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Astronomy 345: Exploring Planetary Systems II
Session 2014-15
11 Lectures, starting January 2015
Lecturer: Dr E. Kontar
Kelvin Building, room 615, extension x2499
Email: Eduard (at) astro.gla.ac.uk
Lecture notes and example problems -
Exploring Planetary Systems II
CONTENTS 2
Contents
1 Introduction to Space Exploration 6
1.1 Recommended literature and useful resources: . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Time and Energy considerations and space exploration . . . . . . . . . . . . . . . . . . . . . 8
1.4 Solar system probes: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 History of rocket propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5.1 First man-made satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Voyager mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Solar Probe Plus mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7.1 Benefits of space exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Rocket (Tsiolkovsky) equation 18
2.1 Rocket thrust, exhaust velocity and rocket equation . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Rocket thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Example of rocket equation application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Multi-staging, vertical motion in Earth gravitational field 28
3.1 Principle of multi-staging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Vertical motion in Earth gravitational field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Rocket launching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Vertical range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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CONTENTS 3
4 Rocket Launch aspects 38
4.1 Efficiency of delivering energy to payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Rocket Launch with pitch angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Flight path angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Angle of attack and aerodynamic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Dynamic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Evolution of the flight speed and path angle 48
5.1 Gravity turn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Path angle evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 Uniformly changing path angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Orbital injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.5 Actual launch trajectory: Ariane 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.6 Actual launch trajectory: Pegasus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Orbits and spaceflight 60
6.1 Elliptical transfer orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Energetic considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3 Orbital transfer fuel requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.4 Orbital transfer to a moving target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7 Gravity assist or slingshot 74
7.1 Gravity acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.2 Gravity deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.3 Example: Pioneer 10 encounter with Jupiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
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CONTENTS 4
7.4 Maximum boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.5 Oberth effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.6 Lagrange point parking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.7 L-points and astrophysical missions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8 Thermal rocket engines 91
8.1 Thrust and the effect of the atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.2 Optimising the exhaust nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.3 Exhaust velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.4 Optimising exhaust velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.5 Mass flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.6 Vulcaine engine of Ariane 5 launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.7 Saturn V Rocket engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.8 Liquid fuel characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9 Electric propulsion 107
9.1 Basics of electric propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
9.2 Vehicle velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.3 Electric thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.4 Electrothermal thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
9.5 Ionising thrusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
10 Electric thrust 118
10.1 Space charge limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
10.2 Electric field and potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
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CONTENTS 5
10.3 Choice of the propellant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.4 How efficient are ion thrusters? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
11 Solar sails and space environment 131
11.1 Solar sails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
11.2 Radiation pressure vs gravitational force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
11.3 IKAROS solar sail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
11.4 Solar wind pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
11.5 Space environment and hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
11.6 Radiation in space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
11.7 Solar energetic particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
11.8 Plasma environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
11.9 Space debris, micro-meteroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Exploring Planetary Systems II
1 INTRODUCTION TO SPACE EXPLORATION 6
1 Introduction to Space Exploration
1.1 Recommended literature and useful resources:
These lecture notes are based on the material from the following books:
Martin Turner, Rocket and spacecraft propulsion: Principles, Practice
and New Developments, Springer Praxis Books, 2006, e.g. Amazon
George P. Sutton and Oscar Biblarz, Rocket Propulsion Elements,
Wiley, 2001 see, e.g. 8th edition from Wiley, 2010
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1 INTRODUCTION TO SPACE EXPLORATION 7
1.2 Background and motivation
Since much of the current solar system knowledge is from exploration
rather than observation,
EPS1 course concentrates on planetary systems, i.e. observations or
‘what’ is observed. The observations are, of course, is based on remote
sensing.
EPS2 course is devoted to exploration, i.e. spaceflight technique or
‘how’ of exploration
Why most of the extra-solar system science is ‘observational’? - Be-
cause of the energy budget and timescales.
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1 INTRODUCTION TO SPACE EXPLORATION 8
1.3 Time and Energy considerations and space exploration
Time constraint: Suppose we have 1-tonne (10
3
kg) probe sent c/3
to a star 15 lightyears away (for simplicity we also ignore relativity)
Travel time is 45 years
Communication time is 15 years
In total we need 60 years to retrieve information from the probe, i.e. a
long time !
Energy budget: Kinetic energy of the spacecraft is mv
2
/2,
i.e. 0.5 ×10
3
×10
16
=0.5 ×10
19
J.
In 2008, total worldwide energy consumption was 470 exajoules
5 ×10
20
J, (or the UK energy production in 2012
1
was 5 exajoules
5 ×10
18
J)
1
see
Exploring Planetary Systems II
1 INTRODUCTION TO SPACE EXPLORATION 9
Taking into account efficiency and man-
ufacturing costs increases the energy
requirement, indeed just getting the probe
we need 1% of the entire planet energy
production (which is approximately the
entire UK energy production for 1 year)!
Hence interstellar probes are not a likely
prospects at the moment.
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1 INTRODUCTION TO SPACE EXPLORATION 10
1.4 Solar system probes:
Contrast this with solar system probes:
Time to travel 1 AU is about 0.5 year.
We need probe speed 10 km/s (Earth escape speed)
Hence energy requirements 0.5 ×10
3
10
8
J, e.g. 10
7
of interstellar
probe - feasible.
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1 INTRODUCTION TO SPACE EXPLORATION 11
1.5 History of rocket propulsion
Konstantin Tsiolkovsky
(1857-1935)
Rocket propulsion has surprisingly
long history. Theory was done about
140 years ago:
1883 - space travel concept (escape
velocity and weightlessness)
1895 - artificial satellites
1903 - rocket equation
Initially all works were theoretical...
Exploring Planetary Systems II