TIRSELOREEN
RM
µ
RE
there
tramty
construct a mathematical model for how much the
velocityof the spacecraftshould be changedcous to
travel alongthe Hohmann transfer orbit from RE to
RM specify both magnitudehdirectionrelative to
initial velocity
are conserved
T.IE
EEE
if
Emcee
vp
vJEE
su EmCRES FEE
fifty.fi
svsiims
rE
T
EEE EEE FEE.geIgin
oyoum.EE
It I
velocity
a what assumptions
mass of spacecraftcc sun
is the sun's mass is fixed h central
the
sun's
2
considering
gravity none from other planets
only
37 Earth and Mars orbits are perfectly circular ce on
3 Assumption the Earth's gravitational field does not affect thetrajectory of the
spacecraft Does this result in an overestimate or underestimate of calculated su
vs actual v
Earth's gravitational field makes the space craft slow down so neglecting it
results in an underestimated v the formulasusedneglectthe fact that the
spacecraft must escape the Earth's gravity neglectingthe extra ou the
spacecraft must provide
and Me 5 97 1024
kg
T.at 8inEgit i
y
2
in ia
mt
ii
ansmis
whyis that value smaller than thetypical9.8 misausuallyused
The Earth is not perfectlycircular therefore REchangesdepending where on earth you
are Thevaluegivenis
likelythelargestradius value where as a radius value towards
thepoleswouldgiveg 9.81misa 9 81misa is theaverage mostlikely
37 g at the top of mount everest where h 8850m similar toheightcommercial planes
57whyare astronauts weightless
9.76miss
astronauts in space are in free fall No normal force
Ia
a
means there is no sensation ofweight
go at 400km
E
EEEIEE.ms
27THEMOON the moon circlesthe Earth with periodT 27.3days The distance from the center
of the Earth to the center of the moon is R 3.85 105 what is a in terms of T R and Memas
EEE
Ei t.fi I
p
a
122 9 2
a
me
2112123 4111123
41213
Moon orbits the Earth in a circle ac towards center
whyare weusingRaccelerations
we are
so make
n F ma for all
T Also know
Fg
given
1 1
YiE
Y.EE
yto mist
is_n.ouxio.tt
c An apple falls to the Earth with acceleration
Eg 1am
I.gsga En
9 1125,2
objects
g 9.8 misa re 6370km G in terms of g r
Em
on a in terms ofMonly
9.8m 527,96370km
9
9.8m 527,96370000ms 3 9,110 523
3 THEMOONORBIT the acceleration ove togravity on the surface ofthe moon isnearlytothe
acceleration ove to
gravityon Earth RM 1.74 106m what is theperiod of aspacecraft
the moon'ssurface
orbitingjust above
t 9.87 163m sa
912 y39m
91
Rgˢ
II 2R
71.63
2121174 106 a.tl ioa 12
War
4 GEOSYNCHRONOUSSATELLITE is itpossiblefor an
the same point on Earth
TheEarth spins so this is
2 4 2
24309
a
orbitingstaff Gulag'skermain abov
onlypossible if the satellite isdirectlyovertheequator rotating
1 2ltE the
n
FEET RE 39000km above the Earth
Is EMI or317EURfrom centerof Earth to satellite
57THEBLACKHOLE A distant star is found not to remain fixed but rather to execute uniform
circularmotion itishypothesized that this isbe of a black hole
a what canyou
say about the mass of star ms and mass of black hole mn
7
mI
I Emmett's
o
g
itemotne
ble mu's pto overathet
centripetalforce at a constant speedh radius diff mass
would make the center of mass be not fixed aka not
circular
i
r
I
I
is the mass of the black hole in terms of a tho
192 19122stiffft
114111,4
M 4122023
911 4120
67THEMETEOR A meteor moves towards the solar systemw aspeedvo in a direction such
that it would miss the sun
by a distanced if it were not attracted by thesun's gravitat
force Denotethe mass of the sun by M Find the distance b of the meteor from the sun
at the point ofclosest approach in terms of void Mina
conserved
so
Ige
in
close mub von to mys
E 27m 3a_Gym 2m v03
0252 2Gmb v2 02 0
24Mt
ragged
M
Gtm
am
GIFT
D
v8
7 THREEMASSES Threeparticles of mass m each are located at thevertices of an equilateral
triangleand arespinningabout their centerof mass in space that is otherwiseemptyThe
sidesof thetriangleare oflengtho which doesnotchange with time
as what is the potential
mesystem
gygrgyc.tn
on
myma amyms mgm
o
o
a
m
mod
o
boy
sizeunencenergy system tearts
of
Fa
we2am Wtf
wr
iv
379202 5mn20
w.to
in
7g9 2
53822
Fneteach
Tim artists
n 2m 3877102
muzo Bg
m
327,02 3m29
my 5c ᵗ
8 KEPLER'SLAWS a planetof mass m orbits a star of mass M M is much larger than m so the
star can be consideredstationary The orbit is an ellipseand the star is at one of its foci
The total
energyof thesystemis E which will benegativesince the planet is bound to
the star Letthemagnitude of the planet'sangularmomentum bee
ra
m
on
III
EE
infithorpanora
EEE aEonamanet
EE Esther
o
mm
Ecosorpe
1dam'm
r
a
flaymat
AMMI CAMM
m EMMAILGIMI ZEE
a catcsatca
c ratcaa.ro29
29
9
ra
up
dec12
2EE
E
stqcttosnowmata ratr
b
4
cg
a a
rptcaa rps an
d Express a and b in terms of E e mm anoa
a
rpgraanoifb rraijustpiuginfromparta.li think
e usethesecond law to find the period of the orbit in terms of a M and a
1am
givingup
only
a Dust RING Ringscomprisingsolid material such as oust and moonletssurround
giant
planets consider the simplifiedcaseofathinringrandmassm.mevingssymmetry
lies on the z axis
a Find the force exerted on a mass m located on the axis of the
from
ring
page
its
som
setter
ection
I
c
2
am
case
of
OF
am crates312 am
E
ii mil
ra
192
52722 2
agin
traa t
rate
case
2
9727 7312
Tea
9227227312 Fz indirection of 2
b suppose the particle starts from rest
passes throughthe center of the
IE eansnopotentiaeEn
veryfar away what will itsvelocitybe when it
ring
E Yitk verge
Itm tamua
escapevelocity
youmighthave guessedthis answer who need for calculation
its just the escape
All parts of the
distance r so to push thru center of
Explain now
velocity
ringrata
ving
0
