The Earth’s orbital speed around the sun provides an initial velocity in space when heading to another part of the solar system. The time of the year.

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.