Topic 1: Space

9.2.1.2.1 Define weight as the force on an object due to a gravitational field.

Weight is the force on an object due to a gravitational field.

9.2.1.2.2 Explain that a change in Gravitational Potential Energy (GPE) is related to work done

Potential energy is energy which is stored in an object by doing work on that object.

Gravitational potential energy of an object is the energy that an object possesses due to its position in a gravitational field

- Change in energy = work done

- When gravitational potential energy increases, work is done on the object

When gravitational potential energy decreases, work is done by the object

9.2.1.2.3 Define GPE as the work done to move an object from a very large distance away to a point in a gravitational field.

Where Ep is the GPE

G is the universal gravitational constant (6.67x10-11)N.m2.kg-2

m1 and m2 are the two masses of the objects

r is the distance between their centres of masses.

We say an object has zero gravitational potential energy at an infinite distance away from a massive object. So as it reaches a finite distance away from the massive object, its gravitational potential energy must be must be decreasing, therefore it is negative

9.2.1.3.1 Determining ‘g’ using a simple pendulum

1. Attach a 50g mass carrier to the end of a string and tie the opposite end to the clamp on the retort stand

2. Measure the length of the pendulum from the point of support to the base of the mass

3. Set the pendulum in motion with <30° deviation and using a stopwatch time 10 complete oscillations

4. Repeat steps 2 and 3 at least 5 times varying the length of the pendulum

5. Calculate g using the formula below and average results

T is time of period

L is length of string

T2 = 4pi2 l/g

g = (4pi2l)/T2

If you plot T2 vs L

gradient = (4pi2)/g

Assumptions:

- No friction or air resistance
- String has no mass and string always tight
- Motion only occurs in two dimensions

9.2.1.3.2 The physics of the gravity of different planets

and

9.2.1.3.3 Calculating the weight of objects on other planets

and

The weight of an object near the surface of the Earth is the same as the force due to gravity of the Earth acting on the mass of the object. So equating the two:

Thus you can predict the value of any object on any planet using this formula.

9.2.2.2.1 Describe the trajectory of an object within the Earth’s gravitational field in terms of vertical and horizontal components.

2 Components:

Horizontal Component

- In systems we analyse it does not change.

Vertical Component:

- Affected by gravity

At any time on its flight the projectile is undergoing motion in the vertical and horizontal axises.

9.2.2.2.2 Describe Galileo’s analysis of projectile motion.

Galileo showed that projectile motion could be understood by analysing the horizontal and vertical components of the motion separately. He considered a canon and reasoned that while gravity is pulling the object down the projectile is also moving forward.

9.2.2.2.3 Explain the concept of escape velocity in terms of the Gravitational constant and the mass and radius of the planet

At an infinite distance from earth EP = 0, so to reach that far (as kinetic energy is converted into GPE):

As EK = ½ MV2 , the formulae can be rearranged to get:

9.2.2.2.4 Outline Newton’s concept of escape velocity

Newton thought that if you put a canon on a hill and fired it the ball would crash into the ground further and further away at higher velocities. Therefore he reasoned that there was a velocity that would cause the cannonball to go into orbit around the Earth. He also said that if the ball was fired faster than that value it could travel into space. The lowest speed at which that happens is the escape velocity.

9.2.2.2.5 Identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch.

G forces are equal to apparent weight over real weight. Thus they are a multiple of the felt gravity.

Ra is what is on the bathroom scales (wherever)(sum of forces opposing true weight)

Wa is your weight (on earth 9.8 times m)

Simply: 1+ a/g

9.2.2.2.6 Discuss the effect of the Earth’s orbital motion and its rotational motion on the launch of a rocket

- Rockets are launched in an easterly direction to gain extra momentum from Earth’s rotational motion (Earth spins on its axis West to East)
- As the earth moves the quickest at the equator then they try to launch closest to there
- Extra momentum results in increased velocity hence increasing kinetic energy
- Greater momentum and kinetic energy results in less fuel requirements and ability to carry greater loads
- Cape Canaveral is perfect for this as launching east is into the ocean and it is the southernmost part of mainland USA.

- Space probes are launched in the same direction as the Earth’s orbit to gain the Earth’s orbital velocity
- Increases space probes initial velocity, increasing momentum and kinetic energy resulting in less fuel and ability to carry greater loads

9.2.2.2.7 Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts.

The mass of the rocket decreases as fuel is burned and exhaust is expelled from the rocket. With a constant thrust, the magnitude of the acceleration of the rocket will increase.

After engine cut-off, the rocket is still experiencing the gravitational force of the Earth, so it experiences acceleration towards the earth even though it is still moving away from the earth. As a = (t-w)/m

Law of Conservation of Momentum does not apply to a rocket-fuel system near Earth as it is not isolated (force of gravity). If we ignore this then we can say that the momentum before (0) is equal to the momentum as it launches (rocket fuel out of the back and thrust forward). However it does apply in deep space where the external effects of gravity are negligible.

Forces on an Astronaut:

On ground:

- If they are lying in a seat on a stationary rocket then the net force on the astronaut is zero.
- 1G

Liftoff:

- Upwards thrust (T)
- Downward weight (mg)
- As the thrust gets greater the Astronaut experiences more forces (from the thrust)

Weightlessness:

- When the engines get turned off or in between stages, reaction force is zero.
- Only force is weight

9.2.2.2.8 Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth

To maintain a circular orbit the net force must be acting towards the centre of the circle. This force is called the centripetal force. For a satellite, this is typically provided by gravity (from the earth).

Motion: | Centripetal force provided by: |

Whirling mass on a string | The tension in the string |

Electron orbiting atomic nucleus | Electron-nucleus electrical attraction |

Car cornering | Friction between tyres and road |

Satellite revolving around Earth | Gravitational field of Earth |

9.2.2.2.9 Compare qualitatively low Earth and geostationary orbits

Low Earth Geostationary

Radius | Low | High |

Orbital Velocity | Faster | Slower |

Orbital Period | Short | Long (24 hours) |

Position in Sky | Moves fast across the sky | Fixed (above equator) |

Uses | Photography | Weather, telecommunications |

Type | Polar/elliptic | Circular, equatorial and east |

9.2.2.2.10 Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the satellite and the radius of the orbit using Kepler’s Law of Periods.

Orbital Velocity: The velocity an object must travel to stay in orbit.

- Depends on the radius of the planet.

Orbital velocity occurs when centripetal force = Gravitational Force

Where M is the mass of the planet

9.2.2.2.11 Account for the orbital decay of satellites in low Earth Orbit

- Satellites in low Earth orbit experience friction due to the atmosphere and ionosphere, resulting in a loss of energy as heat energy
- The satellite drops to an altitude that corresponds with its lower energy in an even denser region of the atmosphere leading to further loss of energy
- Orbital decay is continuous and speeds up until eventually heat from collisions causes the satellite to burn up

9.2.2.2.12 Discuss issues associated with the safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface

- The earth’s atmosphere provides aerodynamic drag on the spacecraft and as a result high temperatures are generated by friction.
- Can be tolerated using radiation tiles with ablating surfaces or insulators that absorb heat
- Can be minimised by attacking at a flatter (blunt) angle, generates a shock wave dissipating heat.

- Too shallow and the spacecraft will bounce back into space
- Too steep and the g forces too great to survive and temperatures high

- Particles ionise as they collide with the spacecraft preventing communication signals to Earth- may last for 16 minutes
- This problem has been solved for the space shuttle by communicating via a satellite above it, since only the bottom of the shuttle has significant ionisation.

- Parachutes can be used prior to splashing into the ocean or touching down on the ground
- Landing on an airstrip
- Wings to slow the spacecraft near the earth’s surface

9.2.2.2.13 Identify that there is an optimum angle for safe reentry for a manned spacecraft into the Earth’s atmosphere and the consequences of failing to achieve this angle.

The optimum angle of reentry is 6.2o +- 1o relative to the earth’s horizon.

- Too shallow and the craft will bounce into space (like a skipping stone)
- Too deep and the g forces will be too large to bear and heat.

9.2.2.3.1 Be able to solve problems involving projectile motion

and

9.2.2.3.2 Examine projectile motion

Break down initial vector into components.

Look at y axis

Look at x axis

(Recreate final vector)

9.2.2.3.3 The Early Rocket Scientists who contributed to space flight.

- Werner Von Braun (1912-1977) was a visionary who initially was a rocket scientist but later worked for NASA.
- During the war Von Braun developed the V2 rocket which was used to hit England, however he dreamed of sending rockets to other planets. The V2 was manufactured using slave labour and used ethanol and liquid oxygen as fuel.
- After the war Von Braun and his team developed the first high-precision inertial guidance system on the redstone rocket.
- In 1952, Von Braun suggested the development of a space station which later inspired the on in 2001: A Space Odyssey. He also proposed the construction of a lunar base.
- He also published a plan for a manned flight to Mars and proposed a precursor to the space shuttle.
- His team developed the Saturn V which took Armstrong and Aldrin to the moon.

9.2.2.3.4 Centripetal forces and circular motion calculations

As we know f = ma you can solve for acceleration. M refers to the thing moving in a circle.

9.2.2.3.5 Solve problems using Newton’s modification of Kepler’s Third Law

M is the mass of the thing being orbited.

9.2.3.2.1 Describe a gravitational field in the region surrounding a massive object in terms of its effect on other masses in it.

- Newtonian gravity is the force of attraction that exists between two masses
- A gravitational field exerts a force on objects within its field which pulls the object towards the centre of the field
- The heavier the masses the greater the gravitational force between them

g = f/m

9.2.3.2.2 Define Newton’s Law of Universal Gravitation

and

9.2.3.3.2 Solve problems with Newton’s universal gravitation equation.

9.2.3.2.3 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 greatly important in understanding and calculating orbital motion as it depends on the force of gravity acting on the satellite
- Satellite motion/centripetal force is only possible due to gravity between the satellite and the planet that it’s orbiting
- Newton’s law can be used to derive Kepler’s Law of Periods forming an integral tool in understanding orbital motion

9.2.3.2.4 Identify that a slingshot effect can be provided by planets for space probes.

The slingshot effect is performed to achieve an increase in speed and/or a change of direction of a spacecraft as it passes close to a planet. As it approaches, the spacecraft is caught by the gravitational field of the planet, and swings around it. The speed acquired is then sufficient to throw the spacecraft back out again, away from the planet. By controlling the approach, the outcome of the manoeuvre can be manipulated and the spacecraft can acquire some of the planet’s velocity, relative to the Sun.

Relative to the Planet

Relative to the Sun

9.2.3.3.1 Discuss the factors affecting the strength of the gravitational force.

- Distance from the equator

- g is larger near the poles as the earth bulges near the equator as a result of the rotation of the earth.
- The apparent strength of g is also less at the equator as the earth is rotating.

- Local variations in the density of crust or lithosphere

- g will be greater near geological layers with greater density

- Altitude

- g decreases with altitude due to greater distance from the centre of the earth

- Location of the Moon and Sun

- g will vary depending on the location of the Moon and Sun relative to the earth.

- Mass/Size of planet

9.2.4.2.1 Outline the features of the aether model for the transmission of light

- The aether was a hypothetical medium which was believed to fill all space and would carry light waves as all waves were thought to require a medium for their propagation.
- It was thought to be the absolute reference frame.
- The aether:

- Filled all space
- Was perfectly transparent
- Permeated all matter but was permeable to all material objects
- Had low density in free space
- Was very stiff to accommodate light waves through it

9.2.4.2.2 Describe and evaluate the Michelson-Morley (MM) attempt to measure the relative velocity of the Earth through the aether

and

9.2.4.2.3 Discuss the role of the MM experiments in making determinations about competing theories.

and

9.2.4.3.1 Interpret the results of the Michelson-Morley experiment

The aim was to measure the speed of the earth relative to the aether. An experiment like this was set up:

It was based on the notion that if the earth was moving through the aether, there would be an aetherial wind which could impact the speed of light relative to it.

The experiment was then rotated and the interference patterns were compared in order to attempt to calculate how much of an impact the Aether wind had and so the relative velocity could be calculated.

HOWEVER

There was no interference and so no difference in the interference pattern. This made a null result.

It suggested

- Aether was at rest with respect to earth (however this is not possible)

Many other physicists tried to explain the result including

Lorentz-Fitzgerald:

- Suggested that one arm of the experiment contracts in the direction of motion through the aether.

Einstein:

- Twenty years later Einstein proposed the theory of relativity producing a set of predictions, not all of which were testable at the time
- In modern times the predictions have been tested and found to be correct
- The null result of the Michelson-Morley experiment supported evidence for Einstein’s theory of relativity

9.2.4.2.4 Outline the nature of inertial frames of reference

- Frame of reference is what you are measuring against
- Inertial frame of reference

- Stationary or travelling at a constant velocity
- Newton’s 3 laws apply

9.2.4.2.5 Discuss the principle of relativity

- The basic laws of physics are the same in all inertial frames of reference

9.2.4.2.6 Discuss the significance of Einstein’s assumption of the constancy of the speed of light.

- Explained the null result of Michelson-Morley experiment
- Rendered the Aether model superfluous
- Logically resulted in relative space and time
- He stated:

- Laws of physics have the same form in all inertial frames of reference
- Light travels through space with a definite speed c independent of the speed of the source of observer

9.2.4.2.7 Identify that if c is constant then space and time become relative

- Velocity is distance divided by time. This means that if the speed of light is constant (v) when seen by two observers travelling at different speeds, then the length and time interval which is measured by both observers must be different in different reference frames
- That is, if ‘c’ becomes constant, then space and time both become relative, and vary depending on the frame of reference

9.2.4.2.8 Discuss the concept that length standards are defined in terms of time in contrast to the original length standard.

- 1st length standard was a platinum iridium rod however it expands and contracts
- 2nd was a multiple of wavelength of krypton 80
- 3rd was the length of a path travelled by light in a vacuum in a given time interval.

- Best as we can measure time with atomic clocks to a greater accuracy than mass or length

9.2.4.2.9 Explain the consequences of special relativity in relation to: simultaneity, equivalence between mass and energy, length contraction, time dilation, mass dilation.

Length contraction

- In any frame of reference in motion other than its rest frame, an object will appear shorter in the direction of this motion

Time dilation

- In any frame of reference other than its rest frame, a time interval between two events will be measured to be longer than its rest frame

Mass dilation

- In any frame of reference other than its rest frame, an object will appear to have greater mass than its rest frame

The relativity of simultaneity

- Two events which are simultaneous in one reference frame, may not necessarily be simultaneous in another reference frame which is in relative motion to the first

The equivalence between mass and energy

- As objects cannot exceed the speed of light, the extra energy goes into the mass of the object (E = MC2)

9.2.4.2.10 Discuss the implications of mass increase, time dilation and length contraction for space travel

- Mass increases, therefore greater force must be applied to accelerate the spaceship
- Time dilates, occupants of spacecraft experience a shorter time of flight than that measured by people that are in the inertial frame of reference
- Length contracts, thus distance to travel appears shorter
- This is why spacecraft can never travel at the speed of light
- Also means we are limited and so to get anywhere would take years at the fastest possible speeds

9.2.4.3.2 Distinguish between Inertial and Non Inertial frames of reference

- A mass will only hang directly down in an inertial (or non-accelerated) frame of reference; it will hang in other directions in non-inertial (or accelerated) frames of reference. Try letting one hang from your hand while you are standing still or walking with a steady velocity (that is, a steady speed in a straight line). Next, try accelerating to a run, stopping quickly or changing direction. How did the mass react under each of these conditions?
- You should be able to test these observations by taking your mass on a ride in a car or bus. Do not look out the window, but only observe the mass.

9.2.4.3.3 Analyse some of Einstein’s thought experiments involving mirrors and trains

Einstein’s thought experiments were a way of communicating his ideas in a simple, easy to understand way. They allowed his ideas to be considered before proofs became available

- Einstein predicted that he would see his face normally in a mirror if sitting in a train travelling at the speed of light as he was in an inertial frame of reference
- However with vector addition, a stationary observer would see light travelling away from Einstein’s face at c, but as the train was also moving at c, the observer would see light travel twice the distance in the same amount of time.

Similtenuinty:

- Therefore the time observed for light to travel that distance had increased, so that a stationary observer would see light travelling at c.

9.2.4.3.4 Analyse information to discuss the relationship between theory and the evidence supporting it, using Einstein’s predictions based on relativity that were made years before evidence was available to support it.

In 1924 Sir Arthur Eddington showed that light was bent by the gravity of the moon (Einstein predicted that this would happen)

Atomic clocks

- Using the Hafele-Keating experiment, it was proven that faster clocks were seen to pass time less quickly than slower
- Four synchronised atomic clocks were used. Two were placed on commercial air flights and were flown in opposite directions around the world
- When later compared after circumnavigating the world, it was found that both clocks showed less time had passed than the clocks on the ground.
- This proves Einstein’s Time Dilation theory (clocks on moving objects can slow)

9.2.4.3.5 Perform calculations using Einstein’s special relativity equations.

Clocks on moving objects run slow - observer sees longer time.

Proper time: Time seen on observer’s own clock.