Spacecraft Simulation Games Fundamentals © by Jarek Francik Kingston 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:

Gravity Gravity at the surface of our planet: this formula is useless in the space Newton’s gravity formula:

Zero Gravity v FGFG FCFC F G = -F C Images: “The Blue Marble“ Earth image by NASA, “Sputnik 1” spacecraft from claudelafleur.qc.ca/ (GNU License)claudelafleur.qc.ca/ both available at Wikimedia Commons

Zero Gravity Balance between Gravitational & Centrifugal Force

Cosmic Speed Newton’s cannonball will never return to the ground if it exceeds the First Cosmic Speed: (for the Earth)

Cosmic Speeds First Cosmic Speed minimum speed for Newton’s cannonball to stay on the orbit for the Earth for the Sun Second Cosmic Speed a.k.a. Escape Velocity speed required to break permanently from the gravity field can be calculated from energetic equation: for the Earth for the Sun

Cosmic Speed Calculation of the Second Cosmic Speed (advanced)

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 images by NASA, Wikimedia Commons

Orbits Rules of planetary motion was first formulated by Johannes Kepler in 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 condition most spacecraft achieve the closed orbit Most time the engines are off Engines are switched on to correct the orbiting parametrs

Spaceflight Simulation FgFg 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

Spaceflight Simulation // calculate distance between the rocket and planet int R = rocket.GetPosition().Distance(planet.GetPosition()); // assume gravity constant (C – not G!) double C = ; // calculate acceleration double a = C / R / R; // decompose acceleration into horizontal and vertical directions double 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);

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 for detailshttp://en.wikipedia.org/wiki/Reduced_gravity_aircraft

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.