HSC Science Teacher Professional Development Program Physics

1
HSC Science TeacherProfessional Development
ProgramPhysics

• 830am Space and Gravity
• Michael Burton
• 945am Physics of Climate
• Michael Box
• 15 minute tea break
• 1100am The age of silicon semiconductor
  materials and devices
• Richard Newbury
• 100pm Lunch

2
Presentations will appear onwww.phys.unsw.edu.au/
hsc
3
Space and GravitySome ideas for HSC Physics

• Michael Burton
• School of Physics
• University of New South Wales

4
Gravity and the Planets

• Escaping from a Planetary Surface
• Acceleration due to Gravity
• Escape Velocity
• Geostationary Orbit and the Space Elevator
• Keplers Third Law
• The Planets
• Jupiter and its Moons
• Travelling the Solar System
• Slingshot effect
• Mission to Mars and the Hohmann Transfer Orbit

5
What is an Orbit?

• Falling at just the right speed so that we travel
  around the planet rather than toward it.
• No energy is required to maintain the orbit once
  it has been obtained!

6
Assumed Knowledge
7
Weight and Escape Velocity

• mgGMm/R2 and 1/2mvesc2GMm/R
• Compile for each planet and compare
• e.g. how heavy would a bag of sugar be on Earth,
  Mars, Venus and Jupiter?
• how fast must you launch it to escape each planet?

Weight Escape Speed (km/s)
Earth 1.0 11
Mars 0.4 5
Venus 0.9 10
Jupiter 2.5 40
8
(Geo-)Synchronous Orbit and the Space Elevator

• Synchronous Orbit when
• orbital period rotational period of the planet
• Space Elevator ascends to the synchronous orbit
• Lower escape speed
• 1/2mvesc2GMm/(rsyncrplanet)

9
rsync Vescape (surface) Vescape (elevator) Tascent (_at_100 km/hr)
1000 km km/s km/s days
Earth 36 11 4 15
Mars 17 5 2 7
Venus 1532 10 0.7 638
Jupiter 89 60 40 37
10
Question and Exercises

• Calculate (geo-)synchronous orbit
• Compare between planets
• Which might be feasible, which impossible?
• How might it be built??? (carbon nanotubes?)
• How massive?
• How long would it take to ascend?
• What gain in reduced escape speed?
• How much more mass for the same thrust?
• (extra energy available for accelerating the
  payload)

11
Keplers Laws

• Empirical Laws
• Kepler 1 Elliptical orbits, Sun _at_ a focus
• Kepler 2 Equal areas equal times

12
Keplers Third Law

• Exercise 1 Research r and T for planets and
  investigate the relation between them
• Plot r vs. T then log r vs. log T

r T T2/r3
106 km Years yr2/km3
Earth 150 1.0 3x10-25
Mars 228 1.9 3x10-25
Venus 108 0.6 3x10-25
Jupiter 778 11.9 3x10-25
13
K3L and the Moons of Jupiter

• Use a web application, e.g.
• jersey.uoregon.edu/vlab/tmp/orbits.html
• Record positions of moons every day (use ruler)
• Plot on graph paper
• Determine orbital period and radius for each
  moon.
• Do they fit K3L? (yes!)
• What relationship between their periods?
  (1248)

14
Journey to Mars

• Gravitational Slingshot
• Hohmann Transfer Orbit

15
Gravity Assist to the PlanetsCassini mission to
Saturn

• Venus, Venus, Earth, then Jupiter, on way to
  Saturn!
• Took 6.7 years, with ?V2 km/s
• Hohmann transfer orbit would have taken 6 years
  but required a ?V15 km/s impracticable!

16
How GravityAssist works

• Relative to Stationary Observer
• Spacecraft enters at -v, Planet moving at U
• Goes into circular orbit
• Moving at Uv relative to surface of planet
• Leaves at Uv relative to surface in opposite
  direction
• Thus leaves at 2Uv relative to observer
• e.g. Spacecraft moving at 10 km/s encounters
  Jupiter moving at 13 km/s. Leaves at 36 km/s!
• Conservation of energy and momentum applies
  planet must slow (very!) slightly
• In practice we would need to fire engines to
  escape from a circular orbit. However, one could
  enter on a hyperbolic orbit, with a gain in speed
  of slightly less than 2U.

17
Mars
Discuss!

• The planet Mars, I scarcely need remind the
  reader, revolves about the Sun at a mean distance
  of 230 million km, and the light and heat it
  receives from the Sun is barely half of that
  received by this world. It must be, if the
  nebular hypothesis has any truth, older than our
  world and long before this Earth ceased to be
  molten, life upon its surface must have begun its
  course. The fact that it is scarcely one seventh
  the volume of the Earth must have accelerated its
  cooling to the temperature at which life could
  begin. It has air and water and all that is
  necessary for the support of animated existence.

H.G. Wells, The War of the Worlds, 1898
18
(No Transcript)
19
Olympus Mons
600 km across x 24 km high!
20
The Gorgonum Chaos
21
Water on MarsPolar Ice Caps
22
(No Transcript)
23
Sedimentary Rock layers of time
24
Recent water flow on Mars
24 April, 2005
22 December, 2001
25
The Hohmann Transfer Orbit

• Most Fuel Efficient orbit to the planets
• Three Parts
• Circular orbit around Earth
• Elliptical orbit, perihelion _at_ Earth, aphelion _at_
  Mars
• Circular orbit around Mars

Wolfgang Hohmann, German Engineer, 1925
26
Energy in an Orbit
Applies for elliptical orbit, semi-major axis
a Etotal GMm/2a constant in an orbit
27
Assumptions MadeHohmann Transfer Orbit

• Only considering gravitational influence of the
  Sun (OK)
• Apply thrust without changing mass of spacecraft
  (Wrong!)
• Assume circular orbits for the planets (OK)
• Consider only impulsive thrusts (i.e. no slow
  burns)

28
Energy Changes

• Step 1 Heliocentric orbit around Earth to
  elliptical orbit with Earth at perihelion and
  Mars at aphelion
• E1 GMm/R
• E2 GMm/(RR)/2
• Step 2 Elliptical orbit to heliocentric orbit
  around Mars
• E3 GMm/R

m50 tonnes Orbit, a EGMm/2a ?E
x 106 km x 1013 J x 1012 J
Earth Orbit 150 -2.2
Transfer Orbit 189 -1.8 4.6
Mars Orbit 228 -1.5 3.0
29
Time Launch

• Time taken is half the orbital period for the
  elliptical orbit.
• Use K3L!
• i.e. T/2 where T2(RR)/23 when measured in
  Years and Astronomical Units
• T(1.01.5)/23/21.4 years
• Thus it takes 0.7 years
• Launch Window
• Mars covers T/2/Tmars x 360 135.9
• Spacecraft covers 180
• Thus, Launch when Earth 180-135.944.1 behind
  Mars

Harder Problem how often do launch windows occur?
30
Questions to consider?

• How do we know this is the cheapest fuel orbit?
• Cant be less (wouldnt arrive), neednt be more
  (overshoot)
• How much change in energy is needed?
• Relate to amount of fuel?
• Best time to launch a few months before
  Opposition
• Why? (44.1) Why not at Opposition?
• How long will the journey to Mars take?
• Compare to Journey to Moon (3 days), to Jupiter
  (2.8 yrs).
• How often can we launch (every 2.1 years for
  Mars)?
• Implications for return journey (first window
  after 1.5yrs)
• Implications for human exploration of the Solar
  System
• What do we need humans for, what can a robot do
  better?
• What about lift-off from Earth, landing on Mars?

31
The End