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Transcript
HSC Physics – Core Module 1 – Space
1.
Many factors have to be taken into account to achieve a successful rocket launch,
maintain a stable orbit and return to Earth.
 Describe the trajectory of an object undergoing projectile motion within the Earth’s
gravitational field in terms of horizontal and vertical components.
A projectile is any object that is launched into the air. Projectiles are projected into the air and then
left to complete their unpowered flight.
Throughout the flight the projectile is subject to only one force - the force of gravity and just one
acceleration – acceleration due to gravity. This rate of acceleration applies to all objects large or
small.
The trajectory of a projectile is the path that it follows during its flight. In the absence of air
resistance, the path to the flight of a projectile will trace out the shape of a parabola.
To understand and analyse this motion we must make a very important observation: The motion of
a projectile can be regulated as two separate independent motions superimposed on each
other. The first is a vertical motion which is subject to acceleration due to gravity, and the
second is a horizontal motion, which experiences no acceleration.
Because the two motions are perpendicular, therefore independent, we can treat them separately
and analyse them.
4 Acceleration Equations:
1)
2)
3)
4)
The Vertical Motion
When a ball is thrown directly up, it is accelerated due to gravity directly down. As a result it will rise
up, slow to a halt in the air and then fall back to the Earth. As it falls it will speed up until, when back
at its starting point, it is going as fast as it was when thrown. Furthermore, the time taken to fall
from its peak height to the ground is exactly the same as the time taken to rise to the peak height.
Note: In this scenario up is taken to be the positive direction but this may not always be the case.
In adapting the acceleration equations for the vertical motion we need to note the following
variables:
Hence our three equations become:
The Horizontal Motion
If a ball is pushed horizontally, ideally, once it is under way, it experiences no acceleration at all in
its direction of movement. If no acceleration is experienced then the ball will travel at a uniform,
unchanging velocity.
This is also the nature of the horizontal portion of a projectile’s motion. Once free of the ground,
there is no frictional force (air resistance is negligible at this point), so the ball will travel uniformly in
the horizontal direction.
In adapting the acceleration equations for the horizontal motion we need to note the following
variables:
Hence our three equations become:

Describe Galileo’s analysis of projectile motion
All objects are accelerated towards the Earth at the same rate. This was first realised by Galileo
Galilei.
Galileo postulated that all masses, whether large or small, fall at the same rate, and he conducted
experiments to prove just that. However, air resistance gets in the way of such experiments and
made the job quite difficult. He eventually overcame this difficult by rolling balls down highly polished
inclines instead of simply dropping them, thereby reducing the effective acceleration. This lower rate
of acceleration was less affected by air resistance and was easier to measure.
Galileo was also able to break down motion into horizontal and vertical components. He reasoned
that motion could be thought of as the sum of a constant horizontal velocity (Ux) and a vertical
motion (Uy) which is accelerating due to the influence of gravity.
Galilean Theory of Relativity
“ The law of mechanics applies equally in all inertial frames of reference ”
An inertial frame of reference is one which is at rest or travelling with a constant velocity.
OR
“An inertial frame of reference is one in which Newton’s first law holds”
A non-inertial frame of reference is one that is accelerating.
Galilean Theory of Relativity led to the understanding of projectile motion.
“Projectile motion consists of two independent motions, namely that of the horizontal and the vertical
components. The horizontal motion is a uniform velocity motion whereas the vertical is an
accelerating motion.
Air Resistance
In all examples we have previously seen, we have ignored the effect of air resistance on the motion
of the projectile. The reason for this is that it is simply too difficult for us to account for,
since it depends on numerous factors such as shape, texture, surface air, velocity and so on.
In the real world, air resistance acts as a retarding force in both the vertical and horizontal
directions. As a result, the path of the projectile is distorted away from a perfect parabola as shown
in the figure below:
i.
ii.

Explain the concept of escape velocity in terms of the:
Gravitational Constant
Mass and Radius of the planet
Escape Velocity is the minimum velocity required for an object to escape a gravitational field and
go to infinity.
Consider the following:

Outline Newton’s concept of escape velocity
Isaac Newton wrote that it should be possible to launch a projectile fast enough so that it achieved
an orbit around the Earth.
He hypothesised this by observing the projectile of a stone thrown from a tall tower. He noticed that
as the stone is thrown faster, it will travel further before stopping. He hypothesised that if the stone
was thrown fast enough then, as the stone falls, the Earths surface will curve away so that the falling
stone never actually lands on the ground and thus orbits the Earth.
He had no way of testing this hypothesis, but it led to the important concept that at any given
altitude, there is a specific velocity required for any object to achieve a stable orbit.
Consider the following:
If instead of throwing the stone horizontally to the Earth surface, rather it was thrown directly
perpendicular. As the stone is thrown faster it will reach a greater height. Thus the conclusion can be
made, that if the stone is thrown fast enough it will continue to rise and continue to slow down but
never fall back down – thus escaping the Earth’s gravitational field. The initial velocity required to
achieve this is known as escape velocity.
As previously stated:
By considering the kinetic and GPE of a projectile, it can be shown that the escape velocity of a
planet depends only upon the universal gravitational constant, the mass and the radius of the planet.
Note: The mass of an object has no influence on the escape velocity. This means that a rocket and a
tennis ball need the same escape velocity to escape any gravitational field.

Identify why the term ‘g forces’ is used to explain the forces acting on an astronaut
during launch
Apparent weight for a person standing on the surface of the Earth is equal to the sum of the forces
that are resisting your true weight.
The term ‘g force’ is used to express a person’s apparent weight as a multiple of his/her normal
true weight (that is the weight when they are standing on the surface of the Earth).
Hence:
g force = (apparent weight) / (normal true weight)
The figure shows the forces that are acting upon an astronaut
during a launch. The astronauts body is exerting a downward
weight force on the floor and the floor meets this with an
upward reaction force. In addition, the floor is exerting an
upward acceleration force (m x a).
Therefore the astronaut feels an apparent weight = mg + ma
Therefore g force =
And hence,
(mg + ma) / 9.8m
g force =
(g + a) / 9.8
Where
g = acceleration due to gravity at altitude (
m = mass of the astronaut.
)

analyse the changing acceleration of a rocket during launch in terms of the:
– Law of Conservation of Momentum
– forces experienced by astronauts
Projectiles receive an initial velocity and are then left to fall through a trajectory, rockets receive a
force called thrust from their engine(s) for a significant portion of their upwards flight and become
more conventional projectiles only after their engines are exhausted.
Rockets
A rocket engine is different from most other engines in that it carries with it both its fuel and its
oxygen supply. Any fuel needs oxygen to burn and most engines obtain the necessary oxygen from
the air around them. However, in space there is no air or other atmosphere, which makes a rocket
engine the natural choice.
Modern rockets either use solid or liquid propellants. Solid rocket propellants are manufactured with
a mixture of fuel and oxidizer. The dry solid propellant is packed into an insulated cylindrical vessel,
usually with a hollow core (which isn’t necessary), but increases surface area available for burning
and thus the thrust will increase. Once ignition starts, hot gases are produced at an extreme rate
and forced out through the nozzle.
Liquid propellant rockets keep both the liquid fuel and the oxidizer in separate storage tanks. There
are pipes which lead both these substances to the ignition points where the hot gases will again be
forced out through the nozzle.
The forward motion of the rocket can be described using the Law of conservation of momentum.
This law states that during any interaction in a closed system the total momentum of the system
remains unchanged.
This means that during the launch, the momentum of the gases shooting out of the rear of the
rocket must be equal to the forward momentum of the rocket itself.
This means that during any one-second time interval:
Total change in momentum = 0
Where
= change in momentum (
)
= mass (kg)
= velocity (
)
This means that the backward momentum of the gases ( ) is exactly equal in magnitude to the
forward momentum of the rocket ( ), thus the rocket will have forward velocity.
Note: the mass of the gases is considerably less than the rocket, but their velocity is much greater,
so their momenta are equal but opposite.
Where
F = Force (N)
t = time (s)
so that
-(Ft)Gases = (Ft)Rocket
or for any one second interval,
- F Gases = F Rocket
This is Newtons Third Law of Motion. The rocket is forcing a large volume of gasses backward behind
it, and the gases in return force the rocket forward (as shown below). Although the two forces are
equal and opposite, the rocket experiences just one of them – the thrust.
Thrust and Acceleration
As a rocket is a mass it is subject to several forces, and thus it will accelerate according to Newtons
second Law.
The Rocket is subject to the following forces:
- Its weight force directed downwards
- Its thrust directed upwards
- The reaction force of the ground on the rocket (equal to the difference between the weight and the
thrust while the rocket is still on the ground) directed upward.
- Air resistance directed downward against the motion of the rocket once it has left the ground. This
air resistance force can become significant as the speed of the rocket builds, but at the relatively
low speeds of early lift-off its effect can be ignored.
Note:
A rocket’s acceleration will not be constant, however, because fuel constitutes up to 90% of the
mass of a typical rocket. As the fuel is burnt, the mass of the rocket decreases but the thrust
remains the same. Additionally the gravitational field vector, g, reduces slightly with increasing
altitude. The result is that a rockets rate of acceleration will increase and its velocity will increase too
Consequently, the acceleration equation of a rocket will only be at an instant, provided that the mass
and the thrust are known at that instant.

Analyse the forces involved in uniform circular motion for a range of objects,
including satellites orbiting the Earth
Uniform Circular Motion is motion with a uniform orbital velocity.
A force is required to keep a spacecraft in orbit around the earth, or any object in circular motion –
some force is needed to keep it there, and that force is directed back towards the centre of the
circle. In the case of the spacecraft, it the gravitational attraction between the Earth and the
spacecraft that acts to maintain the circular motion, known as an centripetal force, can be
determined using the following equation:
where
Fc
m
v
r
=
=
=
=
centripetal force (N)
mass of the object in motion (kg)
instantaneous or orbital velocity of the mass (m/s)
radius of circular motion (m)
Newton’s Second Law stares that wherever there is a net force acting on an object there is an
associated acceleration. Since this centripetal force is the only force acting on the motion it can be
said:
Note: Velocity is a vector quantity. Since the object is constantly changing direction – it must be
changing its velocity – hence it must be accelerating
Centripetal acceleration is always present in uniform circular motion. It is associated with
centripetal force and is also directed towards the centre of the circle.
Why does an astronaut feel weightless when orbiting the Earth?
Weightlessness occurs when the g-force experienced by the astronaut is 0. In the case of an
astronaut orbiting in a spacecraft, there are no resistance forces on the person so there is no
apparent weight.
Furthermore, when in orbit, the spacecraft is constantly falling (but never hitting the earth due to the
Earth’s curvature). This means that the acceleration experienced is –g (taking up to be the positive
direction). Hence:
G – force = (g + a) / g
= [g + (-g)] / g
= 0 – apparent weight.
Therefore the astronaut feels ‘weightless’

Discuss the importance of Newton’s Law of Universal Gravitation in understanding
and calculating the motion of satellites
The application of Newton’s Law of Universal Gravitation to the orbital motion of a satellite will
produce an expression for the critical orbital velocity.
This gravitational force of attraction also serves as the centripetal force for the circular motion
hence:
Therefore we can equate the formula for FG with that for Fc:
Where:
Note: The radius of the orbit, r, is the sum of the radius of the Earth and altitude of the
orbit.
R = RE + altitude (m)
Where:
From these last two expressions, it can be noted that the orbital velocity for a particular object
depends only on the mass of the Earth, the radius of the Earth + the altitude orbit. Given that the
mass of the Earth and the radius have fixed values, this means that altitude is the only variable that
determines the specific velocity required. In addition, the greater the radius of the orbit, the lower
the orbital velocity required.
Economical Launching
Rocket launch planners use the rotational speed of the Earth, about 1700 kph, to assist the launch of
their rockets. To reach a low earth orbit (the minimum height needed to significant atmospheric
drag, about 250 kph) a spacecraft needs to reach an orbital speed about of 30 000 kph.
Launching a spacecraft into its orbit in the direction of the Earth’s rotation from WEST TO EAST will
give the spacecraft an additional 1700 kph for free.
Mission planners also use the speed of the earth around the sun, about 107 000 kph, to increase the
starting velocity of an intra solar system rocket. The advantages are obvious. Just as obvious as the
fact that the Earth must the facing in the right direction of this orbital speed. For this reason there
are “launch windows” during which a rocket must be launched. If it is launched outside these
windows, the rocket will start its journey in the wrong direction.

Compare qualitatively and quantitatively low Earth and geo-stationary orbits
In past theory, it has been assumed that the motion of the planets and satellites are circular. In
reality, however, this is not the case. The most common orbital shape is an ellipse, or oval shape.
Kepler also realized this and stated it as his first law. (Law of Ellipses)
Ellipsis can be round or elongated – the degree of stretch is known as the eccentricity.
The eccentricity is defined as the ration of c : a.
A circle is an ellipsis with an eccentricity of 0.
No planet in our solar system has a perfect circular motion. They all have difference values
of eccentricity.
Types of Orbit
There are two main types of orbits in which satellites or spacecrafts will be placed into. One is known
as the geostationary orbit, the other is known as the Low Earth Orbit.
The Low Earth Orbit is generally an orbit higher than approximately 250km, in order to avoid
atmospheric drag, and lower than approximately 1000km, which is the altitude at which the Van
Allen radiation belts begin to appear.
The space shuttle utilizes a low Earth orbit somewhere between 250km and 400km altitude
depending on the mission. At 250km, an orbiting spacecraft has a velocity of 27900 km/h and takes
just 90 minutes to complete an orbit of the earth.
A geostationary orbit is at an altitude at which the period of the orbit precisely matches that of the
Earth. If over the equator, such an orbit would allow a satellite to remain parked over a fixed point
on the surrounding surface of the Earth. From the Earth such as satellite appears to be stationary in
the sky, always located in the same direction regardless of the time.
This is particularly useful for communication satellites because a receiving dish need only point to a
fixed point in the sky in order to remain in contact with the satellite.
The altitude of such an orbit can be calculated from Kepler’s Third Law. Firstly, the period of the orbit
must equal to length of one day. This is 86164 s. The radius of the orbit then works out to be
42168km. Subtracting the radius of the Earth gives an approximate altitude of 35 800 km. This
places the satellite at the upper limits of the Van Allen belts, and near the edge of the
magnetosphere.
If a satellite at this height is not positioned over the equator but at some other latitude, it will not
remain fixed at one point in the sky. Instead from Earth, the satellite will appear to trace out a figure
8 path each 24 hours. It still has a period equal to Earths, however, and so this orbit is referred to as
geosynchronous.
Low Earth Orbit (Summary)
- Occurs at an altitude between a few hundred to a few thousand km above the ground
- Here the atmospheric may be thick enough to exert enough drag force to slow the craft enough to
cause it to re-enter
Low Orbit Satellites
- Can communicate with the Earth quickly due to their shorter distance from the surface
- Suffer less data corruption from outside interference also due to shorter distance
- Shorter life due to air friction – requires regular maintenance
- The atmosphere slows the satellite down, cause it to spiral into the earth – burn up
- Do not stay at fixed position above the Earth’s surface – interruptions in communication
Geostationary Orbit
- Have the same period as the earth’s rotation (24 hours) and is an East-West equatorial path
- The altitude is about 36000 km (Tangential orbital velocity of a satellite in this orbit is about 3075)
Geostationary Satellites
- Suffer from less orbital decay due to less air in the higher atmosphere
- Stay fixed above a particular position above the Earth allowing for constant communication, as
opposed to low-earth satellites that drift across the sky.
- Suffer more data corruption from outside interference due to large distance.
The radius of orbit of a satellite, the period of that orbit, and the mass of the planet being orbited is
related accordingly:
Note that
is constant for all satellites orbiting a common planet.

Describe how a slingshot effect is provided by planets for space probes.
The slingshot effect or planetary swing by, is a manoeuvre used with space probes and proceed
onto another target.
In order to fully understand the slingshot affect, it must be considered as a perfectly elastic onedimensional collision. Even though there is no contact, the interaction behaves like a collision.
However, because the bodies do not touch in any way, there are no energy losses and hence the
“collision” is elastic.
It is described by the formula:
Derivation on next page.
The expression represents the maximum velocity achievable from the slingshot affect. This is
achieved by a head on rendezvous as shown below:
At other angles, a spacecraft will achieve lower velocities.
Note: The kinetic energy of the system has been conserved as the spacecraft gains some kinetic
energy, whereas the planet loses an equivalent amount.
Example:
A satellite approaches Jupiter almost head on for a slingshot manoeuvre. Jupiter has an orbital
velocity of 13 000 m/s relative to the Sun, and the spacecraft has a velocity of 15 000 m/s relative
to the Sun.
Calculate the final velocity of the Satellite after completing the slingshot.
Advantages of the Slingshot Affect
The slingshot affect can be used to:
-
Increase the velocity with respect to the sun
-
Changes the direction of travelling, without needed any excess fuel
Hence, can carry less fuel – more equipment.

Account for orbital decay of satellites in low Earth Orbit.
All satellites in a low earth orbit are subject to some degree of atmospheric drag that will eventually
decay their orbit and limit their lifetimes. As thin as the atmosphere is 1000 km above the surface of
the Earth, it is still sufficient to significantly slow the satellite down over a period of time. In turn,
this will reduce the altitude of the satellite.
The amount of atmospheric drag experienced by a satellite depends on the size of the satellite and
the density of the air along the orbit. This air density is affected by many variables such as
time of day, season, latitude and longitude – all of which are predictable. However, there are
also unpredictable influences such as solar wind.
An increase in solar wind can heat up the outer atmosphere causing it to expand, thereby increasing
its density and height. This will subject satellites to drag that would not otherwise have been
anticipated.
As the satellite slows it loses altitude and begins to spiral downwards. As it descends, it encounters
higher density air and higher drag, speeding up the process. By the time the satellite is below an
altitude of 200 km it only has a few hours left before colliding with the Earth.
The re-entry process generates much heat and most satellites burn up (vaporize) before impacting,
though some pieces have struck the Earth.
Why must a satellite lose altitude if it slows down?
The total mechanical energy, E, of a satellite in a stable orbit is the sum of its kinetic and potential
energies. It can be shown that:
E=
This expression shows that the energy of an orbiting satellite is always negative and that its
maximum value is zero (much like that of gravitational potential energy).
Higher orbits correspond to higher energies, lower orbits correspond to lower energies.
A loss of energy by a satellite, due to atmospheric friction or deliberate slowing, means that the
radius of the orbit, and the altitude must also decrease.
Note: As r decreases – E becomes ‘more negative’ – hence it becomes smaller.
DON’T GET CONFUSED – REMEMBER THE NEGATIVE SIGN

Discuss issues associated with safe re-entry into the Earth’s atmosphere and
landing on the Earth’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.
As previously discussed, when the velocity of the spacecraft will reduce in magnitude – the
spacecraft will be pulled down to the Earth. This mechanism is deliberately used by astronauts
wishing to re-enter the Earth’s atmosphere and return to the Earth’s surface.
Typically, astronauts will retrofire their spacecraft’s rockets and execute a short burn that will slow
down the spacecraft, allowing it to drop down into the atmosphere. The time, direction and duration
of the burn must be controlled carefully to achieve an optimum re-entry angle.
If the angle of re-entry is too shallow, the spacecraft may skip off the atmosphere. If the
angle of re-entry is too steep, the spacecraft will burn up due to the heat of re-entry.
For example: In the Apollo missions the optimum angle of re-entry was between 5.2 and 7.2 degrees
Some issues associated with safe re-entry include:
- Extreme Heat:
A spacecraft has a significant velocity, and thus will have significant kinetic energy.
Additionally, due to the spacecrafts orbit, there is considerable gravitational potential energy
applied on the spacecraft. But this is lost as the space-craft’s altitude decreases during
re-entry.
As the spacecraft re-enters, it experiences friction with the molecules of the atmosphere. This
friction is a force directed against the motion of the spacecraft which causes it to decelerate.
The enormous kinetic energy the spacecraft possesses is converted into heat, and the heat can
cause the spacecraft to reach extreme temperatures.
Research into re-entry initiated with the idea of a nose (pointed) spacecraft. However it was
determined that upon re-entry this would generate temperatures exceeding 7500 degrees. This
was clearly too hot to prevent the vaporization of the cone. Thus as research continued, it was
determined that a blunt nose was the most efficient mechanism for re-entry.
When the blunt shape collides with the upper atmosphere at re-entry speeds, it
produces a shockwave in the air that would absorb much of the heat generated as the
object re-entered and slowed in the atmosphere.
This led to the new design of warhead – one that would detach from the rocket at altitude and
re-enter the atmosphere backwards, presenting its blunt rear as it fell.
The space shuttle still uses this idea – by keeping its nose well up while re-entering the most
critical phase of re-entry, it presents its flat underbelly to the atmosphere thereby using its
blunt shape to create the shock wave.
However, the blunt shape design would still need to cope with high temperature and some
protective layer would therefore need to be devised to cover it. After considerable research a
technique called ablation was established. This idea is that the nose-cone is covered with a
ceramic material, such as fiberglass, which is vaporized or ablated during re-entry heating.
The vaporizing of the surface dissipates the heat and carries it away.
The space shuttle uses a different approach. In uses a covering of insulating tiles. These
tiles are made of approximately 90% air, with the rest fiberglass. This gives them excellent
thermal insulation properties and also conserves mass (which is important in any rocket design)
The tile construction is denser near the surface to make the tiles more resistant to impact
damage, but the surface is also porous. This presents a difficulty as the glass fibre absorbs
water that can be held by the pores. This necessitates waterproofing of the surface between
each flight.
- Decelerating G-Forces:
Greater angles of re-entry mean greater rates of deceleration. This means a faster rate
of heat build up as kinetic energy is converted, but it also means that greater g-forces are
experienced by the occupants of the spacecraft.
It was known that optimum g-force was 3g, with the max tolerance being 8g (with some slight
chest pain, and perhaps loss of consciousness). However, studies had shown that during reentry the spacecraft’s optimum angles would generate up to 20 g-force.
Research was conducted into ways to increase tolerance of g-forces.
-
A transverse application of g-load is easiest to cope with as the blood is not forced
away from the brain. This means lying down instead of standing up during re-entry.
-
An eyeballs-in application is easier to tolerate rather than eyeballs, out. This means
that the astronaut should lift off forwards (facing-up) but re-enter backward (facing
down) since the g forces are always directed upwards.
-
Supporting the body in as many places as possible increases tolerance. A fiberglass
couch moulded to suit the body of a specific astronaut was ideal. This allowed for
successful experiments, with up to 20g experienced by the astronauts successfully.
- Ionisation Blackout
As heat builds up around a spacecraft during re-entry, atoms in the air around it become
ionized, forming a layer around the spacecraft. Radio signals cannot penetrate this layer of
ionized particles, preventing communication between the ground and the spacecraft. All
telemetry and verbal communication by radio is cut off for the duration of this ionisation
blackout, the length of which depends on the re-entry profile.
Ionisation Blackout is a period of no communication with a spacecraft due to a
surrounding layer of ionized atoms forming in the heat of re-entry.
- Reaching the surface
In a typical Apollo mission, the capsule would contain three astronauts, which would reach an
altitude of 120km, considered the “entry interface” (at an angle of 5.2 – 7.2 degrees). It
would then descend from this altitude over a range of approximately 3000 km, continually
slowing down, and at some point suffering ionisation blackout. In the last portion of the
descent, the parachutes would be released to slow it to about 33 km/h, Finally it would splash
down into the ocean, awaiting recovery.
This was one strategy used. Another involved, re-entry over land. However, in this case, the
cosmonauts would eject at a suitable altitude, descending to the ground by parachute on their
own.
The space shuttle, however has a unique solution for reaching the surface of the Earth. It does
not subject its occupants to a g-force greater than 3-g. As it has wings, the pilot is able to
control the altitude of the space shuttle and direct its descent.
During the period of maximum deceleration and heat, its nose is held up at an angle of 40
degrees, which slows its progress and presents the underbelly as a protected blunt surface.
Past this stage, it is flown in a series of sharp S-turns in order to control its descents. When it is
just 1.5km from the runway, it is gliding down an 18 degree gradient, much steeper than the 3
degree approach of a large airliner. When 500m above the ground, speed brakes are applied
(specialised flaps that increase drag) so that it settles to a 1.5 degree final approach. The crew
deploys landing hear and within seconds, the space shuttle touches down on its runway.

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 the orbit using Kepler’s Law of Periods
Orbital Velocity it the velocity required for an object to retain orbit around a body.
Orbital Velocity is defined by the following formula:
Derivation using Kepler’s Third Law:
Hence, it can be noted that the orbital velocity of an object is dependant solely upon the mass of the central
body and radius of the orbit and the gravitational Constant.
Therefore if the Mass of the central body were to be raised by a factor of 4, considering that the radius of
orbit, stayed the same, this meant a double in the magnitude of velocity of the satellite.
If the radius were to increase by a factor of 4, then considering the mass remained constant, the orbital
velocity would be cut in half.
It is independent upon the mass of the satellite.
This means a satellite of 1000 kg and a feather, need the same orbital velocity at any given
altitude.

Identify data sources, gather, analyse and present information on the contribution of
one of the following to the development of space exploration: Von Braun
Wernher von Braun was one of the most important rocket developers and champions of space exploration
during the period between the 1930s and the 1970s. From his teenage years, von Braun had held a keen
interest in space flight, becoming involved in the German rocket society, Verein fur Raumschiffarht (VfR), as
early as 1929. As a means of furthering his desire to build large and capable rockets, in 1932 he went to
work for the German army to develop ballistic missiles. While engaged in this work, von Braun received a
Ph.D. in physics on July 27, 1934.
Von Braun is well known as the leader of what has been called the “rocket team” which developed the V–2
ballistic missile for the Nazis during World War II. The V–2s were manufactured at a forced labor factory
called Mittelwerk.
The brainchild of von Braun’s rocket team operating at a secret laboratory at Peenemünde on the Baltic
coast, the V–2 rocket was the immediate antecedent of those used in space exploration programs in the
United States and the Soviet Union. A liquid propellant missile extending some 46 feet in length and
weighing 27,000 pounds, the V-2 flew at speeds in excess of 3,500 miles per hour and delivered a 2,200pound warhead to a target 500 miles away. First flown in October 1942, it was employed against targets in
Europe beginning in September 1944. By the beginning of 1945, it was obvious to von Braun that Germany
would not achieve victory against the Allies, and he began planning for the postwar era.
Before the Allied capture of the V–2 rocket complex, von Braun engineered the surrender of 500 of his top
rocket scientists, along with plans and test vehicles, to the Americans. For fifteen years after World War II,
von Braun worked with the U.S. Army in the development of ballistic missiles. As part of a military operation
called Project Paperclip, he and his rocket team were scooped up from defeated Germany and sent to
America where they were installed at Fort Bliss, Texas. There they worked on rockets for the U.S. Army,
launching them at White Sands Proving Ground, New Mexico. In 1950 von Braun’s team moved to the
Redstone Arsenal near Huntsville, Ala., where they built the Army’s Jupiter ballistic missile.
In 1960, his rocket development center transferred from the Army to the newly established NASA and
received a mandate to build the giant Saturn rockets. Accordingly, von Braun became director of NASA’s
Marshall Space Flight Center and the chief architect of the Saturn V launch vehicle, the super-booster that
would propel Americans to the Moon.
Thus it is clear that Von Braun had an enormous contribution to the development of space exploration –
mainly in that he was the chief architect of the Saturn rockets which allowed Americans to be the first to
reach the moon.
More on the V-2 rocket.
The A-4, later called the V-2, was a single-stage rocket fueled by alcohol and liquid oxygen. It stood 46.1
feet high and had a thrust of 56,000 pounds. The A-4 had a payload capacity of 2,200 pounds and could
reach a velocity of 3,500 miles per hour. On October 3, 1942 the A-4 was first launched from Peenemunde.
Breaking the sound barrier, it reached an altitude of sixty miles. It was the world's first launch of a ballistic
missile and the first rocket ever to go into the fringes of space.