nuffield report - gravity assist

7/25/2019 Nuffield Report - Gravity Assist

1/19

Gravity Assist andRelated Conceptswithin SpaceExploration

NUFFIELD REPR!

ALICE C"ENG


2/19

#

A$stract!his dissertations explores %ravity

assist& its i'plications and the

physical principles $ehind the or$italtechni()e that helped h)'anity to

explore the %reater depths o* space+ It

incl)des a related experi'ent

de'onstratin% conservation o*

'o'ent)' and trans*er o* ener%y

si'ilar to that d)rin% a %ravity assist

'ane)ver& and the analysis o* the

experi'ent will show the

i'prove'ents that will $e 'ade *or

the experi'ent in order to o$tain

$etter res)lts in the *)t)re


3/19

,

Ac-nowled%e'ents.any than-s to 'y 'entor& Conway

.otho$i *or assistin% )s with o)r pro/ect&thro)%h interestin% tal-s and sortin% o)t

re()ired apparat)s *or the experi'ents+Also than- yo) to Sa' .cCor'ac- *or

wor-in% on the pro/ect with 'e& andhelpin% 'e to explore new concepts that I

haven0t considered $e*ore+ Lastly& I0d li-e to

express 'y %ratit)de to Sarah Fenton andDavid 1ard *or attendin% o)r presentations&

and %ivin% )s the opport)nity to ta-e place

on the N)2eld Research Place'ent+


4/19

3e*ore the existence o* the 'anoe)vre techni()e 4%ravity assist0& lon%

interplanetary travel was dee'ed al'ost )nthin-a$le5 vast a'o)nts o* ener%y isre()ired to $e %enerated to provide heat *or the spacecra*t as the te'perat)re

decreases as the spacecra*t 'oves away *ro' the s)n& while 'ore ener%y is

re()ired to propel the spacecra*t& to co'')nicate with earth and 'ost

i'portantly& %ather the re()ired scienti6c data+

Nevertheless& to $e a$le to %enerate eno)%h ener%y to satis*y all o* the criteria

a$ove& the a'o)nt o* *)el carried wo)ld $e si%ni6cantly 'ore& which 'eant that

that the spacecra*t will need to $e si%ni6cantly lar%er in order to carry the *)el5this will cost si%ni6cantly 'ore co'pared to a 'ission which )tili7es %ravity

assist& and 'ore ener%y will $e re()ired at ta-e8o9 to achieve the sa'e velocity+!he *act that 'ost deep space spacecra*t re()ire pl)toni)' as *)el wo)ld ca)se

political tension with R)ssia& as R)ssia is c)rrently the only s)pplier o* pl)toni)'

,:;& and the s)pplies *or pl)toni)' ,:; is r)nnin% low+

3eca)se o* this& 'any 'issions )tili7e this techni()e to approach the destination

sooner with 'ore *)el le*t to collect and trans'it relevant data $ac- to earth toanalysis+ Exa'ples o* this incl)de


5/19

)se*)l *or sendin% a spacecra*t to planets and $odies with a s'aller %:5 an

exa'ple 'ission o* this incl)de the .essen%er 'ission to the planet .erc)ry&where the planet0s %ravity 6eld stren%th is at a ')ch wea-er :+>co'pared to

earth0s %& which is +;& th)s %ravity assist is re()ired to slow down the spacecra*t

eno)%h to *all $elow the escape velocity o* the spacecra*t and *all into or$it&

whilst 'a-in% s)re that eno)%h *)el is le*t *or the data collection within thehostile environ'ent& $ein% protected *ro' the intense heat and radiation *ro'the s)n at all ti'es& and 'eetin% the *)el re()ire'ent which 'a-e the 'ission

econo'ically via$le+

Nevertheless& to $e a$le to )tilise %ravity assist& a point o* re*erence ')st $e

chosen as all o$/ects are in 'otion relative to each other+ As a *ra'e o*re*erence& the o$/ect will appear stationary while other o$/ects appear to $e in

'otion+ For %ravity assist 'anoe)vres& in partic)lar& the re*erence *ra'e that0s

*re()ently )sed *or is the s)n+

Fro' the planet0s *ra'e& the planet is stationary& th)s a %ravity assist see's li-e

it violates the First Law o* !her'odyna'ics5 this law states that ener%y ')st $econserved& th)s the spacecra*t sho)ld in theory enter and exit the or$it with thesa'e 'o'ent)'& hence the sa'e velocity+ !his can $e shown $y

V=Vout

Where :

V=Velocity of the spacecraft coming intothe plane t's gravity well .

Vout=Velocity of the spacecraft comingout of the planet's gravity well.

Nevertheless& d)rin% %ravity assist& spacecra*t *ro' the planet0s *ra'e appear to

%ain or in so'e cases loose& as this will $e explained laterH *ree 'o'ent)' *ro'the Bstationary planet a*ter exitin% the or$it& where it %ains velocity a*ter exitin%

the %ravity well& as shown $y

VVout

Dependin% on the direction o* the spacecra*t0s approach towards the planet& th)s

it appears that a %ravity assist is violatin% the First Law o* !her'odyna'ics+

"owever& when a %ravity assist is viewed *ro' the s)n0s *ra'e& the planet is no

lon%er stationary *ro' this point o* view and is 'ovin% at a velocity aro)nd thes)n+ I* the spacecra*t need to %ain velocity& s)ch as in the new hori7on 'ission& it

will approach the planet *ro' the opposite direction to the planet0s tra/ectory inthe case o* New "ori7on& the planet that is providin% %ravity assist is =)piterH+ As

the spacecra*t is 'ovin% at a velocity& V and the planet is 'ovin% at a

velocity& U their velocities ')st s)$tract as $oth are 'ovin% in opposite

directions to each other Appendix BS)n0s Fra'eH+ !his 'eant that the velocity

:% is the %ravity 6eld stren%th+

>!o , si%ni6cant 6%)res as %ravity vary on di9erent parts o* the planet dependin% on altit)de and thes)$s)r*ace co'position+ At is @+: ti'es the %ravity o* earth+

>


6/19

o* the spacecra*t co'in% into the planet0s %ravity well& V is VU + As the

spacecra*t c)rves aro)nd the planet& its direction chan%es& th)s the spacecra*t isnow 'ovin% in the sa'e direction as the planet& and %ains velocity as their

velocities add to%ether& so that the velocity o* the spacecra*t is now V+U & and

the chan%e in velocity& V & is 2U +

Si'ilarly& this can also $e )tilised to slow down as spacecra*t li-e in the

'essen%er 'issions+ !o do this& the spacecra*t ')st approach the planet in the

sa'e direction to the planet0s direction o* 'otion& then $end away *ro' the

planet+ A%ain& the spacecra*t is 'ovin% at a velocity V & th)s V=V+U & and

as the spacecra*t c)rves away *ro' the planet& their velocities s)$tract& red)cin%

the velocity to VU & which 'eant that the chan%e in velocity& V is 2U

+ !his 'eant that the an%le o* approach stron%ly a9ects the o)tco'e o* the

%ravity assist& th)s the ti'in% o* the arrival and the direction o* approach o* thespacecra*t are extre'ely i'portant& as the an%le o* approach deter'ines the

6nal velocity o* the spacecra*t& as well as the an%le the spacecra*t leaves the

planet as an%le o* approach is e()al to the an%le o* depart)re relative to theplanet itsel*+ !he ti'in% is i'portant as the ti'in% o* arrival a9ects the an%le o*

approach o* the planet& th)s a9ectin% the 6nal velocity as well as the an%le o*depart)re+

!his proposes a li'itation with %ravity assist5 since the ti'e o* arrival is

extre'ely i'portant to the re()ired chan%e in velocity o* the spacecra*t& a

la)nch window?have to $e set and the spacecra*t have to la)nch within a strict

period o* ti'e+ !he *act that planets all or$it the s)n at di9erent velocities 'eantthat to %ain a sin%le %ravity assist )sin% New "ori7ons .ission as an exa'pleH&the planet =)piter have to $e in position to provide the correct an%le o* depart)re

*or the New "ori7ons Spacecra*t to Arrive to Pl)to+ !he ali%n'ent o* =)piter and

Pl)to re()ired *or a =ovian %ravity assist occ)rs every #,+? years& this 'eant thatthe New "ori7ons 'ission had to $e la)nched $etween ,@@> and ,@@ or the

la)nch window will $e 'issed& and the next 'ission will have to $e la)nched in

,@,; to ,@,+ 1ithin this period& la)nch opport)nities will $e availa$le a*terevery #: 'onths d)e to Earth0s or$it aro)nd the s)n& which ta-es #, 'onths+

Conse()ently& the la)nch periods *or New "ori7ons 'ission are .id8Dece'$er,@@>& .id8=an)ary to Early Fe$r)ary ,@@J and late Fe$r)ary ,@@ were availa$le

*or a y$y 'ission to Pl)toJ

Gravity assist and New Horizons

D)rin% the New "ori7ons 'ission& the opti')' year *or the 'ission was ,@@>& as

Earth& =)piter and Pl)to 'ove o)t o* phase with each other+ Nevertheless New"ori7ons was la)nched in =an)ary ,@@J d)e to ins)2cient *)ndin%& th)s the

?A ti'e *ra'e set *or the la)nch o* a space 'ission

J!he reason *or a y$y 'ission is d)e to the a'o)nt o* *)el re()ired *or an or$iter 'ission is too lar%e asPl)to0s %ravity is too wea- to capt)re the spacecra*t at the velocity it0s travellin%& th)s lar%e a'o)nt o* *)el isre()ired to decelerate the spacecra*t which can $e extre'ely costly+ Alternatively& i* the spacecra*t travels at alower velocity& it will not reach Pl)to within the ti'e re()ired th)s the 'ission is not *easi$le& as the *)el *ro'the radioactive decay will r)n o)t d)rin% that ti'e& and no si%ni6cant data can $e received *ro' s)ch 'ission+

?


7/19

velocity %ained *ro' a =ovian %ravity is lower than opti')' and a 'ore power*)l

la)nch vehicle had to $e o$tained in order to send the spacecra*t to =)piter onti'e& as =)piter is *)rther away *ro' the opti')' position+

D)e to this& alternate 'ission desi%ns were analysed d)rin% 'issions s)ch as

New "ori7ons in case o* events which can lead to 'issin% the la)nch window+

!hese can o*ten incl)de alternate %ravity assists *ro'


8/19

s()are law& whereas the distance increases& the *orces decrease exponentially+ !o

stop New "ori7ons over the ti'e period o* approach to Pl)to& Newton0s secondlaw o* 'otion can $e )tilised

F=(mv)

t

Where

F=Force

m=$ass

t=%ime

=%heChangea Value

Since the 'ass o* New "ori7ons stay constant& and that

v

t=3830m /s

& the

*orce re()ired to stop the spacecra*t is approxi'ately 1.91106

N& which

exceeds the *orce exerted $y $oth the S)n0s and Pl)to0s co'$ined $y an order o*

'a%nit)de o* J+ !h)s& slowin% down the spacecra*t re()ires lots o* ener%y whichcan $e extre'ely expensive and re()ires lots o* propellants+

As the e()ation has shown& the 'ass o* Pl)to a9ects the *orce it exerts on thespacecra*t& there*ore& as the 'ass o* Pl)to is s'all relative to the other celestial

$odies within o)r solar syste'& the *orce exerted $y Pl)to is& there*ore s'all&

even i* the distance& r & $etween Pl)to and the spacecra*t is red)ced& th)s an

or$iter 'ission will $e di2c)lt to desi%n *or a 'ission to Pl)to+

Another way o* de'onstratin% the di2c)lty or an or$iter 'ission to Pl)to is $y

co'parin% the velocities o* the spacecra*t with the escape velocity o* Pl)to5 theescape velocity *or Pl)to is #+,# -'s8#co'pared to Earth0s ##+# -s8#H& and the

approachin% velocity o* New "ori7ons spacecra*t is #>+? -'s 8#& the di9erences in

the val)e itsel* show that Pl)to is not a$le to capt)re the spacecra*t as theescape velocity o* the New "ori7ons spacecra*t is already %reater than the

Earth0s escape velocity+ !he *act that earth has a %ravitational 6eld stren%th o*

+;NK-% co'pared to Pl)to0s @+JJNK-% nearly #? ti'es s'aller than Earth0s%ravitational 6eld stren%thH 'eant that it will $e di2c)lt to slow the spacecra*t to

Pl)to0s escape velocity d)rin% the approach *or Pl)to+

Conservation of Energy and Momentum

D)rin% a %ravity assist& the overall ener%y is conserved as the planet loses the

sa'e a'o)nt o* ener%y as the spacecra*t %ains in a heliocentric re*erence *ra'e+!his is d)e to the conservation 'o'ent)'& shown $y the e()ation

m1u1+m2u2=m1 v1+m2 u2


9/19

Where :

m1=mass of the planet

m2=mass of the spacecraft

u1=initial velocity of the planet

u2=initial velocity of the spacecraft

v1=final velocity of the planet

v2=final velocity of the spacecraft

Since the planet have a %reater 'ass& the chan%e in velocity& v is

insi%ni6cant co'pared to the spacecra*t& which have a ')ch s'aller 'ass+ !h)s&

*or the sa'e 'o'ent)'& the planet hardly loses velocity& while the spacecra*t%ains a si%ni6cant a'o)nt o* velocity+ In the case o* the New "ori7ons 'ission&

the planet =)piter loses 1025

!ho* its ori%inal velocity& which is a ne%li%i$le

a'o)nt *or =)piter as it0s travellin% at a 'ean or$ital velocityo* #:+@J'Ks& th)s

the velocity lost is

1.3061021

m/ s + !he sa'e principle applies to reverse %ravity assist *or

slowin% down a spacecra*t+ As the spacecra*t slow down& the planet %ains a s'all

a'o)nt o* velocity th)s ener%y is conserved+

!his is si'ilar to a stac-ed $all drop experi'ent where a *ew $alls are dropped*ro' a hei%ht to the %ro)nd& in ascendin% order heaviest at the $otto'H& while

the hei%ht and the velocity o* the $alls are 'eas)red+ Nor'ally& as a $all drops

*ro' a hei%ht& its potential ener%y *ro' the wor- done to li*t the $all to a %reaterhei%htH is converted into -inetic ener%y+ Nevertheless& as the $all loses ener%y

d)rin% the drop& it does not have the sa'e a'o)nt o* ener%y it had initially& th)sit will $o)nce to a hei%ht lower than its initial hei%ht where the $alls are ori%inally

dropped+ "owever& d)rin% a stac-ed $all drop experi'ent& the s'allest $all tends

to have the s'allest 'ass& th)s it %ains velocity *ro' the lar%er $alls& whichhave a lar%er 'ass+ !he -inetic ener%y o* the lar%er $all is trans*erred into the

s'aller $all& ca)sin% the s'aller $all $o)nces to a %reater hei%ht than its initialhei%ht where it was dropped at+

Our Ball Drop Experiment

!o prove and de'onstrate the conservation o* ener%y in relation to %ravity assist&

'y tea' 'e'$er and I have planned carried o)t and analysed data *ro' o)r

$all drop experi'ent+ )r hypothesis predicts that when the s'aller $all is

!he val)e is a 'ean d)e to epler0s First Law& where the planets or$itin% a star ')st always $e an ellipse+!his 'eant that the velocity varies at di9erent sections o* the ellipse& slowin% down at the periapsis theshortest distance *ro' the centreH and speedin% )p at the apoapsis the lon%est distance *ro' the centreH& th)sa 'ean velocity has deter'ined+

;


10/19

stac-ed on top o* the lar%er one and dropped si')ltaneo)sly& the s'aller $all will

$o)nce hi%her than the initial hei%ht it was released d)e to the conservation o*ener%y and 'o'ent)'+

.aterials re()ired

8 Stepladder8 3as-et$all8 !ennis 3all8 Pin%8Pon% $all8 S()ash $all8 R)$$er $and $all8 3l)8tac-8 Ca'era capa$le o* recordin% at a hi%h resol)tionH8 !ripod8 .eas)rin% tape8 .ar-er8 Stic-y notes8 Co'p)ter with access to the internetH8


11/19

>H Stac-in% the tennis $all on top o* the 8rin%& and stac- $oth on top o* the

$as-et$all+ Pass the stac-ed $alls to the person on top o* the stepladder+Usin% the ca'era& record the drop+

?H Repeat the previo)s step with the *ollowin% co'$inations

8 3as-et$all& 8rin% and R)$$er $and8 3as-et$all& 8rin%& tennis $all& second 8rin%& s()ash $all8 3as-et$all& 8rin%& tennis $all& second 8rin%& Pin%8Pon% $all8 3as-et$all& 8rin%& r)$$er $and $all& second 8rin%& s()ash $all8 3as-et$all& 8rin%& r)$$er $and $all& second 8rin%& Pin%8Pon% $all8 tennis $all& 8rin%& s()ash $all8 tennis $all& 8rin%& Pin%8Pon% $all

JH A*ter this& )sin% a video editin% so*tware on the co'p)ter to 6nd the exact*ra'e where the s'allest $all reaches its lowest point near the %ro)nd&

and the hi%hest point a*ter the 6rst $o)nce+ !a-e a screenshot o* each

*ra'e and save each as an i'a%e to the co'p)ter+H Usin% the photo editin% so*tware& overlap the i'a%e on top o* each other&

and ad/)st the layer transparency o* the pict)res so $oth pict)res ali%n&

and that $oth the lowest point o* the s'allest $all i''ediately a*ter thedrop& and the hi%hest point o* the $all a*ter the 6rst $o)nce can $e seen

si')ltaneo)sly+ !a-e a screenshot o* this& and open the pixel co)nter

so*tware+;H Usin% the pixel co)nter& 'eas)re the distance $etween the oor and the

#' 'ar- on the stic-y note+ Record this n)'$er& and divide # 'etre $y

the n)'$er o* pixels there is $etween the oor and the #' 'ar- in thepict)re to wor- o)t the scale *actor s)ch that

Scale factor= 1metre

#um!er of &iels

H Repeat step ; *or the re'ainin% *oota%es& and record the res)lts in theta$le Appendix BAct)al !a$leH

Co'parison o* .ethods

For this experi'ent& other 'ethods can $e )sed to %ain si'ilar res)lts as this

one+ An alternative& si'pler 'ethod can $e achieved $y )sin% a stopwatch toti'e the a'o)nt o* ti'e it ta-es *or the s'allest $all to reach its lowest point

i''ediately a*ter droppin% to the hi%hest point o* the s'allest $all a*ter the

drop+ !hen& )sin% the e()ation

s=ut+1

2a t

2

Where :

s=(isplacement

u=)nitial velocity

#@


12/19

a=*cceleration

t=%ime taen

As the $alls are dropped vertically in Earth0s %ravitational 6eld& where

acceleration d)e to %ravity is approxi'ately 9.8m s2

we can ass)'e that the

initial velocity @& th)s the e()ation $eco'es

s=4.9 t2

!h)s& the hei%ht can $e calc)lated )sin% the ti'e ta-en+ Nevertheless& this

'ethod prod)ces a lar%e )ncertainty& as the avera%e reaction ti'e to vis)al

sti')l)s is @+,;? seconds& )ncertainty *or the stopwatch is + @+@# seconds&

while the avera%e ti'e ta-en *or the $all to reach its hi%hest point can $eesti'ated to $e approxi'ately @+? seconds+ As the percenta%e )ncertainty *or

apparat)s error is

&ercentage uncertainty=uncertaintymeasurement

*veragemeasurement 100

!he esti'ated )ncertainty *or experi'ental error *or the ti'e ta-en in this'ethod to : si%ni6cant places is

0.2895+0.10.5 100=+77.9

As the )ncertainty *or this 'ethod is very lar%e& this 'ethod is not )tili7ed *or

the experi'ent+

For the c)rrent 'ethod& the video editor splits the *oota%e into ,> *ra'es persecond this is the *ra'e rate o* the videoH and the sh)tter speed o* the ca'era

)sed was >@@@ ti'es per second& th)s the )ncertainty *or ti'e to : si%ni6cant

places is

1

24+

1

4000

0.5100=+8.38

Altho)%h the )ncertainty o* this val)e is still lar%e& is a si%ni6cant i'prove'ent

*ro' the previo)s 'ethod& th)s this 'ethod is )tili7ed+ Nevertheless& to i'prove

the )ncertainty& the *ra'e rate o* the video can $e increased& which %reatly canred)ce the )ncertainty+ !his will $e ta-en into acco)nt to i'prove the acc)racy o*

the experi'ent in the *)t)re+

Ris- Assess'ent

##


13/19

Ris- "a7ard Preca)tionUnsta$le ladder Ris- o* *allin% *ro' hei%ht A hel'et need to $e worn

and the ladder need to

$e attached to the pillar

with a rope+ !his needs to$e done $y the 'entor#@+

Lar%e $alls )sed Droppin% $alls on *oot "andle with care+.eas)rin% tape Can c)t s-in& and retract

to h)rt eyes

"andle with care+

!ripod !rippin% ha7ard !a-e care when 'ovin%aro)nd the tripod+

.athe'atical .ethods

Usin% the e()ationp=mv

Where :

p=$omentum

m=$ass

v=Velocity

!he 'o'ent)' o* the $alls can $e calc)lated $y o$tainin% the 'ass o* the $alls

)sin% a top pan $alance )ncertainty+

@+@,OH& and the velocity )sin% the ti'eta-en *or the $all to 'ove $etween the two consec)tive *ra'es in the video and

calc)late the velocity )sin% the e()ation

v=s

t

Where :

v=velocity

s="isplacementheight

t=timetaen

Experi'ent Res)lts

For the res)lts& there are two ta$les availa$le *or the experi'ent+ ne is )sed *or

the act)al experi'ent& and the other is the i'proved version *or the experi'ent+

#@In o)r case& we have received the help *ro' o)r 'entor to assist with droppin% the $all *ro' the re()iredhei%ht *ro' the step ladder+

#,


14/19

!he act)al experi'ent ta$le is *airly strai%ht*orward& where the initial and 6nal

hei%ht in pixels is noted and recorded $e*ore a percenta%e is calc)lated where

percentagechangeheight=highest re!oun" height

initial height 100

Experi'ent Analysis

verall& the experi'ent neither proved nor disproved the hypothesis as the data&the validity o* the experi'ent can $e ()estioned d)e to the lac- o* control

varia$les and repeated atte'pts+ !he *act that the $alls were held $y hand'eant that the $alls are dropped *ro' di9erent hei%hts d)e to the way the way

the ar' 'ove when stretched *or an extended period o* ti'e+ !he *act that the

$alls were not held co'pletely perpendic)lar to the %ro)nd also 'eant that therewas a hori7ontal co'ponent to the $all0s position as it $o)nced )p& th)s the

hei%ht achieved is not the 'axi')' hei%ht possi$le& as wor- was done onprovidin% hori7ontal 'otion *or the s'allest $all+ !he wind in the area also 'eant

that ener%y was trans*erred into hori7ontal 'otion *or s'aller $alls& th)s 'a-in%

the 'eas)re'ents inacc)rate+

.oreover& even tho)%h the *oota%e *or individ)al $all drops as controlexperi'entsH were recorded& nevertheless& the *oota%e was lost& th)s& the

experi'ental data cannot $e analysed+ For the *oota%es that were o$tained& the

*ra'es o* the videos were cropped& th)s the %ro)nd cannot $e seen& and'eas)re'ents cannot $e ta-en+

!o i'prove this experi'ent& , ca'era set8)ps will $e )sed& where one is )sed *ora closer shot o* the $all as it *alls& and the other is )sed *ro' a *)rther distance

to 6l' the hi%hest hei%ht achieved a*ter the drop+ 3oth will )se the 'etre 'ar-on the stic-y note as a point o* re*erence to cali$rate the 'eas)re'ents+

Repeated experi'ents will $e carried o)t& where each drop will $e repeated atleast : ti'es )ntil : valid atte'pts are recorded *or each drop+ !o ens)re the

*airness o* the experi'ent& the $alls will $e also $e dropped *ro' reverse order&

hence s'allest $otto'H to lar%est topH as well as the lar%est $otto'H ands'allest topH respectively+

!o i'prove the precision o* the experi'ent& the $alls will $e stac-ed

perpendic)lar to the %ro)nd& and will $e placed placed on top o* a trap doorattached to the pillar& where a rope can $e p)lled to release the $alls+ !hisens)res that the $alls will *all vertically& and that the $all will $e consistently

dropped *ro' the sa'e hei%ht& and this wo)ld also i'prove the sa*ety o* theexperi'ent& as stepladders will not $e re()ired *or this experi'ent+

!he experi'ent ta$le can $e i'proved to loo- li-e the one attached to theappendix Appendix I'proved !a$leH+ !he colo)red sections where the $alls

sho)ld not $e dropped *or the partic)lar co'$ination as this does not apply tothat partic)lar drop+ For instance& i* that drop only incl)ded the $as-et$all drop

as a controlled experi'ent& then the tennis $all& s()ash $all& r)$$er $and $all&Pin%8Pon% $all and the 8rin% will not $e dropped with the $as-et$all& there*ore&

#:


15/19

sections *or those will $e colo)red in and data will not $e collected *or that

partic)lar co'$ination+

For the calc)lations re()ired *or the data in the ta$le& the hi%hest re$o)nd can

$e calc)lated )sin% the 'ethod 'entioned in the previo)s section+ !he i'proved

ta$le also have a section on ener%y lostK%ained which lessens the di2c)lty o*tryin% to spot the trends within the dataset+ !he ener%y lostK%ained can $ecalc)lated )sin%

=mgh

Where :

,=,nergy

m=$ass

h=-eight of the smallest !all thelowest pointof the "rop the highest "rop after the !ounce

Conlusion

As an or$ital 'anoe)vre& %ravity assist plays an essential part in space travel&

especially *or the New "ori7ons 'ission to Pl)to in =)ly ,@#?+ Its principles rely

heavily on the conservation o* ener%y and 'o'ent)' while its principles can $ede'onstrated )sin% the stac-ed $all drop experi'ent+ As *or the experi'ent&

altho)%h the act)al experi'ent did not de'onstrate the principles o* %ravity

assist& it provided the *o)ndations *or a $etter experi'ent& th)s a *)t)reexperi'ent with $etter proced)res 'ay a%ree with the hypothesis& and i* not& it

'ay provide $etter evidence on the reasons $ehind why the relationship$etween the theoretical res)lts and the experi'ental res)lts& and hope*)lly

reveal other concepts that was not considered *or the c)rrent experi'ent+

#>


16/19

Appendix!lutonium in "pae

#rom "un$s #rame!o %ain velocity

!o red)ce velocity

#?


17/19

%a&le '

I'a%e So)rce anPin% G)o and Ro$ert Far()har& New "ori7ons .ission Desi%n&="UKAPL& pa%e #@+

Gravity Assist Analogy

An analo%y *or the spacecra*t0s $ehavio)r in the S)n0s %ravity well is li-e a $i-e

on the hill+ Altho)%h the $i-e %ained -inetic ener%y& it0s 'ovin% 4)phill0& th)s its%ainin% %ravitational potential ener%y and losin% -inetic ener%y+ !his is d)e to the

Conservation o* Ener%y as the First law o* !her'odyna'ics& where

,=G&,

#J


18/19

!h)s1

2m v

2=mgh

Where :

,=inetic energy

G&=gravitational potential energy

m=$ass

v=velocity

g=*cceleration "uegravity

h=-eight

!h)s the $i-e loses speed %oin% )phill+

Li-ewise& d)rin% a %ravity assist& the 4$i-e0 is the spacecra*t %oin% 4)phill0 and4)p0 *ro' the s)n0s %ravity 6eld& hence it loses -inetic ener%y& th)s its velocity as

well+

#


19/19

3i$lio%raphy

.asha$le& ,@#?& B1hat is Gravity Assist+ Availa$le at

httpsKKwww+yo)t)$e+co'KwatchQv@iAGrdI!IiElistPL$3G.:,& R+ A)stin& BS)r*ace Gravitational Field Stren%ths *or N)'ero)s SolarSyste' $/ects+ Availa$le athttpsKKro$ertlovespi+wordpress+co'K,@#>K@;K@#Ks)r*ace8%ravitational86eld8

stren%ths8*or8n)'ero)s8solar8syste'8o$/ectsK

,@#?& ="UKAPL& BC)rrent Position+ Availa$le at

httpKKpl)to+/h)apl+ed)K.issionK1here8is8New8"ori7onsKindex+phpV

N+d+& =+ 3oat& N+ Daiss8Fechner& BSi%ht or So)nd A st)dy o* Reaction !i'es&

Availa$le at httpKKwww+colorado+ed)Kee$Kco)rsesK#,:@/$aseyKa$stractsO,@,@@?K?+ht'

,@#,& R+ Sylvan& BNi-on D:,@@ !he Pro*essional .odes+ Availa$le athttpKKwww+peachpit+co'KarticlesKarticle+aspxQp#:@@:>se(N)'>

#;
https://www.youtube.com/watch?v=0iAGrdITIiE&list=PLbBGM32VSi8xYubkT5NMXHk2WQxyySLyj&index=2https://www.youtube.com/watch?v=0iAGrdITIiE&list=PLbBGM32VSi8xYubkT5NMXHk2WQxyySLyj&index=2http://science.nasa.gov/science-news/science-at-nasa/2007/26feb_grandtheft/http://ccar.colorado.edu/asen5050/projects/projects_2011/project_snow/NewHorizons/Mission_Analysis.htmlhttp://ccar.colorado.edu/asen5050/projects/projects_2011/project_snow/NewHorizons/Mission_Analysis.htmlhttp://messenger.jhuapl.edu/faq/faq_journey.html#7http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.htmlhttps://www.grc.nasa.gov/www/k-12/airplane/thermo1.htmlhttp://solarsystem.nasa.gov/basics/grav/primer.phphttps://www.youtube.com/watch?v=JnPmL7hbGaIhttps://www.youtube.com/watch?v=JnPmL7hbGaIhttp://www.thespacereview.com/article/2787/1http://www.boulder.swri.edu/pkb/ssr/ssr-mission-design.pdfhttps://en.wikipedia.org/wiki/New_Horizonshttps://robertlovespi.wordpress.com/2014/08/01/surface-gravitational-field-strengths-for-numerous-solar-system-objects/https://robertlovespi.wordpress.com/2014/08/01/surface-gravitational-field-strengths-for-numerous-solar-system-objects/http://pluto.jhuapl.edu/Mission/Where-is-New-Horizons/index.phphttp://www.colorado.edu/eeb/courses/1230jbasey/abstracts%202005/5.htmhttp://www.colorado.edu/eeb/courses/1230jbasey/abstracts%202005/5.htmhttp://www.peachpit.com/articles/article.aspx?p=1930034&seqNum=4http://science.nasa.gov/science-news/science-at-nasa/2007/26feb_grandtheft/http://ccar.colorado.edu/asen5050/projects/projects_2011/project_snow/NewHorizons/Mission_Analysis.htmlhttp://ccar.colorado.edu/asen5050/projects/projects_2011/project_snow/NewHorizons/Mission_Analysis.htmlhttp://messenger.jhuapl.edu/faq/faq_journey.html#7http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.htmlhttps://www.grc.nasa.gov/www/k-12/airplane/thermo1.htmlhttp://solarsystem.nasa.gov/basics/grav/primer.phphttps://www.youtube.com/watch?v=JnPmL7hbGaIhttps://www.youtube.com/watch?v=JnPmL7hbGaIhttp://www.thespacereview.com/article/2787/1http://www.boulder.swri.edu/pkb/ssr/ssr-mission-design.pdfhttps://en.wikipedia.org/wiki/New_Horizonshttps://robertlovespi.wordpress.com/2014/08/01/surface-gravitational-field-strengths-for-numerous-solar-system-objects/https://robertlovespi.wordpress.com/2014/08/01/surface-gravitational-field-strengths-for-numerous-solar-system-objects/http://pluto.jhuapl.edu/Mission/Where-is-New-Horizons/index.phphttp://www.colorado.edu/eeb/courses/1230jbasey/abstracts%202005/5.htmhttp://www.colorado.edu/eeb/courses/1230jbasey/abstracts%202005/5.htmhttp://www.peachpit.com/articles/article.aspx?p=1930034&seqNum=4https://www.youtube.com/watch?v=0iAGrdITIiE&list=PLbBGM32VSi8xYubkT5NMXHk2WQxyySLyj&index=2https://www.youtube.com/watch?v=0iAGrdITIiE&list=PLbBGM32VSi8xYubkT5NMXHk2WQxyySLyj&index=2

nuffield report - gravity assist

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