1. HSC Science Teacher Professional Development Program Physics
8:30am Space and Gravity
Michael Burton
9:45am Physics of Climate
Michael Box
15 minute tea break
11:00am The age of silicon: semiconductor materials and devices
Richard Newbury
1:00pm Lunch

2. Presentations will appear on www.phys.unsw.edu.au/hsc

3. Space and Gravity Some 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
Kepler’s 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
mg=GMm/R2 and 1/2mvesc2=GMm/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
1/2mvesc2=GMm/(rsync+rplanet)

9. rsync
Vescape
(surface)
(elevator)
Tascent
km/hr)
1000 km
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. Kepler’s Laws Empirical Laws
[Kepler 1: Elliptical orbits, a focus]
[Kepler 2: Equal areas equal times]

12. [Plot r vs. T then log r vs. log T]
Kepler’s 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
Venus
108
0.6
Jupiter
778
11.9

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? (~1:2:4:8)

14. Gravitational Slingshot Hohmann Transfer Orbit
Journey to Mars
Gravitational Slingshot
Hohmann Transfer Orbit

15. Gravity Assist to the Planets Cassini mission to Saturn
Venus, Venus, Earth, then Jupiter, on way to Saturn!
Took 6.7 years, with V=2 km/s
Hohmann transfer orbit would have taken 6 years but required a V=15 km/s – impracticable!

16. How Gravity Assist works
Relative to Stationary Observer:
Spacecraft enters at -v, Planet moving at +U
Goes into circular orbit
Moving at U+v relative to surface of planet
Leaves at U+v relative to surface in opposite direction
Thus leaves at 2U+v 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

19. Olympus Mons
600 km across x 24 km high!

20. The Gorgonum Chaos

21. Water on Mars Polar Ice Caps

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, Earth, 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 Made Hohmann 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/[(R+R’)/2]
Step 2: Elliptical orbit to heliocentric orbit around Mars
E3= –GMm/R’
m=50 tonnes
Orbit, a
E=–GMm/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=[(R+R’)/2]3 when measured in Years and Astronomical Units
T=[( )/2]3/2=1.4 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 =44.1° behind Mars
Harder Problem: how often do launch windows occur?

30. Questions to consider? How do we know this is the cheapest fuel orbit?
Can’t be less (wouldn’t arrive), needn’t 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