9.2 Space

Michael Burton
School of Physics, UNSW, 
December 2000.   

Contextual Outline:

Humans have progressed in the last thousand years from animal powered transport on land and wind powered ships on water to vehicles that are sufficiently sophisticated to allow travel beyond the Earth into the solar system. 

Scientists have drawn on advances in areas such as aeronautics, materials science, robotics, electronics, medicine and energy production to develop viable spacecraft. Perhaps the most dangerous parts of any space mission are the launch, re-entry and landing. A huge force is required to propel the rocket a sufficient distance from the Earth so that it is able to either escape the Earth’s gravitational pull or maintain an orbit. There are many factors to be taken into account in choosing the time of day for a rocket to be launched. These include consideration of: the weather predictions for the launch date; whether there is an expectation that the craft will rendezvous with another orbiting body; and whether the landing site for an aborted mission is appropriate. Following a successful mission, re-entry through the Earth’s atmosphere provides further challenges to scientists if astronauts are to return to Earth safely. 

Rapid advances in technologies over the past thirty years have allowed the exploration of not only the Moon, but the Solar System and, to an increasing extent, the Universe. Space exploration is becoming more viable. Information and research undertaken in space programs have impacted on society through the development of such things as personal computers, advanced medical equipment, communication satellites, improved weather forecasting and accurate mapping of natural resources.

Speculation continues as we consider where humans will be travelling in the next one thousand years. Meanwhile, space research and exploration of space increase understanding of the Earth’s own environment, the Solar System and the Universe. 
 
 

Syllabus

The Earth has a gravitational field that exerts a force on objects both on it and around it.
  • Learn:
    • define weight as the force on an object due to a gravitational field
    • define the change in gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field, E=G m1 m2 / r
  • Perform:
    • perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion, computer assisted technology and/or other strategies and explain possible sources of variations from the value 9.8 ms-2
    • gather secondary information to identify the value of acceleration due to gravity on other planets
    • analyse information using the expression F=mg to determine the weight force for a body on Earth and the weight force for the same body on other planets


    Pendulum
    http://www.phy.ntnu.edu.tw/java/pendulum30/pendulum.html

    A java applet which simulates a swinging pendulum, allowing the student to calculate the acceleration due to gravity from T = 2 p root(L/g).  The length of the pendulum and height of the swing can be varied.  A more advanced version, which allows one to also vary the mass of the bob and the acceleration due to gravity, can be found at http://www.phy.ntnu.edu.tw/java/Pendulum/Pendulum.html.  However this is probably too complicated to be worth using.

    Weight, Energy
    The concepts in this part of the syllabus can be explained through teaching the physics behind the following formulae:
    F = mg = GMm / R2.
    E = KE + PE = 1/2 mv2 - GMm/R
    From v2/R = GM/R2 then PE = -2 KE, so that E = -GMm/2R
    Also, to escape must have E=0, which gives vesc2= 2GM/R

    Acceleration due to gravity on other planets found from above.  Calculated values shown in the table below.  However, to compare how much heavier/lighter you may be on another planet (a standard exam question!), all you have to do is calculate (M1/R12)/(M2/R22).  Table also shows Kepler's 3rd law (T2/R3).  To calculate mass of Sun we actually have T2=4p2 R3/GM. 
     
     
    Planet Mass Radius Period
    around Sun
    Distance
    from Sun
    g=GM/R2 T2/R3
      kg m s m m/s2 s2/m3
    Mercury 3.18E+23 2.43E+06 7.60E+06 5.79E+10 3.59  
    Venus 4.88E+24 6.06E+06 1.94E+07 1.08E+11 8.87 2.99E-19
    Earth  5.98E+24 6.37E+06 3.16E+07 1.50E+11 9.83 2.96E-19
    Mars 6.42E+23 3.37E+06 5.94E+07 2.28E+11 3.77 2.98E-19
    Jupiter 1.90E+27 6.99E+07 3.74E+08 7.78E+11 25.9 2.97E-19
    Saturn 5.68E+26 5.85E+07 9.35E+08 1.43E+12 11.1 2.99E-19
    Uranus 8.68E+25 2.33E+07 2.64E+09 2.87E+12 10.7 2.95E-19
    Neptune 1.03E+26 2.21E+07 5.22E+09 4.50E+12 14.1 2.99E-19
    Pluto 1.40E+22 1.50E+06 7.82E+09 5.91E+12 0.42 2.96E-19
    Moon 7.36E+22 1.74E+06      1.62  
    Sun 1.99E+30 6.96E+08      274  

    A demonstration of reduced gravity on the Moon can be seen from video clips of the Apollo astronauts walking about the surface.  For instance, in this movie clip of the Moon Rover from Apollo 16 observe how long it takes on the Moon for dirt to fall.  At first you think this is all because dust falls slowly due to air resistance - but then you remember there is no air on the Moon!  In fact if you look carefully you see that everything falls at the same rate, as of course it should do in a vacuum.  Note the Moon dust has been made through  grounding down rocks by micro-meteorite bombardment over the past 4.5 billion years and not by weathering!

Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth.
  • Learn:
    •  
    • 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
    • explain the concept of escape velocity in terms of the:
      •  gravitational constant
      •  mass and radius of the planet
    • discuss Newton's analysis of escape velocity
    • use the term ‘g forces’ to explain the forces acting on an astronaut during launch
    • compare the forces acting on an astronaut during launch with what happens during a roller coaster ride
    • discuss the impact of the Earth's orbital motion and its rotational motion on the launch of a rocket
    • analyse the changing acceleration of a rocket during launch in terms of the:
      •  Law of Conservation of Momentum
      •  forces experienced by astronauts
    • analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth
    • compare qualitatively and quantitatively low Earth and geo-stationary orbits
    • discuss the importance of Newton's Law of Universal Gravitation in understanding and calculating the motion of satellites
    • describe how a slingshot effect is provided by planets for space probes 
    • account for the orbital decay of satellites in low Earth orbit
    • 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
  • Perform:
    • solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components
    • solve problems and analyse information using v=u+at, vx2=ux2, vy2=uy2+2ayDy, Dx=uxt, Dy=uyt + 1/2ayt2 in relation to projectile motion
    • perform a first-hand investigation, gather secondary information and analyse data to describe factors, such as initial and final velocity, maximum height reached, range, time of flight of a projectile, and quantitatively calculate each for a range of situations by using simulations, data loggers and computer analysis 
    • identify data sources, gather and process information from secondary sources to investigate conditions during launch and use available evidence to and explain why the forces acting on an astronaut increase to approximately 3g during the initial periods of the launch
    • identify data sources, gather, analyse and present information on the contribution of Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O'Neill or von Braun to the development of space exploration
    • perform an investigation that demonstrates that the closer a satellite is to its parent body, the faster it moves to maintain a stable orbit
    • solve problems and analyse information to calculate centripetal force acting on a satellite undergoing uniform circular motion about the Earth
    • solve problems and analyse information using r3/T2 = GM/4p2
    • plan, chose equipment or resources for, and perform an investigation to model the effect that removal of the Earth’s gravitational force would have on the direction of satellite motion
    • plan, chose equipment or resources for, and perform a first-hand investigation to model the effect of friction and heat on a range of materials, including metals and ceramics


    Trajectories 1
    The Java applet at http://zebu.uoregon.edu/nsf/cannon.html (from the University of Oregon) allows an investigation of the trajectory of a projectile to be made, while varying the inclination, speed and the acceleration due to gravity.  A simplified version at http://zebu.uoregon.edu/nsf/cannon2.html only allows the angle of launch and the speed to be changed.  It is also possible to look at the effects of air resistance and wind speed, though you probably will want to leave these options turned off.  The aim is to see how far a cannon goes by altering these input variables, and then to hit a target by appropriate choice.  A suggested learning exercise has the student varying the acceleration due to gravity, then examining the relation between PE and KE, then altering the angle of launch, before trying to hit the target.  The basic relations can perhaps be derived mathematically first.  The exercise is as follows (though you may only wish to have your students do the first two parts, before attempting to hit the target in the absence of air resistance):
     

      Experimental Instructions
      (Note: Hit the "more" button when you run out of ammo!) 

      Conservation of energy:
      1.Set the angle of the cannon to 45 degrees.
      2.Set the velocity to 30.
      3. Shoot the cannon and note the distance.
      4. Double the gravitational acceleration (e.g.. move it so it reads -19.6).
      5. What must the velocity be set to, in order to cover the same distance as the previous shot?  Change the velocity, shoot the cannon until you have determined this.
      6. Now reset the gravitational acceleration back to -9.8.
      7. Set the velocity to 40 and the cannon angle to 70.
      8. Repeat steps 3 through 6.
      9. What is the relation between kinetic energy and gravitational acceleration as determined by this experiment? 

      Angles, Angles, Angles:
      1.Set gravity to -9.8.
      2.Set velocity to 50.
      3. Determine the cannon angle which produces the maximum horizontal distance of the shot.
      4. What is this angle and why do you think it has this value? 

      The effects of Drag:
      1.Set gravity to -9.8.
      2.Set velocity to 66.
      3. Shoot the cannon to hit the target.
      4. Now turn on the atmosphere by clicking the button that says drag.
      5. Set the windage to -10 and shoot the cannon and note how far the shot falls from the target.
      6. Set windage to -20,-30,-40 and repeat. Plot the distance from target versus wind velocity.

      The effects of projectile density:
      1. Keep drag turned on and set windage to -20.
      2. Keep velocity at 66; set density to 1.2.
      3. Shoot the cannon and note the distance.
      4. Decrease the density of the projectile by a factor of 2 (e.g. 0.6) and shoot the cannon and note the density.
      5. Now decrease density to 0.3 and then 0.15 shooting the cannon at each new value for density.
      6. Plot the decrease in distance as a function of density.
      7. Repeat steps 2-6 for windages of -10 and -40.

      Artillery Tests:
      In each case you have 4 chances to hit the target:
      1. Turn off drag if its on.
      2.Set the gravitational acceleration to -15.0.
      3. Hit the target (and record the correct velocity and angle).
      4. Turn on drag.
      5. Set windage to -50.
      6. Set density to 0.6.
      7. Hit the target in 4 tries and record the settings.
      8. Leave drag on.
      9. Set gravity to -2.
      10. Set windage to -10.
      11. Set density to 1.2.
      12. Hit the target in 4 tries and record the settings.


    Trajectories 2
    The Java applet at  http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html (from Michael Fowler) allows an investigation of Newton's classical thought experiment of firing cannon balls from a mountain top to find what speed is needed to achieve orbit - ie when the projectile is continuously falling at a rate which matches the curvature of the Earth.  Unfortunately the speeds are in mph not kph!

    Galileo's Experiment
    Let a ball roll from a fixed height down a groove in an inclined ramp.  Keep the bottom of the ramp parallel to the ground so that the ball is launched into the air with a fixed velocity, v, horizontally.  Mark where the ball strikes the ground and measure its horizontal distance from the launch point, x.  Then raise the height of the ramp, y, above the ground and repeat.  Plot x vs y - should get a parabola: y = 1/2 gt2 and x = vt so that y = gx2/2v2.

    Kepler' Laws
    The Table above (showing planetary data) also demonstrates Kepler's Third Law, r3/T2 = GM/4p2, and this can usually be applied by just showing that r3/T2 = constant.  For instance, when measured in AU (1 Astronomical Unit = Earth - Sun distance) and Years, then applying the formula to other planets shows directly either how much further from the Sun they are, or how many times longer their year is.

    The Java applet at http://www.physics.nwu.edu/ugrad/vpl/mechanics/planets.html (from North Western University in Chicago) illustrates Kepler's Laws in action for the orbit of two objects around one another.  The orbits and speeds can be viewed as (i) the relative mass of the planets, (ii) the orbital period, (iii) the step-time interval and/or (iv) the eccentricity are varied.  By selecting "show area", Kepler's Second Law can be demonstrated (equal areas in equal times).  The trajectories can be viewed from the centre of mass frame, or from the frame of either planet.

    The link at http://home.cvc.org/science/kepler.htm by Bill Drennon from a Californian high school provides animated images demonstrating the first two of Kepler's Laws and shows how the planetary orbits obey the Third Law.  There is also some background history on Johannes Kepler and Tycho Brahe, from whose diligent observations Kepler deduced his laws.

    Slingshot Effect
    Also known as gravity-assist, or gravity-boost, this is a way of adding velocity to a spacecraft as it passes by a planet.  It is used for interplanetary travel to reduce journey times and minimise fuel demands.  Essentially the satellite undergoes a "collision" with a planet, gravitationally interacting.  Gravity is a conservative force, so the collision is elastic.  Since the planet is so massive its velocity is effectively unaffected. 

    Consider an encounter where a spacecraft passes Jupiter, arriving in the opposite direction to Jupiter's orbit and leaving in the same direction as the orbit.   Momentum and energy conservation gives (an exercise for the Teacher!), with a little algebra, vpi - vsi = -(vpf - vsf) where p is for planet,  s for satellite,  i for initial and f for final.  Suppose the approach speed, before encounter, is 10 km/s.  Jupiter's orbital speed is 13.1 km/s.  Thus, -13.1-10 = -(-13.1-vsf).  Re-arranging gives vsf = -36.2 km/s - ie the satellite leaves with a speed more than 3 times faster than the approach!

    Satellite Tracking - NASA's J-Track Software
    J-Track is a fantastic resource which allows you to see the location of all satellites orbiting the Earth.  The paths of satellites can be seen in 2D, projected onto a map of the world, or in 3D showing their actual distribution in space.  The latter version, in particular, can be used in a highly educative way to illustrate a number of features of spaceflight, and the different functions of spacecraft. 

    It works using Java applets, so should work on your machine once you download the database. In particular, you can find out where the Hubble Space Telescope, the Mir space station, the Space Station and the Space Shuttle (during missions) are right now, watch their progress across the surface of the Earth and see when they will next be visible from your location.  The 3D version is particularly useful for illustrating orbital mechanics, by studying the varying distributions of satellite orbits, which reflect the purposes for which the satellites are used for.  Some background material on the different types of satellites in use can be found by consulting John Graham's on-line book on "Space Exploration: from talisman of the past to gateway for the future" , particularly chapters 24-27.

    2D Version: http://liftoff.msfc.nasa.gov/RealTime/JTrack/Spacecraft.html 
    Shows Satellite location over Earth map.

    Mouse controls:

     
    Click on craft Change orbital data in lower right 
    Ctrl+Click on craft Toggles on/off ground trace
    Shift+Click on craft Goes to web page about craft
    Click+hold on map Display when first visible at longitude

    For instance, use the software to find when the Space Station will next be visible at night, and what trajectory it will take across the sky, and then go out and watch it pass overhead!

    3D version http://liftoff.msfc.nasa.gov/RealTime/JTrack/3D/JTrack3D.html 
    Shows 3D distribution of satellites 

     Mouse controls:
    Shift+Click Zoom In
    Ctrl+Click Zoom Out
    Click on satellite Show Trace
    Click in list Show Trace
    Drag Rotate in 3d

    Under "Satellite", then "Select" choose the following options for illustrative viewing:

    • Astronomy - IUE, HST, ROSAT, Chandra, XMM - a variety of orbits, some highly elliptical in order to get a long way from the Earth for much of the orbit - to minimise radiation from Earth, but HST is in LEO.
    • Communications - Geostationary orbits - fixed above one location -e.g. Inmarsat with  global phone coverage, but requires high power.
    • Human Crew - all in LEO (Low Earth Orbit).
    • Iridium - Low Earth Polar Orbit for low power phones, with global coverage.
    • Military-  GPS - full-earth coverage from circular orbits - fix your position precisely.
    • Weather-  GOES - geostationary orbits but several older satellites now oscillating above and below equatorial plane - can be used for communication at the South Pole (e.g. GOES 3)!
    Select a satellite, and find what its orbital radius, period and speed are (under "View" then "Satellite Position"), showing that the faster it moves the closer it is to the Earth, and also demonstrating Kepler's Third Law.

    Rocketry, Launch, Re-entry and Orbital Decay
    The fundamental principle for rocketry is Newton's Third Law, for every action there is an equal and opposite reaction, together with the conservation of momentum.  Ejection of propellant at high speed through a nozzle in a direction opposite to that desired will propel a spacecraft forward.  Moreover, this works in a vacuum, as well as an atmosphere (better in fact) (unlike flying)!

    Following the basic force-energy relations (see earlier), to achieve orbit, v2/R = GM/R2 so v = root(GM/R) = 7.9 km/s.  To escape vesc= root(2GM/R) = 11 km/s.  Launch is helped using an equatorial location, where the Earth's rotational velocity of 0.5 km/s, in an eastward direction, reduces the energy requirements a little.

    During launch the maximum acceleration reached by human-crewed spacecraft is 3g.  A description of the experience is given on this NASA Q&A fact sheet.  This is toward the end of the burn in which nearly 2000 tons of fuel is used, 7 minutes after launch.  Once thrust is cut, however, weightlessness follows as the spacecraft is now in orbit, with everything in it continuously "falling".

    To return to Earth the orbital velocity must be reduced to zero.  Firing rockets in the opposite direction to the orbital velocity reduces the speed, decreasing the total energy, and putting the spacecraft into an elliptical orbit which will intersect the Earth's atmosphere.  The primary reduction in speed, however, comes from aerodynamic drag with the atmosphere (otherwise spacecraft would have to carry enormous fuel tanks to return to Earth).  Both through compression of the air and through friction, substantial heat is produced (spacecraft are travelling at Mach 25 at re-entry).  This must be radiated away to avoid melting the spacecraft!  The most efficient means is through a shock wave (think about the bow wave caused by a high speed boat on a river - much of the energy for powering the boat goes into driving this wave).  This is produced best through a blunt shape to the craft (ie exactly the opposite to what's needed at launch!).  It is also essential for the craft to radiate heat away as quickly as possible - hence the special tiles on the underbelly of the Shuttle - to dissipate heat.  These are made of ceramic material, with a porous structure.

    If the angle of approach is too steep, frictional heating will be too fast and burn the spacecraft up.  If the angle of approach is too shallow the spacecraft will skip off the atmosphere into a highly elliptical orbit which will take it far from the Earth (think about skipping a stone across a pond).  There is thus an optimum angle for re-entry.

    For satellites in Low Earth Orbit there will be some residual friction with the atmosphere (space is not a perfect vacuum!), which will continually work to reduce the energy of the satellite.  Since E = -GMm/2R the orbital radius will decrease, increasing the frictional drag.  Thus the orbit gradually decays until the frictional heating with the atmosphere becomes too great and the satellite burns up.

    Demonstration of Rocketry Principle
    Blow up a balloon and let the air escape before tying it up!  Newton's Third Law propels the balloon forward, and conservation of momentum determines the velocity.

    Demonstration of the Effect of Removing Gravitational Field on Orbit
    Attach a ball to a piece of string or ribbon.  Swing it around, say about your head or even around a globe of the Earth (thus simulating a orbit).  Cut or let go of the ribbon at your hand.  The ball with continue in a straight line with the ribbon streaming out behind it, showing its path, and illustrating Newton's First Law (ie state of uniform motion).

    Some Notes on  Historical Figures in  the Development of Space Exploration
    Konstantin Tsiolkovsky (1857-1935)

    • Russian mathematician.
    • "Father" of astronautics.
    • Proposed to escape Earth's gravity through launching from top of tower reaching from Earth to geostationary orbit (36,000 km high).  Wrote book called "Beyond the Planet Earth" about life in a spindle-shaped spacecraft at this position.
    • Conceived idea of the rocket - continuous, propellant driven vehicle to escape the Earth, giving precise control of acceleration and orbit.
    • Conceived of fundamental formula for rocket motion, essentially applying Newton's Third Law to derive the quantity of "specific impulse" (impulse is F/Dt).
    • However his work was virtually unknown outside even his home town (Kaluga) - Oberth and Goddard developed similar principles independently.


    Hermann Oberth (1894-1989)

    • German (actually Transylvanian by birth).
    • Wrote key book in 1923  on "The Rocket into Planetary Space" out of his PhD dissertation.
    • Book inspired rocket societies to spring up all over the world, one of which lead directly to the development of the V2 rocket. 
    • Book covered manned and unmanned rocket flight, liquid fuel rocket construction, propulsion, inertial guidance and navigation, aerodynamics, thermodynamics, flight mechanics, pre-testing, life-support systems, spaceflight hazards and their remedies, bio-astronautics, re-entry and recovery techniques, telescopic tracking and applications of rocket technology to spaceflight.  All in 87 pages!
    • Described the basic theoretical principles for thrust and determining the most favourable velocity to reach a target planet.


    Robert Goddard (1882-1945)

    • American.
    • Conducted practical experiments in rocketry.
    • Determined they worked better in vacuum than in air (when most people mistakenly believed air was necessary for the rocket to push against).
    • Developed solid and liquid-propellant rockets, with first successful flight with liquid in 1926.


    Robert Esnault-Pelterie (main work 1912-1930)

    • French.
    • Calculated trajectories to the planets.
    • Analysed significance of relativity theory to spaceflight, assessed probabilities for extra-terrestrial life.
    • Investigated nuclear propulsion.
    • Coined the word "astronautics".


    Gerard O'Neill (1969)

    • American.
    • Conceived plans for space colonies at stable Lagrangian points between Earth-Moon (L5) - wrote book on this called "The High Frontier".
    • Devised concept of "mass-driver" and "electromagnetic slingshot" to accelerate cargoes into orbit from the Moon (eg after mining) and towards catcher ships.


    Werner von Braun (1912 - 1977)

    • German, then  American.
    • Developed V2 rocket in WW2.
    • Devised concept of space-station.
    • Devised concept of the space-shuttle.
    • Devised first comprehensive scenario for reaching Mars (and inter-planetary travel).
    • Directed NASA's space-flight program in the 1950s and 1960s.
Future space travel and exploration will entail a combination of new technologies based on current and emerging knowledge. 
  • Learn:
    • discuss the limitation of current maximum velocities being too slow for extended space travel to be viable
    • describe difficulties associated with effective and reliable communications between satellites and earth caused by:
      •  distance
      •  van Allen radiation belts
      •  sunspot activity
  • Perform:
    • gather, process, analyse and present information to compare the use of microwave and radiowave technology as effective communication strategies for space travel

    •  

       
       
       

    Extended Space Travel
    Pioneer 10, 11, Voyager 1 and 2 are now heading for interstellar space at speeds of 10-17 km/s.  Will travel 1 light year in ~30,000 years.  Nearest star is 4 light years away (Alpha Centauri) - so an impracticable method for travel to the stars.  Some possible methods of interstellar transportation (all well beyond our current technology) include:
      • Nuclear fusion, ejecting stream of ionized gas, accelerating to ~0.1c.  However only ~0.4% mass released as energy - require stupendous fuel loads.
      • Antimatter rockets - react antimatter with matter, and eject debris through nozzle.  Much more efficient, might only need a few kg of antimatter - however we cant make antimatter in bulk!
      • Light sails - using momentum carried by photons.  Sunlight too weak except for miniature payload, so would need to construct and direct enormous laser (with telescope several hundred km in diameter in order to focus it!) at sails several km across and billions of kms away.
      • Interstellar ram-jet, scooping up interstellar matter and fusing - would need scoop several 1000 km across - magnetic confinement?
      • World ships, taking human colonies that live for several  generations, to reach destination.  Using current technology to accelerate ship.
      • Relativistic time dilation. The Lorentz factor, g = 1/root(1-v2/c2) = 2.3 for v=0.9c, 7 for v=0.99c and 22 for v=0.999c.  This is the factor by which time is slowed for the space travellers.  Need high Lorentz factors to be practicable!
      • Suspended animation - over hundreds of years.
    Warp Drive Now!  There is no such thing as warp drive, but in this site NASA scientist Marc Millis assesses the prospects for achieving propulsion breakthroughs that would make interstellar travel possible.  Particularly relevant to the HSC is his discussion on why interstellar travel is so tough

    Light Travel Time
    Light travels at 300,000 km/s.  Thus, the following delays are encountered for communication within our Solar System.
     
    Object Distance Light Delay
    Space Shuttle 400 km 0.001 seconds
    Geosynchronous Satellite 36,000 km 0.1 seconds
    Moon 384,000 km 1.3 seconds
    Mars (closest approach) 80 million km (0.5 AU) 4 minutes
    Sun 150 million km (1 AU) 8 minutes
    Jupiter (closest approach) 630 million km (4 AU) 35 minutes
    Pluto (closest approach) 6 billion km (39 AU) 6 hours
    Alpha Centauri  (nearest star) 4 million, million km 4 years

    Thus light travel time is significant in our own Solar System; cf operation of Pathfinder spacecraft on Mars or Galileo spacecraft at Jupiter - need robotic operation.  Time delay even noticed in long distance telephone calls, especially if the call is routed through more than one geostationary satellite.

    Communication Disruptions with Satellites
    Van Allen belts are where charged particles from the Sun are trapped in the Earth's magnetic field.  Two doughnut-shaped rings surrounding the Earth - inner and outer belts.  Produce currents which flow along magnetic field lines.  As particles collide with upper atmosphere they create aurorae by exciting the atoms and molecules to excited energy levels.  Produces strong radio emission from synchrotron - charged particles spiralling about the Earth's magnetic field.  Increases in times of Solar Storms, with the extra flux of charged particles from the Sun.  Sunspot activity, associated with magnetic fields on the Sun's surface, are sites for solar flares and mass ejections of particles.  Communication disruptions will be caused when satellites pass through the radiation belts, eg the South Atlantic Anomaly. 

    Microwave and Radiowave Communication Technology for Space Communication
    I am afraid I do not understand what the syllabus writer intends with this concept point.

       


Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light. 

  • Learn:
    • 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 critical experiments in science, such as Michelson-Morley's, in making determinations about competing theories
    • outline the nature of inertial frames of reference
    • discuss the principle of relativity
    • identify the significance of Einstein’s assumption of the constancy of the speed of light
    • recognise that if c is constant then space and time become relative
    • discuss the concept that length standards are defined in terms of time with reference to the original meter
    • identify the usefulness of discussing space/time, rather than simple space
    • account for the need, when considering space/time, to define events using four dimensions
    • 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
    • discuss the implications of time dilation and length contraction for space travel
  • Perform:
    • perform an investigation and gather first-hand or secondary data to model 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: Lv = L0 root(1-v2/c2) and tv = t0 / root(1 - v2/c2)
    • gather, process, analyse information and use available evidence to discuss the relative energy costs associated with space travel
    The Metre
    • 1792 the new Republic of France defined the metre as one ten-millionth the distance from the North Pole to the equator.
    • Not very practicable, so re-defined as the distance between two scratches on a platinum-iridium bar in the International Bureau of Weights and Measures in Paris at STP.
    • Awkward, so new standard defined  based on wavelength of light.
    • In 1960 re-defined as 1,650,763.73 wavelengths of an orange-red line emitted by Kr86 in a gas discharge tube.
    • Available everywhere, repeatable.
    • Re-defined again in 1983 as even this was not proving accurate enough for high precision.
    • Now defined in terms of the speed of light: 1 metre is the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.
    • This now defines the speed of light as 299,792,458 m/s!
    • The mass standard is currently a particular block of metal, but this will eventually be re-defined in terms of the mass of an atom.


    Relativity Teaching Thoughts
    A possible route to to follow when teaching the subject:

    • There are two key concepts to get across, the Postulates of Special Relativity:
      • Laws of Physics are the same everywhere in inertial frames.
      • Speed of light constant for all observers.  This is the one which causes all the apparent paradoxes!
    • Concept of measuring an event, and placing space-time co-ordinates to it.
    • Simultaneity no longer holds, as it takes time for information about an event to reach an observer!
    • By looking at the same event from two reference frames we then find that different observers perceive different time intervals for that event. 
    • It is important to compare measurements to the "Proper Time", t0, which is the time interval for an observer who sees the event at the same place.  Time dilation occurs for observers moving with respect to this frame of reference, tv = t0 / g, where g = root(1 - v2/c2).  ie the moving observer sees the event go more slowly (takes longer).
    • Similarly, comparing the length of an object to the "Proper Length", L0, the length measured in the reference frame where the object is at rest, we get Lv = L0 g.  The object has contracted for the moving observer.
    • This is probably was far as you will wish to take your students.  However, if you wish to introduce E=mc2, and do more than just state the result, you will have to introduce the concept of relativistic momentum, as in the next two points:
      • Momentum conservation still holds if we now consider relativistic momentum, gmv, instead of just mv.
      • Further, by defining the total energy of a particle as gmc2 =  mc2 + K where K is the relativistic kinetic energy, we end up with the famous E=mc2.
    Relativity Simulations on the Web
    There are many sites devoted to Relativity on the web, both Special and General.  However they are generally at too high a mathematical level to be useful for the HSC.  Here are some sites you might like to try, even if only for your own edification.
    • Relativity Visualisation Sites  No longer works - let me know if you find the new link so that I can correct this! A starting point for searching for Relativity on the web.  Broken down into popular science sites, visualisation sites and tutorial sites.
    • Special Relativity  An extensive site from Andrew Hamilton in Colorado with a number of illustrations for Special Relativity, but at a level above the HSC.  However the graphics depicting time dilation might be useable.
    • C-Ship from John Walker offers some spectacular images showing how Special Relativity appears to distort our view, by  ray-tracing images of the effects seen from a space-ship travelling at relativistic speeds through the Galaxy.  Effects like the Lorentz Contraction, Time Dilation, Doppler Shift and the Aberration of Light are all illustrated.  Unfortunately, most of this is at too advanced a level.
    • The Light Cone A tutorial on Relativity, leading you through all the concepts of Relativity, and setting the scene with the historical background.  Extensive animated graphics illustrating the concept of the light cone.
    Relativity Notes and Paradoxes
    • UNSW First Year Physics lecture notes, from Joe Wolfe, in pdf format.  A succinct summary of Special Relativity.
    • The Twin Paradox.  Further notes from Joe Wolfe on this well-known paradox involving time dilation.
    • The Pole Paradox.  Yet more notes from Joe Wolfe on this well-known paradox involving length contraction.
    • Usenet Relativity FAQ.  Frequently asked questions and answers about Relativity. Includes discussion on the paradoxes such as the Pole & Barn and the Twins, amongst many other topics.  A good place to find answers to those curly questions your students might have thrown up!  Incidentally there is no point in your trying to disprove relativity by arguing that special relativity doesn't actually explain the Twin Paradox (as some people are want to do), as SR doesn't deal with acceleration correctly.  Yes, it is true that General relativity needs to be taken into account to study the apparent paradox fully, but this is way beyond the level of HSC.  The simple thought experiment, without any consideration of how one accelerates and decelerates, is more than sufficient for HSC level, and if you want to look further for your own edification then look at one of the references above - but you will need to wade through the mathematics!
    • Stephen Hawking's home page.  OK, its not in the syllabus, but everyone seems to want to know about Hawking.  His work is in GR, not SR though!
    • Listen to Einstein talking about E=mc2.
    • Spacetime 101.  The most readable discussion on the physics of relativity I have come across, by Patricia Schwarz of Cal Tech.  The level is about right (at least for the teachers!) and there are some easy-to-understand animated graphics illustrating key concepts through thought experiments. I suggest looking at the first two sections; (i) what is space-time and (ii) why was relativity needed.  In latter sections you might look at some of the graphics but ignore the maths.


    The Michelson-Morley Experiment
    Possibly the most important null experiment in Physics history.  Designed to measure our motion with respect to the aether, the postulated medium for light.  Found no result from observing the difference in travel times from two orthogonally directed beams, whatever was tried.  Pushed the experimental technique to the limits.  The conclusion: the aether cannot be detected, which is another way of saying there is no medium needed for the passage of light.  Some websites devoted to discussion on the subject include:


    Inertial Reference Frames
    Frames that move at constant velocity with respect to one another.  Rotating frames are not inertial reference frames.  Strictly speaking, the Earth is not an inertial frame of reference, but this only really manifests itself on large-scales, such as weather systems and ocean currents.

    Experimental Tests for Inertial Reference Frames

    • Hang a pendulum in a car or train.  Mark position of stationary bob on a table.  When in motion if bob moves away from this position the system is non-inertial - eg when accelerating, rounding a corner.
    • Place ball on merry-go-round (or rotating table).  As ball is rolled along a radial line if it veers away from that line the frame is non-inertial, as occurs when its rotating.



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