Are you an Angry Birds fan? If you are like the millions of other fans, you might have heard that NASA announced on March 8th the coming release of the Space version on March 22nd. Rovio, the maker of the wildly popular game, has partnered with NASA to design the new version. There are new characters, new controls, and new physics to learn in order to recover the eggs and destroy those nasty pigs. Here is the video released March 8th featuring astronaut Don Pettit announcing the new game.
NASA and Rovio are working together to teach people about physics and space exploration through the internationally successful puzzle game.
Game developers have incorporated concepts of human space exploration into the new game. From the weightlessness of space to the gravity wells of nearby planets, players use physics as they explore the various levels of the game set both on planets and in microgravity.
As a former teacher of physics, I couldn't pass up the opportunity to do a diary about a few of the physics essentials of traveling in space. There are some new terms players of the game will need to learn. Such things as trajectory, parabola, hyperbola, ellipse, orbit, eccentricity, and Kepler are a few of the physics concepts built into the dynamics of this new game. I promise to keep it simple.
Let's go below the binary-pairs-orbit-squiggle for some lessons.
Don Pettit is in a state of continual free-fall as he and the ISS orbit the Earth. This puts him, station, and all the contents in a state simulating no gravity. Actually, the strength of gravity is nearly as strong on them as it is here on the surface of Earth. But, they are moving extremely fast horizontally as they fall around the curve of the planet and feel no support from below. We are standing or sitting on things. That upward push on our bodies balancing the downward gravitational pull is our sensation of weight.
What is Gravitation? How Does it Behave?
Isaac Newton's Law of Universal Gravitation was formulated in Philosophiae Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. It states a simple principle that every mass attracts every other mass in the universe. The strength of this attractive force is governed by only two factors, the product of the masses and the distance between the masses. The pairs of masses exert equal forces upon each other. If m1 and m2 below are released, the two masses will accelerate toward each other. In this particular case, m1 will accelerate less toward m2 because it is more massive. They won't meet in the middle unless they are equal masses. If you stand on a ladder, the mass of the Earth and the mass of your body attract each other equally. The ladder is forcing you apart from the Earth. Step off of the top rung of the ladder. You and the Earth accelerate toward each other. You move a lot down toward Earth. The Earth moves imperceptibly up toward you because it is so much more massive than you.
Cannons From the Mountain Tops
Consider a cannon shooting a projectile horizontally from a very high mountain. Use more and more powder in successive shots to drive the projectile faster and faster. The parabolic paths become flatter and flatter.
Imagine that the mountain is so high that air resistance can be ignored. If the cannon is strong enough, eventually the curvature of the earth needs to be considered in finding where it lands. The speed and curvature of the Earth may mean the projectile never lands. This concept was considered by Newton in his Principia of 1687. The concept was developed several years later in his popular A Treatise of the System of the World in 1728.
You can play with this idea and shoot cannonballs from mountains by clicking on this NASA graphic below. It will take you to a simple interactive.
Trajectories When Moving Past Different Masses
When Don Pettit shot the Red Angry Bird with the bungee cord, it traveled in a straight line through the cabin. It was traveling in a situation that simulated no gravitational field influencing the motion of the bird. In the new game by Rovio, there will be gravitational fields because of the presence of other masses nearby. To help illustrate what happens when a mass is projected in the presence of another gravitational field, consider the short video clips below. The simulator I recorded from uses the Law of Universal Gravitation to calculate the attraction between masses. The values of mass are variable. Each mass can be placed at different locations and be given a speed in any direction. I will provide a link later so you can play with it.
First, we have the trajectory as the object in the upper left corner moves past a very small mass just left of center. There is very little gravitational attraction as defined above by Newton's law. The fast moving mass is not diverted off course very much.
Next, the moving object still moves the same speed as before. But the mass it passes is a greater value. The force of attraction is more. The trajectory is more curved by the greater force.
Finally, the moving object passes another object with a large amount of mass. It seems to be captured in orbit.
Trajectories Moving at Different Speeds Past a Mass
This one has a result like the video clip above. The moving mass is captured in orbit.
Next, the moving mass is traveling at a medium speed past the same mass as before.
Finally, the moving mass is traveling at a fast speed.
As you may have noticed, the trajectory is affected by three things:
• how fast you are going,
• how massive the object is you are passing, and
• how near you come to the passed object.
These factors will all be important in your quest against the pigs.
Orbits, Ellipses, and Johannes Kepler
Trajectories sometimes put you into a path that continues around in an orbit. Orbits have a shape called an ellipse. An ellipse has a property called eccentricity. The eccentricity of an astronomical body is the amount the orbit deviates from a perfect circle. Zero 0.0 is perfectly circular, and 1.0 is a parabola. The trajectory of a parabola is not a closed orbit. Circular orbits are extremely rare. Here is a good example of a circular orbit with zero eccentricity. Earth's orbit has an eccentricity of 0.0167 making it almost circular.
In the next video are three orbits around the same central body. The smallest orbit has the least amount of eccentricity. Many comets have orbits that look like the largest of these three, or even more elongated. Halley has an eccentricity of 0.967 making it very long and narrow.
Notice how the average radius of orbit is different, as are the periods of the orbits. The closer the orbit, the faster you go.
Johannes Kepler, in the early 1600s, had formulated his three laws of planetary motion based on analysis of observations made by Tycho Brahe in the late 1500s.
1. Kepler's first law is summarized by the video above. The orbits of objects are ellipses.
2. Kepler's second law is called the law of equal areas. An orbiting object sweeps out an area of space bounded by a line between the object and the orbited object and by the path of the trajectory. This region is a kind of wedge shaped area. In the animated graphic below, keep your eye on the blue region. Suppose this is a planet in orbit around a star. Consider two different time intervals of perhaps a month each. During a month when it is far away from the star, it is going slow. The blue wedge shaped region is long and narrow. During a month when it is close to the star, it is going fast. The blue wedge shaped region is short and wide. The areas of these blue regions are equal during these equal time intervals regardless of the position in the orbit.
3. Kepler's third law is a relationship between the period (P) of the orbit and the average radius of the orbit. It is often said that the semi-major axis (a) is the "average" distance between the primary focus of the ellipse and the orbiting body. This is not quite precise, but it is close enough most of the time. Kepler found that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The ratio of the period squared to the cube of the semi-major axis is equal to the same value for all of the planets or objects which orbit that star. It is true for all variety of orbits, including highly eccentric ones. In fact, the values of (P) and (a) can be used to calculate the mass (M) of the central body about which the planets orbit. The value of G is a universal gravitational constant. The masses of hundreds of stars is found with this method once planets have been found orbiting them. See the Kepler Mission. To date, the Kepler Science Team has found 1,790 host stars with a total of 2,321 planet candidates as of 2012 Feb 27.
Your Turn to Play
If you are an Angry Birds fan, I hope the lessons above prove helpful and entertaining for you. Good luck in your quest with the pigs. In addition to the game fun, I hope you have learned some physics today about trajectories and orbits. It never hurts to be prepared for the day when you are piloting your own spacecraft.
The simulation I used above for the trajectories is available for you to use. It is found at this link for My Solar System. Just click on the green Run Now! button. You will find several presets in the upper right. You can vary masses and positions and velocities in the lower part of the screen. Try them all. Have a good time. You won't break anything.
The PhET site is an awesome educational site. Here are some comments from their About Us page. Drop them a line. Spread the link to teachers you know. It is a valuable resource for teachers and home schoolers alike.
PhET provides fun, interactive, research-based simulations of physical phenomena for free. We believe that our research-based approach- incorporating findings from prior research and our own testing- enables students to make connections between real-life phenomena and the underlying science, deepening their understanding and appreciation of the physical world.
To help students visually comprehend concepts, PhET simulations animate what is invisible to the eye through the use of graphics and intuitive controls such as click-and-drag manipulation, sliders and radio buttons. In order to further encourage quantitative exploration, the simulations also offer measurement instruments including rulers, stop-watches, voltmeters and thermometers. As the user manipulates these interactive tools, responses are immediately animated thus effectively illustrating cause-and-effect relationships as well as multiple linked representations (motion of the objects, graphs, number readouts, etc.)