Download Space Syllabus Summary

9.2 Space
1. The Earth has a gravitational field that exerts a force on objects both on it and around it
Students learn to:
 define weight as the force on an object due to a gravitational field
The weight force on an object is equivalent to the force that the Earth exerts on that object as a result
of it being in the Earth's gravitational field. An object's weight is the product of its mass and the
acceleration due to gravity.
 explain that a change in gravitational potential energy is related to work done
To lift a body to a greater height requires that we must do work on the body, against the gravitational
field. This work done is equal to the energy released as kinetic energy when it moves back to its
starting point.

define gravitational potential energy as the work done to move an object from a very large
mm
distance away to a point in a gravitational field E p   G 1 2
r
Students:
 perform an investigation and gather information to determine a value for acceleration due to
gravity using pendulum motion or computer-assisted technology and identify reason for possible
variations from the value 9.8 ms-2
A pendulum with a known length was angularly displaced and allowed to swing in one plane. The
period was determined by timing 10 oscillations then dividing the time by 10. This was repeated 5
times and an average period calculated. These steps were carried out with 4 other length pendulums,
increasing by 10cm for each length. The values for the period squared (seconds2) were graphed
against the lengths (in metres), i.e. (L vs. T2) and the slope was found. When divided by 4π2 the
experimental value for the acceleration due to gravity was determined.
Possible variations: - different areas on the Earth have thicker crust = g increases
- the Earth is not a perfect sphere: it is flattened at the poles, so g is higher at the
poles
- g is lower at high altitudes
 gather secondary information to predict the value of acceleration due to gravity on other planets
A moon of Saturn has a mass of 9.1x1020 kg and a diameter of 14500 km. What is the acceleration
due to gravity on that moon?
Use formula g = GM/r2 where G is the gravitational constant: 6.67x10-11, M is the mass of the
moon and r is the radius of the moon.
Diameter = 14500 km = 14500000 m r = 14500000  2 = 7250000 m
So g = (6.67x10-11 x 9.1x1020) (72500002)
= 1.15x10-3 ms-2

analyse information using the expression: F  mg to determine the weight force for a body on
Earth and for the same body on other planets
What is the weight force of a man of mass 84.0 kg on Earth?
F = mg
= 84.0 x 9.8
= 823.2 N
What is his mass on Saturn's moon (in above question)?
F = mg
= 84.0 x 1.15x10-3
= 0.097 N
2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable
orbit and return to Earth
Students learn to:
 describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational
field in terms of horizontal and vertical components
 describe Galileo’s analysis of projectile motion
Galileo described projectile motion as the superposition of two independent and perpendicular
motions. The trajectory of a projectile will follow a parabolic path. Projectile motion involves both a
horizontal and vertical component. The horizontal component is unaffected by the weight force of
the projectile  it remains constant (ignoring air resistance etc). The vertical component is subjected
to the weight force of the projectile and  experiences an acceleration of 9.8 ms-2 towards the centre
of the Earth.

explain the concept of escape velocity in terms of the:
–
gravitational constant
– mass and radius of the planet
The escape velocity is related to the minimum kinetic energy (KE) required to carry a massive body
from the planet's surface to an infinite distance away (GPE=0). Thus, when the GPE is zero, the KE
will also be zero, as all of it will have been converted to gravitational potential energy. Since the
GPE and KE are both equal to zero, the formula for each can be equated:
mm
1
/2m2v2 = E p   G 1 2
If velocity is made the subject, we have a formula for escape velocity:
r
v = √(2Gm1/r). Therefore, the escape velocity is independent of the body's mass, and proportional to
the square root of the mass of the planet and the gravitational constant. It is inversely proportional to
the square root of the radius of the planet.
 outline Newton’s concept of escape velocity
Newton proposed that if a projectile was launched horizontally from an elevated position (eg
mountain) with enough velocity, its rate of fall would be equal to the rate of fall of the Earth's
surface, and it would therefore enter an orbit around the Earth. If the velocity required to stay in orbit
were exceeded, then the projectile would escape the gravitational field of the Earth. The minimum
velocity at which this is possible is called the escape velocity.

identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during
launch
G forces are measured in units of gravitational acceleration. They represent a person's apparent
weight expressed as a multiple of their normal weight. It is used because it is convenient and easy to
understand. For example, astronauts experience up to 4 g's during launch. This means they would
feel 4 times as heavy as they normally would.
 discuss the effect of the Earth‘s orbital motion and its rotational motion on the launch of a rocket
If a rocket is launched in the same direction as the Earth's rotational motion (east), then this motion
will increase the rocket's initial velocity, thus decreasing the amount of fuel required to reach the
escape velocity. If the rocket is launched against the Earth's rotational motion, its initial velocity will
be negative (i.e. in the opposite direction) more fuel/energy is required. Launching a rocket in the
same direction as the Earth's orbital motion will give the rocket a higher orbital velocity than Earth's
and cause the radius of the rocket's orbit around the sun to be greater than Earth's. The opposite
occurs when the rocket is launched against the orbital motion: orbital velocity and radius decrease.

analyse the changing acceleration of a rocket during launch in terms of the:
–
Law of Conservation of Momentum
– forces experienced by astronauts
According to the Law of Conservation of Momentum, during the launch of a rocket, the momentum
of the gases being expelled from the rocket must be equal to the momentum of the rocket as it moves
away from the Earth's surface: mgvg = mrvr. However, as fuel is expended the rockets mass (mr) will
decrease, so to conserve momentum the rocket's velocity (vr) will increase. The continual increase in
its velocity indicates that it is accelerating. Since the thrust (force) is constant and the mass is
decreasing, the acceleration must be changing (increasing) and is  non-uniform.
An increasing acceleration would cause astronauts on board to feel increasingly heavier. If the
acceleration becomes too great, astronauts may experience dangerous effects such as blackouts, and
cardiovascular/respiratory problems.

analyse the forces involved in uniform circular motion for a range of objects, including satellites
orbiting the Earth
In a body undergoing uniform circular motion, the net force is always perpendicular to the object's
velocity. This net force is the centripetal force and is dependent on the body's mass, velocity and
radius, according to the formula: Fc = mv2/r. For a satellite orbiting Earth, the centripetal force is the
gravitational force acting on the satellite due to the Earth's mass. For a car moving in a circular path
(e.g. roundabout) the centripetal force is supplied by the friction between the tires and the road.
 compare qualitatively low Earth and geo-stationary orbits
Orbit
Low Earth
distance above Earth lower, variable
position above Earth variable
velocity
higher, variable
period
shorter, variable
uses
space shuttles, space stations, military
problems
orbital decay
Geostationary
higher, fixed (35800 km)
equatorial
lower, fixed
longer, fixed (24hrs)
communications, weather monitoring

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 is the velocity required by an object to remain in orbit at a fixed distance from a
central body. For circular motion, if the distance/time formula is used, the orbital velocity is equal to
the distance travelled by the body in one revolution (circumference: 2r) divided by the time taken
to complete one revolution (period: T). v = 2r/T. Using Kepler’s Law of Periods, a formula for
3
r
GM
orbital velocity can be derived: 2 
T
4 2
42r3/T2 = GM
42r2/T2 = GM/r
2r/T = (GM/r)
Since v = 2r/T,
v =(GM/r)
Therefore, orbital velocity is proportional to the square root of the gravitational constant (G) and the
mass of the central body, and inversely proportional to the square root of the radius of its orbit. It is
independent of the mass of the orbiting body (satellite).

account for the orbital decay of satellites in low Earth orbit
A satellite in low Earth orbit collides with gaseous molecules as it moves through the atmosphere.
These collisions create friction between the satellite and atmosphere, known as atmospheric drag,
which slows the speed of the satellite over time. Consequently, the altitude of its orbit decreases.
Atmospheric drag increases as the altitude decreases, thus the orbit decays and the satellite spirals
down toward Earth.
discuss issues associated with safe re-entry into the Earth’s atmosphere and landing on the
Earth’s surface
Re-entry at too steep an angle can have dangerous consequences, such as high g-forces that could
injur or kill astronauts, and at too shallow an angle the craft will bounce off the atmosphere.
Therefore, for safe re-entry, the spacecraft enters the stmosphere at an optimum angle of 5-7. Once
the spacecraft is in the atmosphere, atmospheric drag occurs, producing large amounts of heat that
may damage the spcecraft. To prevent damage, silica tiles are placed on the exterior of the spacecraft
to absorb heat. For a safe landing, it is important that the spacecraft steadily slows down. This is
achieved by "breaking ellipses": without using fuel, the spacecraft glances off the atmosphere on the
first approach and is slowed by atmospheric friction. This causes it to move in an elliptical path. The
process is then repeated until its speed is such that it is safe to land.

identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earth’s
atmosphere and the consequences of failing to achieve this angle
The optimum angle for safe re-entry into the Earth's atmosphere is between 5 and 7. If the
spacecraft were to enter at a steeper angle (7-9) the g-forces would kill those on board, and entering
at >9 will cause the spacecraft to burn up, while if the angle were too shallow (0-5) the spacecreaft
would "bounce" off the atmosphere.

Students:
 solve problems and analyse information to calculate the actual velocity of a projectile from its
horizontal and vertical components using:
v2x  u2x
v  u  at
2
2
v y  u y  2a y y
x  u x t
1
y  u yt  a y t 2
2
A projectile is launched at an angle of 45o to the horizontal and just clears a fence 6 metres high at a
horizontal distance of 100 metres from the launch site. Determine the velocity at which the
projectile was launched.
First, use x = uxt :
100 = uxt
Since the angle is 45 o, ux = uy so
100 = uyt
Now we use y = uyt + 1/2at2 :
6 = uyt + 1/2 x -9.8t2
From above right, we know that uyt = 100 so,
6 = 100 - 4.9t2
-94 = - 4.9t2
19.2 = t2
t = 4.4s
Now sub this value into x = uxt
100 = ux x 4.4
ux = 22.7 ms-1
N.B.
ux = uy = 22.7ms-1, so to calculate the
actual velocity use Pythagoras:
a2 + b2 = c2
22.72 + 22.72 = 1030.6
1030.6 = 32.1 ms-1
6m
45o
100m
 perform a first-hand investigation, gather information and analyse data to calculate initial and
final velocity, maximum height reached, range and time of flight of a projectile for a range of
situations by using simulations, data loggers and computer analysis

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, EsnaultPelterie, O’Neill or von Braun
Robert Goddard was the first person to prove that rockets would work in a vacuum, reasoning that an
atmosphere was not required for thrust and therefore established the possibility of spaceflight. In
1926 he successfully developed the first liquid propellant rocket. Many of Goddard's techniques and
methods in designing rockets are still in use.

solve problems and analyse information to calculate the centripetal force acting on a satellite
2
mv
undergoing uniform circular motion about the Earth using: F 
r
Calculate the size of the centripetal force acting on a satellite of mass 2000kg moving in a circle of
radius 6680km with a period of 24hrs.
Use displacement on time formula to find velocity: v = s/t
= 2r/T (circumference of circle/period)
= (2 x 6680000m)/(24x60x60)
= 485.8ms-1
2
Now find force: F = mv /r
= 2000 x 485.82/6680000
= 70.7 N
3
r
GM
 solve problems and analyse information using: 2 
T
4 2
Using Kepler's Law of Periods show that the altitude required for a satellite to have a period of 24hrs
is 42247 km.
r3 = GMT2/42
= 6.67x10-11 x 6x1024 x (24x60x60)2/42
= 7.57x1022
r = 3(7.57x1022)
= 42297524m
 42300km (the discrepancy here is due to values of G, M etc being rounded off)
3. The Solar System is held together by gravity
Students learn to:
 describe a gravitational field in the region surrounding a massive object in terms of its effects on
other masses in it
A gravitational field is a region around a massive body where a force of attraction is exerted on other
masses.
mm
 define Newton’s Law of Universal Gravitation: F  G 1 2 2
d
A gravitational force of attraction exists between any two masses in the universe. The force between
two masses (m1 and m2) whose centres are separated by a distance (d), is proportional to the product
of their masses and inversely proportional to the square of their separation.
 discuss the importance of Newton’s Law of Universal Gravitation in understanding and
calculating the motion of satellites
Newton’s Law of Universal Gravitation is very important in predicting the motions of satellites
around the Earth and planets around the sun. By equating the formula for gravitational force,
F = GMm/d2 with the formula for centripetal force, F = mv2, a range of formulae can be derived
which give values for a satellite's velocity and period for any given distance from Earth, and viceversa. However, the orbits of satellites are elliptical rather than circular, so formulae must be
modified in order to yield accurate values.

identify that a slingshot effect can be provided by planets for space probes
Students:
 present information and use available evidence to discuss the factors affecting the strength of the
gravitational force
Factors affecting the strength of the gravitational force are the masses of both objects and their
distance of separation. Mass is proportional to the strength of the gravitational force. For example,
consider the gravitational force between the Earth and a 1kg object on its surface:
F = GMm/d2
= (6.67x10-11 x 6x1024 x 1) / (6.37x106)2
= 9.86 N
Now when the mass of the object is 100kg:
F = (6.67x10-11 x 6x1024 x 100) / (6.37x106)2
= 986 N
Therefore the strength of the force increases as the mass increases.
The strength of the force is inversely proportional to the distance between the two objects. If the 1kg
object discussed above is placed at a height of 100km above the Earth's surface, we should expect
the strength of the force to decrease:
F = (6.67x10-11 x 6x1024 x 1) / (6.37x106 + 100,000)2
= 9.56 N  the strength of the force decreases as the distance increases.
mm
 solve problems and analyse information using: F  G 1 2 2
d
4. Current and emerging understanding about time and space has been dependent upon
earlier models of the transmission of light
Students learn to:
 outline the features of the aether model for the transmission of light
 describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth
through the aether
 discuss the role of the Michelson-Morley experiments in making determinations about competing
theories
 outline the nature of inertial frames of reference
 discuss the principle of relativity
 describe the significance of Einstein’s assumption of the constancy of the speed of light
 identify that if c is constant then space and time become relative
 discuss the concept that length standards are defined in terms of time in contrast to the original
metre standard
 explain qualitatively and quantitatively the consequence of special relativity in relation to:
- the relativity of simultaneity
- the equivalence between mass and energy
- length contraction
- time dilation
- mass dilation
 discuss the implications of mass increase, time dilation and length contraction for space travel
Students:
 gather and process information to interpret the results of the Michelson-Morley experiment
 perform an investigation to help distinguish between non-inertial and inertial frames of
reference
 analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and
discuss the relationship between thought and reality
 analyse information to discuss the relationship between theory and the evidence supporting it,
using Einstein’s predictions based on relativity that were made many years before evidence was
available to support it
 solve problems and analyse information using:
E  mc 2
lv  l0 1
tv 
c2
t0
1
mv 
v2
v2
c2
m0
1
v2
c2