad/s.

= Angular velocity of the Earth in rad/s.

= Mass of the spacecraft

R Distance of the earth centre from the spacecraft in m.

= Right ascension at closest approach in rad.

= Calculated anomalous acceleration using Velocity

Dependent Inertial Induction in m/s.

The anomalous accelerations due to velocity dependent

inertial are obtained by putting the values of , , R and

in the above expression and then integrating using MATLAB.


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Graphical Comparison:

0.0001

0.001

0.01

0.1

1

10

observed calculate

d

observed calculate

d

observed calculate

d

observed calculate

d

observed calculate

d

observed calculate

d

Galli 1 Galli 2 NEAR Cassini Rosetta Messenger

Series1 3.92 2.02E-03 4.6 3.98E-03 13.46 2.34E-03 2 4.34E-03 1.8 7.73E-04 0.02 6.84E-04

Anomalousvelocity


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In this thesis work we considered the velocity dependent

inertial induction as the perturbing force for explaining theanomaly. Using numerical integration of MATLAB, first we

determined the acceleration due to VDII for all the six

spacecraft at the time of flyby. Then the acceleration isagain numerically integrated for one hour to determine

the anomalous velocity. The calculated anomalous velocity

is coming in the order of 10

3 mm/s where as the

observed velocity is in the order of 10 mm/s. So VDII is not

responsible for this anomaly. Though we could not explain

the anomaly by considering VDII, it will be helpful for

further research.

Discussion and Conclusion:

R f


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References:[1] Ghosh A Originof inertia

[2] J. D. Anderson, J. K. Campbell, and M. M. Nieto, The energy transfer

process in planetary flybys,New Astronomy, vol. 12, no. 5, pp. 383397, 2007.[3] Curtis Howerd D.Orbital Mechanics for Engineering Students, Second

edition

[4] Schaub Hanspeter, Junkins John L. Analytical Mechanics of Aerospace

Systems.

[5] Dicau Florin OrbitalAnomalies

[6] Gilat Amos MATLABan Introduction with Applications

[7] Sciama D. W.On the Origin of Inertia, Monthly notices of the royal

Astronomical Society, v.113, 1953, p.34.

[8] John D. Anderson a, James K. Campbell, Michael Martin Nieto

The energy transfer process in planetary flybys Jet Propulsion Laboratory,

California Institute of Technology, Pasadena, CA 91109, USA[9] French A.P. NewtonianMechanics, The MIT Introductory Physics Series.

[10] Butrica J. Andrew TheGrand Tour of Big Science


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