Spacecraft Simulation Games Fundamentals © by Jarek Francik Kingston University, London 2012.
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Transcript of Spacecraft Simulation Games Fundamentals © by Jarek Francik Kingston University, London 2012.
Realistic vs Unrealistic
• Unrealistic Simulation– Popular in films and games since
the times of Star Wars (long time ago...)– Spacecraft considered as Aircraft in the space
• Realistic Simulation– no aerodynamic drag– no streamlined shapes– gravity and inertia being the most significant forces
(besides the thrust)
Star Wars logo image is in public domain at Wikimedia Commons
Gravity
• Gravity at the surface of our planet:
this formula is useless in the space
• Newton’s gravity formula:
mgFg
2R
MmGFg
211 )/(10674.6 kgmNG
Gravity
• Gravity at the surface of our planet:
this formula is useless in the space
• Newton’s gravity formula:
mgFg
2R
MmGFg
gR
MG
2
211 )/(10674.6 kgmNG
Zero Gravity
v
FG
FC
FG = -FC
Images: “The Blue Marble“ Earth image by NASA,“Sputnik 1” spacecraft from claudelafleur.qc.ca/ (GNU License)
both available at Wikimedia Commons
Zero Gravity
Balance between Gravitational & Centrifugal Force
CG FF
2R
MmGFg
R
mvFC
2
R
mv
R
MmG
2
2
1
2v
R
MG
R
MGv
2v
MGR
Cosmic Speed
• Newton’s cannonball will never return to the ground if it exceeds the First Cosmic Speed:
(for the Earth)skm
R
MGv 91.7
Cosmic Speeds
• First Cosmic Speedminimum speed for Newton’s cannonball to stay on the orbit for the Earth
for the Sun
• Second Cosmic Speed a.k.a. Escape Velocityspeed required to break permanently from the gravity fieldcan be calculated from energetic equation: for the Earth
for the Sun
R
MGvI
R
MGvII 2
skmvI 91.7
skmvI 74.436
skmvII 19.11
skmvII 64.617
Cosmic Speed
Calculation of the Second Cosmic Speed (advanced)KG EE
R
MmGEg
2
2mvEK
2
2mv
R
MmG
22 vR
MG
R
MGvII 2
Orbits
• Orbits are in fact not circles: they are ellipses• The planet is located in one of the focus point
slow
fast
Near-planet gravitational acceleration is often used to launch spacecraft onto long-distance journeys, for example to the Moon or Mars
Orion spacecraft and Earth imagesby NASA, Wikimedia Commons
Orbits• Rules of planetary motion was
first formulated by Johannes Kepler in 1609-1619
• Kepler’s laws of planetary motion(extra-curricular):1. The orbit of every planet is an ellipse
with the Sun at one of the two foci.2. A line joining a planet and the Sun
sweeps out equal areas during equal intervals of time.3. The square of the orbital period of a planet is directly
proportional to the cube of the semi-major axis of its orbit.
Spaceflight Basics
• Spaceflight most often occurs in zero-g conditions
• Although it is not a necessary conditionmost spacecraft achieve the closed orbit
• Most time the engines are off• Engines are switched on to correct the
orbiting parametrs
Spaceflight Simulation
Fg
• Gravity acceleration is:
(we find the value of C in experiments)
• Remember: acceleration is a vector and must be decomposed to vertical and horizontal components
222 R
C
R
MG
mR
MmG
m
Fa gg
Spaceflight Simulation// calculate distance between the rocket and planetint R = rocket.GetPosition().Distance(planet.GetPosition());
// assume gravity constant (C – not G!)double C = 28000.0;
// calculate accelerationdouble a = C / R / R;
// decompose acceleration into horizontal and vertical directionsdouble ax = a * (planet.GetX() - rocket.GetX()) / r;double ay = a * (planet.GetY() - rocket.GetY()) / r;
// apply to motion!rocket.SetMotion(rocket.GetXVelocity() + ax, rocket.GetYVelocity() - ay);
2R
Cag
Zero Gravity on Earth
You don’t have to travel to the outer space to experience Zero Gravity
All images from Wikimedia Common, under various copyright,check http://en.wikipedia.org/wiki/Reduced_gravity_aircraft for details
This image is a screenshot from a copyrighted film (Star Wars A New Hope), and the copyright for it is owned by LucasFilm. It is believed that the use of a single low resolution screenshot for illustration of spacecraft flight concepts presented here by Kingston University (educational institution based in the UK) qualifies as fair use under US and UK copyright law. Any other uses of this image may be copyright infringement.