NASA's Microgravity Teachers Guide

form motion in a straight line. A body force acts on the entiremass as a result of an external effect not due to direct contact;gravity is a body force. A surface force is a contact force that actsacross an internal or external surface of a body.Mathematics Standards oo o o ooAlgebraConceptual Underpinnings of CalculusGeometryGeometry from an Algebraic PerspectiveMathematical ConnectionsMathematics as ReasoningTrigonometryScience Standards o Physical Science o Unifying Concepts and ProcessesVelocity is the rate at which the position of an object changeswith time; it is a vector quantity. Speed is the magnitude ofvelocity.Mathematics Standards o Mathematical Connections o Mathematics as ReasoningScience Standards o History and Nature of Science o Science as Inquiry o Unifying Concepts and ProcessesNewton’s discovery of the universal nature of the force ofgravity was remarkable. To take the familiar force that makes anapple fall to Earth and be able to recognize it as the same forcethat keeps the planets on their quiet and predictable pathsrepresents one of the major achievements of human intellectualendeavor. This ability to see beyond the obvious and familiar isthe mark of a true visionary. Sir Issac Newton’s pioneering workepitomizes this quality.Mathematics Standards o Algebra Computation and Estimationo Functions o Mathematical as Communication Number and Number Relationships Patterns and FunctionsScience Standards o Unifying Concepts and Processes2More than 300 years ago the great Englishscientist Sir Isaac Newton published theimportant generalization that mathematicallydescribes this universal force of gravity. Newtonwas the first to realize that gravity extends wellbeyond the domain of Earth. The basis of thisrealization stems from the first of three laws heformulated to describe the motion of objects. Partof Newton’s first law, the law of inertia, states thatobiects in motion travel in a straight line at aconstant velocity unless acted upon by a netforce. According to this law, the planets in spaceshould travel in straight lines. However, as earlyas the time of Aristotle, scholars knew that theplanets travelled on curved paths. Newtonreasoned that the closed orbits of the planets arethe result of a net force acting upon each of them.That force, he concluded, is the same force thatcauses an apple to fall to the ground—gravity.Newton’s experimental research into the force ofgravity resulted in his elegant mathematicalstatement that is known today as the Law ofUniversal Gravitation. According to Newton, everymass in the universe attracts every other mass.The attractive force between any two objects isdirectly proportional to the product of the twomasses being considered and inverselyproportional to the square of the distanceseparating them. If we let F represent this force, rrepresent the distance between the centers of themasses, and m1 and m2 represent the magnitudesof the masses, the relationship stated can bewritten symbolically as:From this relationship, we can see that the greaterthe masses of the attracting objects, the greaterthe force of attraction between them. We can alsosee that the farther apart the objects are fromeach other, the less the attraction. If the distancebetween the objects doubles, the attractionbetween them diminishes by a factor of four, andif the distance triples, the attraction is only oneninth as much.Microgravity — A Teacher’s Guide with Activities in Science, Mathematics, and Technology,EG-1997-08-110-HQ, Education Standards Grades 5–8 ( ), 9–12 ( )

The eighteenth-century English physicist HenryCavendish later quantified Newton’s Law ofUniversal Gravitation. He actually measured thegravitational force between two one kilogrammasses separated by a distance of one meter.This attraction was an extremely weak force, butits determination permitted the proportionalrelationship of Newton’s law to be converted intoan equality. This measurement yielded theuniversal gravitational constant, G. Cavendishdetermined that the value of G is 6.67 x 10-11 Nm2/kg2. With G added to make the equation, theLaw of Universal Gravitation becomes:indicates proportionalityindicates equalityis an expressionis an equationMathematics Standards o Algebra o Mathematical Connections o Mathematics as Communication MeasurementScience StandardsWhat is Microgravity?The presence of Earth creates a gravitational fieldthat acts to attract objects with a force inverselyproportional to the square of the distancebetween the center of the object and the center ofEarth. When we measure the acceleration of anobject acted upon only by Earth’s gravity at theEarth’s surface, we commonly refer to it as one gor one Earth gravity. This acceleration isapproximately 9.8 meters per second squared (m/s2). The mass of an object describes how muchthe object accelerates under a given force. Theweight of an object is the gravitational forceexerted on it by Earth. In British units (commonlyused in the United States), force is given in unitsof pounds. The British unit of masscorresponding to one pound force is the slug.While the mass of an object is constant and theweight of an object is constant (ignoringdifferences in g at different locations on theEarth’s surface), the environment of an objectmay be changed in such a way that its apparentweight changes. Imagine standing on a scale in astationary elevator car. Any vertical accelerationsof the elevator are considered to be positive o Science and Technology o Science as Inquiry o Unifying Concepts and ProcessesThe internationally recognized Systeme International (Sl) is asystem of measurement units. The Sl units for length (meter) andmass (kg) are taken from the metric system. Many dictionariesand mathematics and science textbooks provide conversion tablesbetween the metric system and other systems of measurement.Units conversion is very important in all areas of life. forexample in currency exchange, airplane navigation, and scientificresearch.Units Conversion Examples1 kg 2.2lb1 in 2.54cm1 yd 0.9 m1 liter 1 qtQuestions for Discussion What common objects have a mass of about 1 kg? What are the dimensions of this sheet of paper in cm andinches? How many liters are there in a gallon?Mathematics Standards Computation and Estimation o Mathematics as Communication Number and Number Relationships Number Systems and Number TheoryMicrogravity — A Teacher’s Guide with Activities in Science, Mathematics, and Technology,EG-1997-08-110-HQ, Education Standards Grades 5–8 ( ), 9–12 ( )3

Science Standards o Science as Inquiry o Science in Personal and Social Perspectives o Unifying Concepts and ProcessesScientific notation makes it easier to read, write, and manipulatenumbers with many digits. This is especially useful tor makingquick estimates and for indicating the number of significantfigures.Examples:0.001 10-310 1011000 103Which is bigger, 6 x 10-3 or 8 x 10-4? 6 x 103 or 8 x 104?How much bigger?Mathematics Standards o Mathematical Connections o Mathematics as ReasoningScience Standards o Science and Technology o Science as Inquiry o Unifying Concepts and ProcessesQuestions for Discussion How does a scale work ? What does a scale measure? How many different kinds of scales can you list? Do they need gravity for them to work? Would you get different results on the Moon or Mars? How can you measure the mass of an object inmicrogravity?4upwards. Your weight, W, is determined by yourmass and the acceleration due to gravity at yourlocation.If you begin a ride to the top floor of a building,an additional force comes into play due to theacceleration of the elevator. The force that thefloor exerts on you is your apparent weight, P, themagnitude of which the scale will register. Thetotal force acting on you is F W P mae, where aeis the acceleration of you and the elevator andW mg. Two example calculations of apparentweight are given in the margin of the next page.Note that if the elevator is not accelerating thenthe magnitudes W and P are equal but thedirection in which those forces act are opposite(W -P). Remember that the sign (positive ornegative) associated with a vector quantity, suchas force, is an indication of the direction in whichthe vector acts or points, with respect to a definedframe of reference. For the reference framedefined above, your weight in the example in themargin is negative because it is the result of anacceleration (gravity) directed downwards(towards Earth).Imagine now riding in the elevator to the top floorof a very tall building. At the top, the cablessupporting the car break, causing the car and.you to fall towards the ground. In this example,we discount the effects of air friction and elevatorsafety mechanisms on the falling car. Yourapparent weight P m(ae-g) (60 kg)(-9.8 m/s2(-9.8 m/s2)) O kg m/s2; you are weightless. Theelevator car, the scale, and you would all beaccelerating downward at the same rate, which isdue to gravity alone. If you lifted your feet off theelevator floor, you would float inside the car. Thisis the same experiment that Galileo is purportedto have performed at Pisa, Italy, when he droppeda cannonball and a musketball of different massat the same time from the same height. Both ballshit the ground at the same time, just as theelevator car, the scale, and you would reach theground at the same time.Microgravity — A Teacher’s Guide with Activities in Science, Mathematics, and Technology,EG-1997-08-110-HQ, Education Standards Grades 5–8 ( ), 9–12 ( )

Mathematics Standards o Algebra Computational and Estimationo Conceptual Underpinnings of Calculus o Mathematical Connections o Mathematics as Problem Solving MeasurementNormalweightScience StandardsLighterthan normalHeavierthan normalNo apparentweightAcceleration and weightThe person in the stationary elevator car experiences normalweight. In the car immediately to the right, apparent weightincreases slightly because of the upward acceleration.Apparent weight decreases slightly in the next car because ofthe downward acceleration. No weight is measured in the lastcar on the right because of free fall.For reasons that are discussed later, there aremany advantages to performing scientificexperiments under conditions where the apparentweight of the experiment system is reduced. Thename given to such a research environment ismicrogravity. The prefix micro- (m) derives fromthe original Greek mikros meaning small. By thisdefinition, a microgravity environment is one inwhich the apparent weight of a system is smallcompared to its actual weight due to gravity. Aswe describe how microgravity envifonments canbe produced, bear in mind that many factorscontribute to the experienced accelerations andthat the quality of the microgravity environmentdepends on the mechanism used to create it. Inpractice, the microgravity environments used byscientific researchers range from about onepercent of Earth’s gravitational acceleration(aboard aircraft in parabolic flight) to better thanone part in a million (for example, onboard Earthorbiting research satellites). ooooPhysical ScienceScience and TechnologyScience as InquiryUnifying Concepts and ProcessesF W P maeRewriting yields P mae-mg m(ae- g).If your mass is 60 kg and the elevator is aeceleratingupwards at 1 m/s2, your apparent weight isP 60 kg ( 1 m/s2-(-9.8 m/s2)) 648 kg m/s2while your weight remainsW mg (60 kg)(-9.8 m/s2) -588 kg m/s2.If the elevator aceelerates downwards at 0.5 m/s2,your apparent weight isP 60 kg (-0.5 m/s2-(-9.8 m/s2)) 558 kg m/s2.Mathematics Standards o Mathematics as Communications o Mathematics as ReasoningScience Standards o o oScience as InquiryScience in Personal and Social PerspectivesUnifying Concepts and Processes1 micro-g or 1 µg 1 x 10-6 gQuestions for Discussion What other eommon prefixes or abbreviations tor powers often do you know or ean you find ? In what everyday places do you see these used ?Grocery stores, farms, laboratories, sporting facilities,pharmacies, machine shops.Common prefixes for powers of gaG109Quantitative systems of measurement, such asthe metric system, commonly use micro- to meanone part in a million. Using that definition, theacceleration experienced by an object in aMicrogravity — A Teacher’s Guide with Activities in Science, Mathematics, and Technology,EG-1997-08-110-HQ, Education Standards Grades 5–8 ( ), 9–12 ( )5

Mathematics Standards o Algebra Computation and Estimationo Conceptual Underpinnings of Calculuso Discrete Mathematics o Mathematical Connections o Mathematics as Problem Solving o Mathematics as Reasoning Number and Number RelationshipsScience Standards o Unifying Concepts and ProcessesCalculate the times in these examples. Teachers canuse these examples at several different scholasticlevels.Provide the equation as:Provide the equation as d (1/2) as t2, and have thestudents re-order the equation.Making measurements and calculating results involvethe concepts of accuracy and precision, significant figures, andorders of magnitude. With these concepts in mind, are the droptimes given in the text “correct”?Mathematics Standards o AlgebraComputation and Estimationo Mathematical Connectionso Mathematics as Problem Solvingo Mathematics as ReasoningMeasurementScience Standards o Science and Technology o Science as Inquiry o Unifying Concepts and ProcessesQuestions for Discussion How far away is the Mooon? How far away is the center of Earth from the centerof the Moon? Why did we ask the previous question? How far away is the surface of Earth from the surfaceof the Moon What are the elevations of different features ofEarth and the Moon? How are elevations measured?6microgravity environment would be one-millionth(10-6) of that experienced at Earth’s surface. Theuse of the term microgravity in this guide willcorrespond to the first definition. For illustrativepurposes only, we provide the following simpleexample using the quantitative definition. Thisexample attempts to provide insight into whatmight be expected if the local accelerationenvironment would be reduced by six orders ofmagnitude from 1 g to 10-6 g,If you dropped a rock from a roof that was fivemeters high, it would take just one second toreach the ground. In a reduced gravityenvironment with one percent of Earth’sgravitational pull, the same drop would take 10seconds. In a microgravity environment equal toone-millionth of Earth’s gravitational pull, thesame drop would take 1,000 seconds or about 17minutes!Researchers can create microgravity conditions intwo ways. Because gravitational pull diminisheswith distance, one way to create a microgravityenvironment (following the quantitative definition)is to travel away from Earth. To reach a pointwhere Earth’s gravitational pull is reduced toonemillionth cf that at the surface, you wouldhave to travel into spa

The purpose of this curriculum supplement guide is to define and explain microgravity and show how microgravity can help us learn about the phenomena of our world. The front section of the guide is designed to provide teachers of science, mathematics, and technology at many levels with a foundation in microgravity science and applications.