Spacecraft Simulation

Games Fundamentals© by Jarek FrancikKingston University, London

2012

Spacecraft Simulation

International Space Station image by NASA, Wikimedia Commons

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

Orbiting object in fact move around their common centre of mass...

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

Angry Birds in Space

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

Zero Gravity on Earth

You don’t have to travel to the outer space to experience Zero Gravity

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.