Space Flight

8/6/2019 Space Flight

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SPACE FLIGHT

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CONTENTS

Space flight

Phases of space flight

Types of space flight

Spacecraft and launch systems

Challenges associated with space flight

Applications of space flight

Space vehicles

Lagranges equation

Orbit equation Space vehicle trajectories

Circular or orbit velocity

Escape velocity 2


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SPACE FLIGHT

Travelling into or through outer space with or

without humans on board.

Human

y Russian Soyuz program,y U.S. Space shuttle program

Unmanned

y

space probes which leave Earth's orbit,y satellites in orbit around Earth, such as

communication satellites.

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USES OF SPACE FLIGHT

Spaceflight is used in

space exploration

commercial activities like

y

space tourism andy satellite telecommunications.

Non-commercial uses of space flight include

y space observatories - is any instrument in outer spacewhich is used for observation of distant planets,

galaxies, and other outer space objectsy reconnaissance satellites - Earth observation satellite

or communications satellite deployed for military orintelligence applications. and

y other earth observation satellites. 4


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SPACE FLIGHT

Begins with a rocket launch - initial thrust to

overcome the force of gravity and propels the

spacecraft from the surface of the Earth.

Astrodynamics - Once in space, the motion of aspacecraftboth when un-propelled and when

under propulsion.

Some spacecraft remain in space indefinitely,

some disintegrate during atmospheric reentry,

and others reach a planetary or lunar surface

(the surface of the moon) for landing or impact.

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PHASES OF SPACEFLIGHT

Spaceports

Reaching space

y Launch pads, takeoff

y Other ways of reaching space Leaving orbit

Astrodynamics

Reentry

Landing

Recovery

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SPACEPORTS

Is a site for launching (orreceiving) spacecraft, byanalogy with seaport forships or airport for aircraft.

A spaceflight usually starts

from a spaceport. launch complexes and

launch pads - vertical rocketlaunches,

runways - takeoff andlanding of carrier airplanesand winged spacecraft.

Spaceports are situated wellaway from humanhabitation for noise andsafety reasons.

7

Soyuz TMA-3 is launched from

Gagarin's Start


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REACHING SPACE

Minimum delta-v.

This velocity is much lower

than escape velocity.

For manned launch systemslaunch escape systems are

frequently fitted to allow

astronauts to escape in the

case of catastrophic failures.

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Launch pads, takeoff

Fixed structure - dispatch airborne vehicles.

Launch tower and flame trench.

Equipments

y erect,

y fuel, and

y maintain launch vehicles.

Other ways of reaching space

Rocket assisted jet planes such as Reaction

Engines or the trickier scramjets.

Gun launch has been proposed for cargo.

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LEAVING ORBIT

Speed which spacecraft need to achieve to exceed

Earth escape velocity.

The escape velocity from a celestial body

decreases with altitude above that body. However, it is more fuel-efficient for a craft to

burn its fuel as close to the ground as possible.

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ASTRODYNAMICS

Astrodynamics is the study of spacecraft

trajectories, particularly as they relate to

gravitational and propulsion effects.

Astrodynamics allows for a spacecraft to arrive atits destination at the correct time without

excessive propellant use.

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REENTRY

Atmospheric entry is the movement of human-

made or natural objects as they enter the

atmosphere of a celestial body from outer space

in the case of Earth from an altitude above the

Krmn Line, (100 km).

Vehicles in orbit have large amounts of kinetic

energy.

This energy must be discarded if the vehicle is to

land safely without vaporizing in the atmosphere.

Typically this process requires special methods to

protect against aerodynamic heating.12


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RECOVERY

After a successfullanding thespacecraft, itsoccupants and cargo

can be recovered. In some cases,

recovery has occurredbefore landing:

while a spacecraft isstill descending on itsparachute, it can besnagged by a speciallydesigned aircraft.

Recovery of Discoverer 14 return

capsule

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TYPES OF SPACEFLIGHT

Human spaceflight

Sub-orbital spaceflight

Orbital spaceflight

Interplanetary spaceflight

Interstellar spaceflight

Intergalactic spaceflight

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HUMAN SPACEFLIGHT

Spaceflight with a human crew and possibly

passengers. The first human spaceflight was accomplished on

April 12, 1961 by Soviet cosmonaut Yuri Gagarin.

The only countries to have independent humanspaceflight capability are

y Russia,y United States and

y China.

As of today, human spaceflights are being activelylaunched by the

1. Soyuz programme conducted by the Russian FederalSpace Agency,

2. the Space Shuttle program conducted by NASA, and

3. the Shenzhou program conducted by the ChinaNational Space Administration.

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SUB-ORBITAL SPACEFLIGHT

Spaceflight in which the spacecraft reaches space, but

its trajectory intersects the atmosphere or surface ofthe gravitating body from which it was launched, sothat it does not complete one orbital revolution

For example, the path of an object launched fromEarth that reaches 100 km above sea level, and thenfalls back to Earth, is considered a sub-orbitalspaceflight.

Some sub-orbital flights have been undertaken to testspacecraft and launch vehicles later intended fororbital spaceflight.

Other vehicles are specifically designed only for sub-

orbital flight;

- examples - manned vehicles such as the X-15 andSpaceShipOne, and

- unmanned ones such as ICBMs and soundingrockets..

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ORBITAL SPACEFLIGHT

Spaceflight in which a spacecraft is placed on a

trajectory where it could remain in space for at

least one orbit.

To do this around the Earth, it must be on a freetrajectory which has an altitude at perigee

(altitude at closest approach) above

100 kilometers.

To remain in orbit at this altitude requires an

orbital speed of ~7.9 km/s.

Orbital speed is slower for higher orbits, but

attaining them requires higher delta-v.17


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INTERPLANETARY SPACEFLIGHT

Interplanetary spaceflight or interplanetary

travel is travel between planets within a single

planetary system.

In practice, spaceflights of this type are confinedto travel between the planets of the Solar

System.

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INTERSTELLAR SPACEFLIGHT

Interstellar space travel is manned or

unmanned travel between stars.

Interstellar travel is tremendously more difficult

than interplanetary travel. Intergalactic travel, the travel between different

galaxies, is even more difficult.

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INTERGALACTIC SPACEFLIGHT

Intergalactic travel involves spaceflight between

galaxies, and is considered much more

technologically demanding than even interstellar

travel and, by current engineering terms, is

considered science fiction.

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SPACECRAFT AND LAUNCH

SYSTEMS

Spacecraft propulsion

method used to accelerate spacecraft andartificial satellites

Chemical rockets - bipropellant or solid-fuel

Pegasus rocket and SpaceShipOne - air-breathingengines on their first stage.

Expendable launch systems

Uses an expendable launch vehicle (ELV) to

carry a payload into space. Designed to be used only once (i.e. they are

"expended" during a single flight), and theircomponents are not recovered for re-use afterlaunch.

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The vehicle typically consists of several rocket

stages, discarded one by one as the vehicle gains

altitude and speed.Reusable launch systems

Reusable launch vehicle, RLV - capable of

launching a launch vehicle into space more than

once. Orbital RLVs - low cost and highly reliable access

to space.

Reusability - weight penalties such as non-

ablative reentry shielding and possibly a stronger

structure to survive multiple uses, and given the

lack of experience with these vehicles, the actual

costs and reliability are yet to be seen.22


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CHALLENGES ASSOCIATED WITH

SPACEFLIGHT

Space disasters

Weightlessness

Radiation

Life support Space weather

Environmental considerations

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APPLICATIONS OF SPACEFLIGHT

Uses for spaceflight include:

Earth observation satellites such as Spy

satellites, weather satellites

Space exploration Space tourism is a small market at present

Communication satellites

Satellite navigation

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SPACE VEHICLES

Spacecraft - machine designed for spaceflight.

Launch vehicle - carry a payload from theEarth's surface into outer space.

Used

y communications,

y earth observation,

y Meteorology - scientific study of the atmosphere,

y navigation,

y

planetary exploration and transportation of humansand cargo.

1. Earth satellite launch vehicles

2. Lunar and interplanetary vehicles

3. Space shuttles25


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ISRO SATELLITE LAUNCH VEHICLES

SLV, ASLV, PSLV, GSLV, GSLV III.

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EARTH SATELLITE LAUNCH

VEHICLES

Velocities are of the

order of 7.9 km/s.

This velocity is

necessary to place avehicle in orbit about

the earth.

These orbits are

generally elliptical.

On October 4, 1957 Soviet Union

launched Sputnik I27


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LUNAR AND INTERPLANETARY

VEHICLES

These are launched with

enough velocity to

overcome the

gravitational attraction

of the earth and totravel into deep space.

Velocities of the order of

11.2 km/s or larger are

necessary for this

purpose.

Such trajectories are

parabolic or hyperbolic.28


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SPACE SHUTTLE


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The orbiter is a reusable winged "space-plane", amixture of rockets, spacecraft, and aircraft. Thisspace-plane can carry crews and payloads into Earthorbit, perform on-orbit operations, then re-enter the

atmosphere and land as a glider, returning her crewand any on-board payload to the Earth.

External Tank (ET) - contains the liquid hydrogenfuel and liquid oxygen oxidizer. During lift-off andascent it supplies the fuel and oxidizer underpressure to the three space shuttle main engines

(SSME) in the orbiter. Unlike the Solid RocketBoosters, external tanks have not been re-used. Theybreak up before impact in the Indian Ocean awayfrom known shipping lanes. The tanks are notrecovered.

Solid Rocket Boosters - pair of large solid

rockets.Together they provide about 83% of liftoffthrust for the Space Shuttle. The spent SRBs arerecovered from the ocean, refurbished, reloaded withpropellant, and reused for several missions.

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SPACE SHUTTLE

LAUNCHING LANDING

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LANGRANGES EQUATION

Lagrangian mechanics is a re-formulation

of classical mechanics that combines

conservation of momentum with conservation of

energy. It was introduced by the French

mathematician Joseph-Louis Lagrange in 1788.

Consider a single particle with mass m and

position vector r, moving under an applied force

F, which can be expressed as the gradient of a

scalar potential energy function V(r, t):

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F V!


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Such a force is independent of third- or higher-

order derivatives of , so Newton's second law

forms a set of 3 second-order ordinary differential

equations. Therefore, the motion of the particlecan be completely described by 6 independent

variables, or degrees of freedom.

An obvious set of variables is ,

the Cartesian components of r and their time

derivatives, at a given instant of time (i.e.

position (x,y,z) and velocity (vx,vy,vz)).

The position vector, r, is related to thegeneralized coordinates by some transformation

equation:

34

. .

j , j r r where j 1,2,3!

i j kr r( q ,q ,q ,t )!


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35

Consider an arbitrary displacement r of the particle.

The work done by the applied force F is

W F

. rH!

Using Newton's second law, we write:..

F. r m r . r H H!Since work is a physical scalar quantity, we should be

able to rewrite this equation in terms of thegeneralized coordinates and velocities. On the left hand

side,

iii

rF. r V. q

qH H

x!

x

ji

j ii, j

rVq

r qH

xx! x x

i

ii

Vq

q

Hx

!

x


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36

On the right hand side, carrying out a change of

coordinates to generalized coordinates, we obtain:

.. ..ii jji , j

rm r . r m r qq

H Hx!x

Rearranging slightly:

.. ..ii j

jj i

rm r . r m r qq

H H x! x

Now, by performing an "integration by parts"

transformation, with respect to t:

.. . .i i

i i jj jj i

r rd dm r . r m r r q

dt q dt qH H

x x ! x x


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Recognizing that. .

i ii i

. j j j j

r rd r rand

dt q q qq

x xx x! !

x x x x

We obtain.

.. . .ii

i i jj jj i

rd r

m r . r m r r qdt q qH H

x x

!

x x

Now, by changing the order of differentiation, we obtain:

. .. . . ii

i i jj jj i

rd rm r . r m r r q

dt q qH H

x x ! x x


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38

Finally, we change the order of summation:

2 2 .. . .

i i jj jj i i

d 1 1

m r . r m r m r qdt q 2 q 2H H

x x ! x x

Which is equivalent to:

..

i.ii

i

d T Tm r . r qdt q

q

H H

x x! x x

Where. .1

m r .r2

! is the kinetic energy of the particle.

Our equation for the work done becomes

i.

ii

i

T Vd Tq 0

dt qq

H

x x

! x x


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39

However, this must be true for any set of generalized

displacements qi, so we must have

. ii

T Vd T0

dt qq

x x

! x x

for each generalized coordinate qi. We can further

simplify this by noting that V is a function solely of r

and t, and r is a function of the generalized

coordinates and t. Therefore, V is independentof the generalized velocities:

.

i

d V0

dtq

x!

x

Inserting this into the preceding equation andsubstituting L = T V, called the Lagrangian, we

obtain Lagrange's equations:

.i

i

d L L0

dt q

q

x x

! x x


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LANGRANGES EQUATION

Dynamics of space vehicles

Newtons 2nd law

A body of mass m subject

to a net force F undergoesan acceleration a that hasthe same direction as theforce and a magnitude thatis directly proportional tothe force and inverselyproportional to the mass,

i.e., F = ma. Alternatively, the total

force applied on a body isequal to the timederivative of linearmomentum of the body.

F m a! v (1)

EQUATION OF MOTION USING NEWTONS2ND LAW

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2 ..

2

d xa x

dt| |

..

mg m x !

. .

x g!

The force is weight, directed downward.

F W mg! !

Acceleration

(2)

(3)

From Eqns. 1, 2 and 3

(4)Equation of Motion

EQUATION OF MOTION USINGLAGRANGES EQUATION

Kinetic energy of the body, T 2.21 1

T mV m x

2 2

! !

(5)41


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B T J|

2.

1B m x mgx 2

!

.

d B B0

dt xx

x x !

xx

.

.

Bm x

x

x !

x

Potential energy of the body,

W x mgxJ ! !

Lagrangian function, B Difference between kinetic energyand potential energy

(6)

(7)

Combining Eqns. 5 and 7

(8)

Lagranges Equation

Differentiation of Eqn. 8

(9)

(10)42


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Bmg

x

x!

x

.d

m x mg 0dt

!

.d

m x mg 0dt

!

..x g!

(11)

From Eqns. 9, 10 and 11,

m = constant.

..

m x mg 0 !

(12)

Equation of Motion

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. . .

1 2 3 1 2 3T T q , q , q , q , q , q

!

1 2 3q ,q ,qJ J!

B T J|

1 .1

1

2 .2

2

3 .3

3

d B Bq coordinate : 0

dt qq

d B Bq coordinate : 0dt q

q

d B Bq coordinate : 0

dt q

q

x x

! x x

x x

! x x

x x

! x x

Considering a body moving in 3D

Lagranges Equation

(13)

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ORBIT EQUATION

FORCE AND ENERGY

2

GMmF

r!

Newtons law of universal gravitation:

The gravitational force between two masses varies universely

as the square of the distance between their centers.

Universal gravitational

constant,

G = 6.67xe-11 m3/kg(s2)

Potential energy = 0 at r =

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2

GMmd Fdr dr

r

J ! !

r

2

0

GMmd dr

r

J

J

g

!

Potential Energy:

The potential energy at a distance r is defined as the work

done in moving the mass m from infinity to the location r.

Change in Potential Energy,

Potential energy, = 0 at r = and = at r = r

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GMm

rJ !

22 ..21 1T mV m r

2 2r U

! !

(14)

Kinetic energy in terms of polar coordinates,m = mass of vehicle.

V = velocity of the vehicle of mass m.

Velocity component parallel to r and

Velocity component perpendicular to r,.

r

.

drV r

dt

dV r rdt

UU U

! !

! !

(15)47


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EQUATION OF MOTION

22 ..1 GMmB T m r

2 rrJ U

| !

32 14

2

mk 3.986 10

s| !

Lagrangian function

Mass of the earth, M = 5.98 x e24 kg

22 2..1 mkB m r

2 rr U

!

Lagrangian function

(16)

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.

d B B0

dt UU

x x ! x

x .

2

.

B

mr UU

x

!x

B

0U

x!x

Using polar coordinates,

q1 = and q2 = r

First diff Eqn. 16 w.r.t, to

. .1 2

1 2

d B B d B B0, 0

dt q dt qq q

x x x x

! ! x x x x

.2d

mr 0dt

U

!" !

(17)49


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.2

1mr const cU ! !

.

2mr angular momentum constU ! !

.

d B B

0dt rr

x x

! xx

.

.

Bm r

r

x!

x

Eqn. 17 is the Equation of motion of space vehicle in

direction.

Integrating Eqn. 17

For angular motion, angular momentum =.

IU

Now diff Eqn. 16 w.r.t, to r

22 .

2

B mkmr

rr

Ux

! !x

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22. .

2

d mkm r mr 0

dt rU!" !

2 2 .. .

2

mkm r mr 0

rU !

.2

r h a gular mome tum per u it massU | ! 2.4 2..

3 2

r mkm r m 0

r r

U !

(18)

2 2..

3 2

h kr 0

r r !

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1r

u!

..

2

2

The , h r

u

UU| !

Eqn. 18 is the Equation of motion of space vehicle in r

direction.

Solution to differential Eqn. 18 is r = f(t).

To get equation of the path of the vehicle in space in terms of

geometrical coordinates r and Eqn. 18 must be reworked.

.

2

d 1 /dr 1 d Hence, r

dt dt dt | ! !

(19)

(20)

(21)52


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..

2 2

1 du d du dur h

d dt d d u u

U UU U U

! ! ! (22)

Now diff Eqn. 22 w.r.t, to t,

.. d du d du d r h h

dt d d d dt

UU U U

! !

2 2 ..

2 2

d u d d uh h

dtd d

UU

U U

! !

Substituting Eqn. 20 in 23,

(23)

From Eqn. 20, . 2u hU !

2..2 2

2

d ur h u

dU

! (24)53


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22 2 2 3 2 2

2

d uh u h u k u 0

dU !

Substituting Eqn. 19 and 24 in 18 yields,

Dividing by ,2 2h u

2 2

2 2

d u ku 0

d hU

!

2

2

k Acos( C )U!

(25)

Solution of Diff Eqn. 25 is

From Eqn. 19

1u

r

!

(26)

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2 2

1r

k h cos( )U!

2 2

2 2

h kr

1 h k cos( )U!

Substituting Eqn. 19 into 26 yields,

(27)

Multiplying and dividing Eqn. 27 by2 2

k

(28)

Eqn. 28 is called ORBIT EQUATION.

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SPACE VEHICLE TRAJECTORIES

pr

1 e cos( )U!

If e=0, the path is a circle.

If e1, the path is a hyperbola.

2 2 2 2

p k ,e A k ,C p ase angle! ! !

(29)

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b is point of burnout.

is arbitrarily chosen as zero at burnout

C is phase angle that orients the x and y axes with

respect to burnout point

x axis is line of symmetry for the conic section.

Circular a d Elliptical paths result i a orbit about

the large mass (the earth), whereas parabolic a d

hyperbolic paths result i escape from the earth57


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On physical basis, the eccentricity, hence the type of

path for the space vehicle, is governed by the

difference between the kinetic and potential energies

of the vehicle.

Proof:Kinetic Energy

22 ..21 1

T mV m r

2 2

r U ! !

Diff Eqn. 29 w.r.t to t,

? A.

. re sin( C )drr

dt 1 e cos( C )

U U

U

! !

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? A

2.

2.re sin( C )1T m r

2 1 e cos( C )

U UU

U

!

.2

r hU !2 2.

4

h

rU !

? A

2 2 2 2

2 22

1 h e sin ( C ) hT m

2 rr 1 e cos( C )

U

U

!" !

Sub Eqn. 29 into above Eqn.

We know that

(30)

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? A2

222

2

r 1 e cos( C )

k

U

!

Squaring Eqn. 29

? A2 2

2

2 2

k1 e cos( C )

rU !

? A2 2 2 2

2

2 2

1 k e si ( C ) k T m 1 e cos( C )

2 1

UU

!

22 2 2 2

2

1 kT m e si ( C ) 1 e cos ( C ) 2e cos( C )

2U U U !

Substituting above Eqn. into 30

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42

2

1 kT m 1 2e cos( C ) e

2 hU !

2GMm k m

r rJ ! !

? A

4

2

k m1 e cos( C )

hJ U!

Considering absolute value ofPotential Energy from

Eqn. 14

Sub Eqn. 29 into Eqn. 31

(31)

Let , H T J|

(32)

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42

2

1 k

HT

m 1 e2J

| !

2

4

2 He 1

mk

!

Subtracting Eqn. 32 from Eqn. 31

Solving for e

TYPE OF

TRAJECTORY

e ENERGY RELATION

ELLIPSE 1

21 mmV

2 r

21 GMmmV2 r

!

21 GMmmV2 r

"

(33)

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Conclusion:

A

vehicle intended to escape the earth and travel intodeep space (a parabolic or hyperbolic trajectory)

must be launched such that its kinetic energy at

burnout is equal to or greater than its potential

energy.

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CIRCULAR ORBIT VELOCITY

A circle has zero eccentricity, e = 0

2

4

2h0 1

mk

!

4

2

mk

2h!

21 GMmT mV2 r

J! !

42

2

1 mk GMmmV

2 r2h

!

We know that

(34)

(35)

(36) 64


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2

2

hr

k

!

From Eqn. 29

pr

1 e cos( C )U

!

Pu t e = 0

(37)

Substitute Eqn. 37 into 36 and solve for V2 2 2

21 m k k m k mmV

2 2 r r 2r ! !

2k

V circ lar velocityr

! (38)65


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143

6

3.986 10V 7 .9 10 m s

6.4 10

v! ! v

v

k2 = GM = 3.956e14 m3/s2

r = 6.4e6 m, radius of earth

Circular or Orbital velocity is = 7.9 km/s

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ESCAPE VELOCITY

A vehicle will escape if it has a parabolic (e=1) or a

hyperbolic (e>1) trajectory.

Considering a parabolic trajectory.

T J!2

21 m k mmV

2 r r

! !

Solve for V2

2kV parabolicvelocity

r! (39) 67


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Comparing Eqns. 38 and 39, the escape velocity is

larger than the orbital velocity by a factor of 2

k2 = GM = 3.956e14 m3/s2

r = 6.4e6 m, radius of earth

Escape velocity is = 11.2 km/s

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REFERRENCES

John D. Anderson, Jr. Introduction to flight. Ch 8

Space flight. Tata McGraw-Hill Publication.

http://en.wikipedia.org/wiki/Space_flight

http://www.grc.nasa.gov/WWW/k-12/airplane/topics.htm

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