the earth’s orbital speed around the sun provides an initial velocity in space when heading to...
TRANSCRIPT
1. Launch into low Earth orbit using the Earth's rotation for extra speed. 2. Circle the Earth under rocket power to reach escape velocity and loop out to where the moon's
gravitational field can draw the craf t into its orbit. 3. Land under rocket power. 4. To return, reverse the process and use the earth's atmosphere as a breaking mechanism.
The Earth’s orbital speed around the sun provides an initial velocity inspace when heading to another part of the solar system. The time ofthe year for launch is chosen depending on which direction the Earth is heading and where you want to go.
Discuss the effect of the Earth‘s orbital motion and its rotational motion on the launch of a rocket
‘g forces’ refers to the ratio of apparent weight during launch to normal true
weight. It is a convenient indicator of the forces on astronauts body.
CAUTION: a ‘6g’ launch may also refer to an acceleration of a = (6 x 9.8), giving an apparent
weight of 7g ! (and a g-force of 7)
A rocket accelerating upwards at 9.8 m/s2 causes the astronaut to experience a g-force of 2.
A rocket accelerating upwards at 19.6 m/s2 causes the astronaut to experience a g-force of 3.
A stationary or constant velocity rocket causes the astronaut to experience a g-force of 1.
A rocket accelerating upwards at 49 m/s2 causes the astronaut to experience a g-force of 6.
Identify why the term ‘g forces’ is used to
explainthe forces acting on
anastronaut during
launch
Rollercoaster simulation
If we know theinitial mass of therocket, the Rate of expulsion (kg/s)and how long it hasburnt for, we canwork out the new mass of the rocket.
During launch, the momentum of the propellant expelled downwards (per second) produces a thrust
force upwards.
For a moving (inertial) frame of reference:
thrustexrr
exr
r
exrr
exrr
exrf
FRvam
vt
m
t
vm
mvvm
mvvm
ppp
0
0
fi ppi.e. total momentum is unchanged
0 ip
exrrrthrust RvgmamF
exvt
mF
If this thrust force exceeds the weight of the rocket system, the rocket begins to accelerate
upwards.
As the rocket expels more and more propellant, the mass of the rocket system decreases. If the thrust force remains constant, Newton’s Second Law tells us that the acceleration will increase.
Conservation of momentum tells us that the change in momentum (= Impulse = Force x time ) down produces an Impulse up. So an upwards force
(thrust) is produced.
Water Rocket Experiment
Analyse the changing acceleration of a rocket during launch in terms of the:– Law of Conservation of Momentum
If we know theinitial mass of therocket, the Rate of expulsion (kg/s)and how long it hasburnt for, we canwork out the new mass of the rocket.
During launch, the momentum of the propellant expelled downwards (per second) produces a thrust force upwards.
For a moving (inertial) frame of reference:
thrustexrr
exr
r
exrr
exrr
exrf
FRvam
vt
m
t
vm
mvvm
mvvm
ppp
0
0
fi ppi.e. total momentum is unchanged
0 ip
exrrrthrust RvgmamF
Analyse the changing acceleration of a rocket during launch in terms of the:– Law of Conservation of Momentum– forces experienced by astronauts
exvt
mF
If this thrust force exceeds the weight of the rocket system, the rocket begins to accelerate
upwards.
As the rocket expels more and more propellant, the mass of the rocket system decreases. If the thrust force remains constant, Newton’s Second Law tells us that the acceleration will increase.
Conservation of momentum tells us that the change in momentum (= Impulse = Force x time ) down produces an Impulse up. So an upwards force
(thrust) is produced.
The astronauts will experience g-forces produced by this net increasing acceleration while the rockets burn propellant. When the burn finishes, the rocket will
continue to move at a constant velocity (subject to drag).
(Graphic from HSC Online)
The astronauts will experience changing g-forces produced by this net increasing acceleration while the rockets burn propellant. When the burn
finishes, the rocket will continue to move at a constant velocity (subject to drag).
Analyse the changing acceleration of a rocket during launch in terms of the:– forces experienced by astronauts
The space craft NQ1564 accelerates as fuel is burnt up
at a consistent rate.
Assuming that the burnt fuel gives a constant amount
of thrust, draw a qualitative graph of
(a) acceleration vs time and
(b) velocity vs time
( a ) 1 m a r k
( b ) 1 m a r k
t i m e
acceler
ation
t i m e
velocity
Question 1
A satellite of mass 200 kg is to be fired so that it achieves an orbit at
300 km around the Earth (the Earth has a radius of 6 378 km)
(a) Knowing the mass of the rocket and the energy liberated when burning fuel, what must also be taken into account
when determining how much fuel to take on the rocket?
(a) 1 mark
The mass of the fuel must also be taken into account,
remembering that the mass will be gradually decreasing
Below is a list of some of the key scientists who have contributed to the development of space
exploration.
Tsiolkovsky
Oberth
Goddard
Esnault-Pelterie
O’Neill
von Braun
Select one of the above scientists and describe how they assisted the progress of space
exploration
He proposed the use of reaction motors that were powered by liquid fuels. He suggested the use of green plants to provide oxygen to space crew and dispose of carbon dioxide
Identify data sources, gather,
analyse and present information on
the contribution of one of the following to the
development of space exploration:
Tsiolkovsky, Oberth, Goddard,
Esnault-Pelterie,O‘Neill or von Braun
Tsiolkovsky built the first wind tunnel in Russia which enabled him to observe aerodynamic problems.
Objects which are subject to a centripetal force undergo uniform circular motion.
A centripetal force always accelerates the object in the direction perpendicular to
the velocity of the object. This causes the object to move in a circle.
r
mvFc
2
v
r
mvmg
2
r
vac
2
maF
r
vg
2
If a mass attached to a string is twirled in a circle, the centripetal force is the tension in the
string.For a car turning in a circle, the centripetal force is the frictional force between the road and the
tyres.For a satellite, the centripetal force is the
gravitational pull of the planet.
tangential to the circle
towards the centre of the circle
towards the centre of the circle
Analyse the forces involved in uniform circular motion for a
range of objects, including satellites orbiting the Earth
Solve problems and analyseinformation to calculate
centripetal force acting on asatellite undergoing uniform
circular motion about the Earth usingF= mv2/r
A geostationary satellite has a mass of 200 kg and orbits at an altitude of 35800 km. Calculate the centripetal force on the satellite.
t
Data:Radius of Earth = 6.38 x 106 m
For one revolution of the Earth, t=24hrs=86400sx10-5 rads/sec
rv v=(x10-5)x(6.38 x 106 + 3.58 x 107)= 3066.48 m/s
r
mvFc
2
F=200(3066.48)2/(6.38 x 106 + 3.58 x 107)= 44 N
Compare qualitatively low Earth and geo-stationary
orbits Other Advantages:
1. Remote sensing of the Earth’s weather, oceans, pollution, ozone etc. need low orbits to increase resolution and sensitivity.
2.Spy satellites often need to get as close as possible.
3.Geopositioning needs high accuracy and hence low satellite orbit to reduce errors.
4.It costs more to place objects at high altitudes.
Kepler’s 3rd Law
22
3
4GM
T
r
Solve problems and analyseinformation using:
r3/T2 = GM/42
111067.6 G
Define the term ‘orbital velocity’ and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of
the central body, mass of the satellite and the radius of orbit using Kepler’s Law of Periods
Kepler’s 3rd Law (Law of periods)
Define the term ‘orbital velocity’ and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of orbit using Kepler’s Law of Periods
Orbital velocity is the instantaneous linear velocity of an object in circular motion. It is tangential to the circular motion and can be calculated as the circumference divided by the period.
2object same theorbiting bodiesfor constant
2
3
4
GM
T
r
T
rv
2
r
GMv
GMrv 2
222
32
44 GM
r
rvv
rT
2and then subst.
to give
So, around a central body, mass M, the orbital velocity decreases as radius increases
Solve problems and analyseinformation using:
r3/T2 = GM/42
A planet in another solar system has three moons, all of which travel in circular orbits.
Some information about these moons is given in the table.
Moon Radius of orbit (orbs) Period of revolution (reps)
Alpha 4.0 16 Beta 9.0 54 Gamma 2.5
The radius of orbit and period of revolution are measured in orbs and reps respectively, which are not metric units.
(a) Use the data to show that Kepler’s third law is obeyed for the moons Alpha and Beta.(b) Calculate the speed of moon Gamma in orbs/rep.
We can then find the orbital speed = v=r=2r/T=2x 2.5/7.9 = 2.0 orbs/rep
Account for the orbital decay ofsatellites in low Earth orbit
There may be unpredicted drag due to solar winds producing unexpected heating and expansion of the atmosphere
Discuss issues associated with
safe re-entry into the Earth’satmosphere and landing on
theEarth’s surfaceRetrofire to slow and drop into atmosphere
Friction with atmospheric molecules produces extreme heat
A blunt surface will produce a shock wave in front to absorb heat
MATERIALS : Ablation - Surface vaporises and takes heat away
MATERIALS : Insulation - prevents heat entry
g-forces: prefer 3g, 8g may cause chest pain, loss of consciousness
g-forces: transverse application best, not too much or too little blood to brain
g-forces: eyeballs in!g-forces: contoured body support
Ionisation blackout: heat causes layer of ionised particles preventing radio contact for some minutes
Landing: After re-entry, parachute to water for earlier missions; banked turns and controlled descent to runway for space shuttle
To initiate reentry a retrofire is used to slow the spacecraft and drop into atmosphere
Friction with atmospheric molecules produces extreme heat
A blunt surface is best on the front of the spacecraft. This will produce a shock wave in front to absorb heat
Materials on the outer surface to protect the spacecraft have varied. Early spacecraftsuch as those used in the Mercury, Gemini and Apollo programs used ablation - where the surface vaporises and takes heat away
The space shuttle uses insulating tiles which provide a protective barrier that prevents heat entry
Another issue is g-forces: A deceleration of near 3g is preferable, higher g-forces cause discomfort and affect body function - 8g may cause chest pain, loss of consciousness
g-forces: a transverse (front to back)application is best, as up or down forces cancause too much or too little blood to the brain
g-forces: eyeballs in! g-forces: contoured body support
Ionisation blackout: heat causes layer of ionised particles preventing radio contact for some minutes
Landing: After re-entry, parachute to water for earlier missions so flotation of capsule and location are important; Shuttle: banked turns and controlled descent to runway
Discuss issues associated withsafe re-entry into the Earth’satmosphere and landing on theEarth’s surface
Identify that there is an optimum angle for re-entry into the Earth’s atmosphere and the
consequences of failing to achieve this angle
Too steep means burning up
Too shallow means skipping off atmosphere
Need correct time, direction and duration of retroburn
Too shallow means skipping off atmosphere
Too shallow means skipping off atmosphereToo shallow means skipping off atmosphereToo shallow means skipping off atmosphere
Too shallow means skipping off atmosphere
Too shallow means skipping off atmosphereToo shallow means skipping off atmosphereToo shallow means skipping off atmosphere
For the Apollo spacecraft, the optimum angle was between 5.2 and 7.2 degrees below horizontal
The optimum angle of re-entry is best angle for the spacecraft to approach the
level of the atmosphere
If the angle is too steep, the spacecraft will collide with too many atmospheric molecules too quickly at high speed, causing the temperature to rise dramatically and causing the spacecraft to burn up. The g-forces would also be too great, causing loss of consciousness or fatality.
By ensuring the correct time, direction and duration of the retroburn (forward facing rockets)
If the angle is too shallow the spacecraft will not re-enter, but ‘skip’ off the atmosphere
For the Apollo spacecraft, the optimum angle was between 5.2 and 7.2 degrees below horizontal
What is meant by optimum angle of re-entry?
What is an example of an optimum angle of re-entry?
How is the correct angle achieved?What are the
consequences of failing to achieve this angle?
Question 3
When a space craft re-enters the Earth’s atmosphere it must enter at a certain angle.
Discuss what the effects would be if the space craft entered at too steep an angle.
3 2 marks
The space craft would experience a huge force due to air resistance.
The g-forces would be too great for the passengers and would be fatal.
The friction of the air on the space craft would cause the space craft
to heat up too much causing it to disintegrate.
Question 1
A satellite of mass 200 kg is to be fired so that it achieves an orbit at 300 km around the Earth (the Earth
has a radius of 6 378 km)
(a) Determine the period for this satellite when it achieves orbit.
(b) Describe what will happen to the orbit of this satellite over time.
(a) 1 mark
T = (42r3/GM)0.5
T = (42x(6.678 x106)3/6.67x10-11x6.0x1024)0.5
T = 5 420 s.
(b) 1 mark
The satellite will gradually lose energy. It will orbit more and more slowly and its
height will get lower and lower. Eventually it will plummet towards the Earth and get
burnt up in the Earth’s atmosphere.