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
m
1 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

T
2 = 4pi2 l/g
g = (4pi
2l)/T2

If you plot T
2 vs L


gradient = (4pi
2)/g


Assumptions:

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

Vertical Component:

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)  
W
a 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

Rotational motion:
Orbital motion:

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:

Liftoff:

Weightlessness:

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.

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

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

Heating
g-forces
Ionisation Blackout
Landing

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.

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.


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.

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.

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.

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

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

Many other physicists tried to explain the result including
Lorentz-Fitzgerald:

Einstein:

9.2.4.2.4 Outline the nature of inertial frames of reference

9.2.4.2.5 Discuss the principle of relativity

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

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

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

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

Time dilation

Mass dilation

The relativity of simultaneity

The equivalence between mass and energy

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

9.2.4.3.2 Distinguish between Inertial and Non Inertial frames of reference

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

Mirror thought experiment:

Similtenuinty:

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

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.