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UCSD
Physics 10
Rockets, Orbits, and Universal GravitationRockets, Orbits, and Universal Gravitation
Spring 2008
2
UCSD
Physics 10
Some Questions WeSome Questions Weā
āll Address Today ll Address Today
What makes a rocket go?What makes a rocket go?
How can a rocket work in outer space?How can a rocket work in outer space?
How do things get into orbit?How do things get into orbit?
WhatWhatā
ās special about geo-synchronous orbit? s special about geo-synchronous orbit?
separation?separation?How does the force of gravity depend on mass andHow does the force of gravity depend on mass and
Spring 2008
3
UCSD
Physics 10
What does a rocket push against?What does a rocket push against?
Cars push on the roadCars push on the road
Boats push on the waterBoats push on the water
Propellers push against airPropellers push against air
exhaust (air)exhaust (air)and push against the hotand push against the hotthrough turbines, heat it,through turbines, heat it,Jet engines push airJet engines push air
against in space?against in space?What can you pushWhat can you push
Spring 2008
4
UCSD
Physics 10
Momentum is conserved!Momentum is conserved!
BeforeBefore
AfterAfter
M
v 1
v
= 0 so
p
= 0
m
M
m
v 2
p after
=
Mv
1
mv
2
= 0 as well so
v 1
=
( m
/ M
)
v
2
Spring 2008
5
UCSD
Physics 10
A Rocket Engine: The PrincipleA Rocket Engine: The Principle
Burn Fuel to get hot gasBurn Fuel to get hot gas
more momentum
Shoot the gas out the tail endShoot the gas out the tail end
rocketrocketExploit momentum conservation to accelerateExploit momentum conservation to accelerate
Spring 2008
6
UCSD
Physics 10
A Rocket Engine: The PrincipleA Rocket Engine: The Principle
Burn Fuel to get hot gasBurn Fuel to get hot gas
Shoot the gas out the tail endShoot the gas out the tail end
rocketrocketExploit momentum conservation to accelerateExploit momentum conservation to accelerate
Spring 2008
7
UCSD
Physics 10
Rockets push against the inertia of the ejected gas!Rockets push against the inertia of the ejected gas!
Imagine standing on a sled throwing bricks.Imagine standing on a sled throwing bricks.
- Conservation of momentum, baby!
your own momentumyour own momentumEach brick carries away momentum, adding toEach brick carries away momentum, adding to
Can eventually get goingCan eventually get going
fasterfaster
than you canthan you can
throw bricks!throw bricks!
- In this case, a stationary observer views your thrown
you arebricks as also traveling forward a bit, but not as fast as
Spring 2008
8
UCSD
Physics 10
What counts?What counts?
TheThe ā
āfigure of merit
figure of meritā
ā for propellant is the
for propellant is the
momentum it carries off,momentum it carries off,
mvmv
as possible before releasing itas possible before releasing itIt works best to get the propulsion moving as fastIt works best to get the propulsion moving as fast
speeds of around 6000 km/h!speeds of around 6000 km/h!Converting fuel to a hot gas gives the atomsConverting fuel to a hot gas gives the atoms
Rockets often in stages: gets rid ofRockets often in stages: gets rid of ā
ādead mass dead massā
- same momentum kick from propellant has greater
reducedimpact on velocity of rocket if the rocketās mass is
Spring 2008
13
UCSD
Physics 10
6 km/s: Almost Fast Enough....but not quite!6 km/s: Almost Fast Enough....but not quite!
Spring 2008
14
UCSD
Physics 10
8 km/s: Not Too Fast, Nor Too Slow....Just8 km/s: Not Too Fast, Nor Too Slow....Just
RightRight
Spring 2008
15
UCSD
Physics 10
10 km/s: Faster Than Needed to Achieve10 km/s: Faster Than Needed to Achieve
OrbitOrbit
Spring 2008
16
UCSD
Physics 10
NewtonNewtonā
ās Law of Universal Gravitation s Law of Universal Gravitation
The Gravitational Force between two masses isThe Gravitational Force between two masses is
proportional to the square of their separation.proportional to the square of their separation.proportional to each of the masses, and inverselyproportional to each of the masses, and inversely
FF
GMGM
11 MM
22 // rr
22
a 1
=
F
/ M
1
=
GM
2 / r 2
acceleration of mass #1 due to mass #
(remember when we said grav. force was proportional to mass?)
G
= 6.
10
m
3 /(kgĀ·s^
2 )
Earth:
M
= 5.
10
24
kg;
r
= 6,378,000 m
a
= 9.80 m/s
2
Newtonās Law of Universal Gravitation
Spring 2008
17
UCSD
Physics 10
What up,What up,
GG
GG
is a constant we have tois a constant we have to
to match observationto match observationshove into the relationshipshove into the relationship
gravity, if you willDetermines the strength of
BestBest
measurement ofmeasurement of
GG
toto
date is 0.001% accuratedate is 0.001% accurate
accuratelyaccurately and deflection isand deflection ismasses inside canister,masses inside canister,Large spheres attract smallLarge spheres attract small
measuredmeasured
Spring 2008
18
UCSD
Physics 10
NewtonNewtonā
ās classic picture of orbits
s classic picture of orbits
full circlefull circleminutes to come aroundminutes to come aroundLow-earth-orbit takes 88Low-earth-orbit takes 88
take 24 hourstake 24 hoursGeosynchronous satellitesGeosynchronous satellites
The moon takes a monthThe moon takes a month
FF orbit velocity by settingorbit velocity by settingCan figure out circularCan figure out circular
gravitygravity
==
FF
centripetalcentripetal
, or:, or:
GMm
/ r 2 =
mv
2 / r , reducing to
v 2 =
GM
/ r
M
is mass of large body,
r
is
the radius of the orbit
Spring 2008
19
UCSD
Physics 10
Space Shuttle OrbitSpace Shuttle Orbit
altitude above surfacealtitude above surfaceExample of LEO, Low Earth Orbit ~200 kmExample of LEO, Low Earth Orbit ~200 km
Period of ~90 minutes,Period of ~90 minutes,
vv
= 7,800 m/s= 7,800 m/s
residual gases in upper atmosphereresidual gases in upper atmosphereDecays fairly rapidly due to drag from smallDecays fairly rapidly due to drag from small
- Not a good long-term parking option!
Spring 2008
20
UCSD
Physics 10
Other orbitsOther orbits
MEO (Mid-Earth Orbits)MEO (Mid-Earth Orbits)
- half-day orbit 20,000 kmā GPS nodesā Communications satellites
altitude,
v
= 3,900 m/s
Elliptical & Polar orbitsElliptical & Polar orbits
- Scientific sun-synchronousā Spy satellites
satellites
GPS Constellation
